Discussion Paper No.10

How Fast Do Tokyo and New York Stock Exchanges
Respond to Each Other?: An Analysis with
High-Frequency Data

Yoshiro Tsutsui and Kenjiro Hirayama

October 2008

ＧCOE Secretariat
Graduate School of Economics

OSAKA UNIVERSITY

1-7 Machikaneyama, Toyonaka, Osaka, 560-0043, Japan

How Fast Do Tokyo and New York Stock Exchanges Respondto Each Other?: An Analysis with High-Frequency Data *Yoshiro Tsutsui
Osaka University
Kenjiro Hirayama
Kwansei Gakuin University

Abstract
This paper uses one-minute returns on the TOPIX and S&P500 to examine the efficiencyof the Tokyo and New York Stock Exchanges. Our major finding is that Tokyo completes
reactions to New York within six minutes, but New York reacts within fourteen minutes.
Dividing the sample period into three subperiods, we found that the response time has
shortened and the magnitude of reaction has become larger over the period in both markets.
The magnitude of response in New York to a fall in Tokyo is roughly double that of a rise.
JEL Classification Numbers: G14, G15, F36
Keywords: international linkage, stock prices, market efficiency, high frequency data

Correspondence:
Yoshiro Tsutsui
Graduate School of Economics
Osaka University
1-7 Machikane-yama, Toyonaka
560-0043 Japan
Phone: +81-6-6850-5223
Fax:+81-6-6850-5274
e-mail: tsutsui@econ.osaka-u.ac.jp*

Kenjiro Hirayama
School of Economics
Kwansei Gakuin University
Uegahara, Nishinomiya-shi
662-8051 Japan
Phone: +81-798-54-6438
Fax:+81-798-54-6438
e-mail: hiraken@kwansei.ac.jp

We are especially grateful to the anonymous referee of this journal for many constructive comments which
led to substantial improvements. An earlier version of this paper was presented at MEW (the Monetary
Economics Workshop), the 11th annual convention of the Nippon Finance Association, and the Spring
Meeting of Japan Economic Association. The authors are grateful for helpful comments by Masayuki Ikeda,
Hideaki Kato, Toshio Serita, and participants at the workshop.

1. Introduction
Stock prices of major economies are well known to be interdependent, and there is an extensive
literature on international stock price linkage (Eun and Shim 1989, Jeon and von Furstenberg 1990,
Mathur and Subrahmanyam,1990, Jeon and Chiang 1991, Chan et al. 1992, Kasa 1992, Corhay et al.
1993, Blackman et al. 1994, Chung and Liu 1994, Choudhry 1994, 1997, and Hirayama and Tsutsui,
1998a, 1998b), including a few research papers which investigate the possible causes of the linkage(Tsutsui 2002, Tsutsui and Hirayama 2004b, 2005). One of the findings in this literature is that acountry’s stock prices tend to advance when a neighboring market, closing just before that of thecountry’s market, has advanced (Tsutsui and Hirayama 2004a).
Therefore, one can predict the course of the stock price index of the Tokyo stock market, such as
the TOPIX or the Nikkei 225, by observing whether the stock price indices of the New York stock
market, such as the S&P500 and the New York Dow Jones Industrial Average (henceforth known as
NYDJ), have advanced or declined. This predictability might seem to contradict the market efficiency
hypothesis, but such is not the case. When the New York Stock Exchange (NYSE) is open for trading,
the Tokyo Stock Exchange (TSE) is closed due to time differences. Consequently, one must wait for the
opening of the TSE to execute transactions based on the new information from New York. If the Tokyo
stock market is efficient, the TOPIX reacts fully to the information of the S&P500 on the previous day
at the opening but is not influenced thereafter.
Using daily opening and closing values, Tsutsui (2002) found that the Nikkei 225 reacts to a largechange (over 1.5%) of NYDJ by the closing time of the next day, and the Nikkei 225 does not show asignificant change beyond the following day. Thus, the Tokyo stock market is efficient over the daily
time span.
Although the studies above use daily observations at best, there is a body of literature that utilizes

1observations of high frequency. 1 The markets for foreign exchange and interest rate futures seem toreact extremely rapidly to macroeconomic news announcements, e.g., within forty seconds according to
Ederington and Lee (1995) and Almeida et al. (1998). However, equity markets respond more slowly toearnings and dividend announcements, requiring ten to fifteen minutes (Patell and Wolfson 1984). The
response of the S&P500 index to unexpected changes in the money supply and Consumer Price Index(CPI) is completed within one hour (Jain 1988). In this paper, we will employ one-minute returns on the
TOPIX and the S&P500 to analyze the speed of reactions of each stock exchange to the other.
The only work thus far, to our knowledge, using intraday data in a study of the price linkage
between the U.S. and Japanese stock markets is that of Becker et al. (1992). They used hourly data for
the S&P500 and Nikkei 225 Indices from October 5, 1985 to December 31, 1989. They calculated thecorrelations between hourly returns of one country with the other country’s daily return of the previous
day. 2 They found that the effect of the previous day’s Nikkei return on the subsequent S&P500 returns isabsorbed within the first half hour after opening in New York, while the effect of the previous day’s
S&P500 return on the subsequent Nikkei returns is absorbed within the first hour of trading in Tokyo,
and that the effect of the lagged S&P500 returns on the subsequent Nikkei returns is larger than thereverse effect. Thus, the stock markets in Tokyo and New York seem to absorb the effects from the otherstock exchange rather rapidly. However, due to the hourly observations that they used we cannot infer
how speedily the effects are absorbed.
This paper uses high-frequency data to examine how fast the Tokyo and New York stock markets
respond to each other. We obtained the tick data for the S&P500 from Tickdata.com and the TOPIX dataat one-minute intervals from the Tokyo Stock Exchange. 3 Our data started earlier, but to avoid the1

For an overall introduction to high-frequency finance, see Dacorogna et al. (2001). Goodhart and O’Hara(1997) is also a good review and companion papers in the same Journal of Empirical Finance, vol. 4, no. 2-3
are research results with high-frequency data.
2
Since the New York Stock Exchange opens at 09:30 EST, the first US return of the day is a half-hour returnfrom 09:30 to 10:00.
3
The TOPIX is a capitalization-weighted index of all the stocks listed on the Tokyo Stock Exchange.

2

extreme effects of Black Monday, we discarded data before December 1987. The last day for oursample was November 27, 2003. Since our sample period is considerably longer than that used in
Becker et al. (1992), we can also examine whether there was a change in this reaction time during thesample period.
In this paper we measure how quickly the reaction to the other market at the opening dissipates.
However, the short reaction time does not necessarily imply the market efficiency when one uses
high-frequency data. For example, the market microstructure may explain the difference in reaction
time. Specifically, the TSE accepts buy and sell orders for one hour prior to the market opening and theopening price is determined by the batch process known as itayose. 4 The NYSE, on the other hand, does
not accept orders before the market opening and the prices are formed by continuous auction. Thisdifference in trading rules apparently leads to different reaction time. Another microstructure effectarises due to nonsynchronous trading. 5 It is known that nonsynchronous trading results in seriallycorrelated stock returns (Lo and MacKinlay 1990). 6 The length of reaction time is, thus, affected bysuch microstructure effects.
If the preceding US (Japan) closing price affects the opening price in Japan (the US) systematicallyand significantly, the return volatility at the beginning of daily trading tends to be larger. Indeed, it iswell-known that the intraday return volatility is W-shaped in Japan (Andersen, Bollerslev, and Cai
2000) and U-shaped in the US (Andersen and Bollerslev 1997), both of which imply high volatility at
the opening. Thus, this study also constitutes an analysis of microstructure of the stylized fact of high4

Opening and closing prices of the morning and afternoon session of the Tokyo Stock Exchange are formed
by a batch process, called itayose, while other trades during the day are carried out by continuous trading,called zaraba. Amihud and Mendelson (1991) analyze itayose system and argue that this difference in thetwo price formation processes, itayose and zaraba, may produce differences in prices and trading volumes.
5
The bid-ask bounces are also known to affect autocorrelation in stock returns (Roll 1984). However, they
result in negative autocorrelation while we are concerned with positive autocorrelation in stock price index
returns such as S&P500 or TOPIX.
6
They proved that the degree of autocorrelation becomes stronger, the higher the probability of nontrading
for a given time interval. Tsutsui, et al. (2007) report that this probability of nontrading is greater in the
NYSE than in the TSE.

3

volatility at the beginning of NYSE and TSE.
The rest of the paper is organized as follows. In Section 2 we discuss intraday patterns of
one-minute stock returns in Tokyo and New York. Section 3 analyzes the speed of reaction to the othermarket changes and Section 4 presents analyses with subperiods. In Section 5 we focus on positive andnegative market changes and analyze whether there is an asymmetry in reaction. Section 6 concludes
the paper.

2. Intraday patterns of one-minute stock returns
2.1 Intraday patterns of TOPIX returns
We obtained the TOPIX data at one-minute intervals from 09:01 to 15:00 JST (Japan Standard
Time) from May 23, 1987 to November 27, 2003 from the Tokyo Stock Exchange. There was a
two-hour lunch break between 11:00 and 13:00 until April 26, 1991 and a 90 minute lunch break
between 11:00 and 12:30 after April 30, 1991. Although the actual starting date of our dataset is May 23,
1987, we deleted observations up to the end of 1987 in order to avoid overwhelming influence of theBlack Monday. One-minute returns of the TOPIX are computed as:

RJhhmmt =TOPIX at hhmm − TOPIX at hhmm − 1
× 100,TOPIX at hhmm − 1(1)where hhmm is a four-digit number denoting the hours and minutes in Japan Standard Time andhhmm–1 refers to the time one minute before hhmm. It takes on values from 0901 to 1100 for themorning session and from 1231 to 1500 for the afternoon session. 7 The notation, 1000–1, means 0959,
but 0901–1 refers to 1500 of the previous day. Therefore, note that RJ0901 is actually an overnight
return from the previous day’s close at 15:00. Likewise, 1231–1 is actually 1100, because there is alunch break. Hence, RJ1231 is a 90-minute return from 11:00 to 12:31.
7

Due to a longer lunch break, hhmm starts at 1301 and ends at 1500 for the afternoon session until April 26,
1991.

4

These TOPIX returns, RJ0901, …, RJ1500, are averaged across days during the sixteen-year
period (January 1988 to November 2003), and these means are plotted in Figure 1 along with 95%
confidence bands based on the null of a zero mean. We observe the following five characteristics ofintraday one-minute stock returns in Tokyo. 1) The first four minutes immediately following a day’s
opening exhibit significantly positive returns. 2) There are significantly positive returns for about six
minutes before a day’s closing. 3) There are significantly negative returns for about ten minutes after
the opening (12:31) of the afternoon session. 4) One-minute returns tend to be negative after the firsteight minutes of the day’s opening. Out of 52 one-minute returns from RJ0909 to RJ1000, there are 25
significantly negative values at a 95% level. 5) Most returns other than the above are statistically not
different from zero during the day. There are only six cases of significant non-zero means for 60
one-minute returns during 10:01 and 11:00. For the interval between 12:41 and 14:54, there are 11 suchmeans out of 134 one-minute returns.
Using five-minute returns of the Nikkei 225 Index, Andersen et al. (2000) examined their volatility
during the period from 1994 to 1997. The mean returns averaged across days are plotted in their Figure
1A and these conform to points 2, 3, and 5 above. Although the first observation of the morning session
in their paper exhibits a negative return, this is due to their deletion of the daily initial observation (from9:00 to 9:05).
Table 1 lists summary statistics of selected daily TOPIX returns. 8 To test for serial correlation up to
the fifth order, we use Diebold’s heteroscedasticity-adjusted Ljung-Box statistic (Diebold 1986,
Silverpulle and Evans 1998), because stock returns are widely known to have ARCH effects. The serial
correlation thus measured is significant at or immediately following the opening of either morning or
afternoon session and returns for a longer time period such as RJCC or RJOC. But most of other

8 Normality tests are not shown here, because the Jarque–Bera measure indicates overwhelming rejection of

normality in every variable.

5one-minute returns are not serially correlated.
In Table 1 RJ0901 is actually the daily close-to-open overnight return, the mean of which is positive,
whereas the daily open-to-close return (RJOC) is negative. There is a tendency for the TOPIX to riseduring the night but to decline during the trading hours (Tsutsui 2003). The morning return between
09:01 and 12:31 (RJMN) tends to be negative, but the afternoon return between 12:31 and 15:00 (RJAN)
positive. The volatility as measured by the standard deviation is higher at the opening of either themorning or the afternoon session and at the closing of the day. However, the very high standard
deviation of RJ0901 can be regarded as a natural result of a long time period for this overnight return.
RJ0901 is observed on a 1,080-minute interval (18 hours from 3 pm to 9 am the following morning).
One may have to adjust for this long interval depending on their purpose of the study. If one wants toassess the magnitude of information flow, he or she will compare the standard deviation per minute,which is 0.0091 during night. 9
We next turn to the issue of intraday pattern of volatility. To measure volatility in stock prices, we
computed and graphed the mean of absolute TOPIX one-minute returns (Fig. 2). Volatility is high at the
opening and closing of the morning and afternoon sessions (see also standard deviations in Table 1).
The intraday volatility has three peaks, giving rise to a W-shaped pattern, which is also reported forfive-minute TOPIX absolute returns by Andersen, Bollerslev, and Cai (2000). At the time of market
opening, there is an accumulated stock of new information which may result in higher volatility. This iswhat we focus on in this paper, but it does not explain the W-shaped pattern entirely. The TSE
9The logged stock price is known to follow a random walk model fairly well (or a Wiener process incontinuous time) which has a property that the variance is proportional to the number of periods (or theduration of the elapsed time). Then, the standard deviation is proportional to the square root of theobservation duration. The time length for RJ0901 is 1,080 times the other one-minute returns. Thus, its
standard deviation may be divided by the square root of 1,080 to give 0.0091 (= 0 . 30 / 1080 ). The
magnitude of this looks small compared with standard deviations of other one-minute returns which
typically have values around 0.03, signifying that the information flow during non-trading hours is smallerthat that during trading hours. However, in order to analyze the impact of the whole information accumulated
during non-trading hours, this per-minute standardization does not seem appropriate. Indeed, the subsequent
one-minute returns, RJ0902 and RJ0903, have a standard deviation of 0.123 and 0.067 respectively, which ismuch larger than the per-minute value for RJ0901.

6determines opening and closing prices of two daily sessions by itayose method (TSE 2004, pp. 70-73)
which coincides with the three peaks in volatility, suggesting that itayose is one of the causes for highvolatility (Amihud and Mendelson 1991). Since itayose treats all the outstanding orders as arriving at
the same time, the likelihood of successful transactions is higher than during the normal zaraba
auctioning. As a result, more orders are accumulated for the itayose auction because of the reduced riskof non-execution. This contributes to higher volume and volatility at the opening and the closing of thetwo sessions, giving a partial explanation for three peaks during a day.

2.2 Why does the TOPIX decline at the opening of the afternoon session?
What about the apparent tendency of stock prices to decline at the opening of the afternoon
session (point 3 above)? Our conjecture is that investors give a second thought to rising prices at the
opening. This may also be behind the tendency of declining prices during 09:15 and 10:00 (point 4
above). Correlation coefficients between the overnight return (RJ0901), the return during the lunch
break (RJ1231), and the 45-min. return from 09:15 to 10:00 (denoted by RJ45M1000) are presented inTable 2. RJ0901 is negatively correlated with both RJ1231 and RJ45M1000, which seems to support ourview that advances at the opening are corrected afterwards. 10
Since correlation coefficients measure pair-wise relationships only, we also ran some regressions to
explain the negative return at the opening of the afternoon session. We regressed the over-lunch return(RJ1231) on a constant, the overnight return (RJ0901), five one-minute returns immediately preceding
the lunch break, and the dependent variable lagged by one day. 11 The result is shown under equation (i)in Table 3. The coefficient on RJ0901 is negative at a 15% significance level and the RJ1100 variable
has also a highly significantly negative effect on the dependent variable. 12 RJ1231 lagged one day has a
10

There is, however, sensitivity to the choice of duration. The 50-min. return from 09:10 to 10:00(RJ50M1000) is positively correlated with RJ0901.
11
See the next section for the details of this regression specification.
12
In this paper White’s robust standard error is used to evaluate the significance in regressions. This7

significantly positive effect. Overall this regression gives an adequate explanation of RJ1231.
Before introducing the 45-min. return, RJ45M1000, to the regression for RJ1231, let us consider
what effects it may have on RJ1231. There are two views. First, suppose that the size of correction to an
over-reaction at 09:01 is determined first and that it is divided into RJ45M1000 and RJ1231. Then, if
sufficient second thought is given during the 45-min. interval up to 10:00, the extent of corrective
reaction at 12:31 must be small, making the coefficient on RJ45M1000 negative. Second, suppose thatthe size of correction is not immediately known but is gradually revealed during the actual trading
session. Then, if a relatively large adjustment occurred in RJ45M1000, it would lead to a further
adjustment after lunch. In this instance, the coefficient on RJ45M1000 in a regression for RJ1231 tends
to be significantly positive, indicating a further, strengthened correction after lunch. In any case, thelunch break gives investors further time to reconsider the excessive rise at the opening of the day.
Equation (ii) of Table 3 is the result of regressing RJ1231 on a constant, the overnight return at the
opening (RJ0901), and the 45-min. return to 10:00 (RJ45M1000). The coefficient on RJ0901 is negativeat a 15% significance level and that on RJ45M1000 is positive at a 0.3% level. This result implies thesecond view above is appropriate.
We added five lagged one-minute returns and one-day lag of the dependent variable to theright-hand side and the basic result is the same in this equation (iii) of Table 3. These results imply thatthe mean negative return at the opening of the afternoon session is a reaction to the mean positive returnat the opening of the morning session. Having lunch gives investors reflective time to digest theexcessive rise at the day’s opening.

2.3 Intraday patterns of S&P500 returns
For the U.S. stock prices we obtained tick data on S&P500 from January 2, 1987 to November 27,

procedure adjusts for serial correlation and heteroscedasticity.

82003. As noted above, we discard observations up to the end of 1987. We compute one-minute returnsof S&P500 as:

RUhhmmt =S & P500 at hhmm − S & P500 at hhmm − 1
× 100 .
S & P500 at hhmm − 1(2)

Since the New York Stock Exchange opens at 09:30 and closes at 16:00, hhmm takes on values from0931 to 1600. Unlike Tokyo, the NYSE has no lunch break and trades shares continuously for six and ahalf hours every day. The time difference between Tokyo and New York is fourteen hours (thirteen
hours during the Daylight Saving Time period). Expressed in Greenwich Mean Time, the trading hours
are from 0:00 to 6:00 GMT in Tokyo and from 14:30 to 21:00 GMT in New York. Thus, the two markets
are never synchronously open.
Mean one-minute returns of S&P500 are plotted in Figure 3 along with 95% confidence bands
based on the null of a zero mean. We observe the following features from this Figure similar to those of
TOPIX one-minute returns: 1) The first seven minutes after the day’s opening tend to exhibit
significantly positive returns. However, their absolute magnitude is smaller than that of Tokyo. 2) The
last four minutes before the day’s closing are also significantly positive, but their absolute magnitude issmaller than in Tokyo or the first few minutes after opening. 3) Some of the returns tend to be negative
between 9:51 and 10:13. Out of 23 one-minute returns during this interval, nine are significantly
negative. 4) Except for these intervals noted above, most of the mean returns are statistically not
different from zero. Out of 343 one-minute returns during 10:13 and 15:56, only 28 are significant at a
5% level.
The correlation coefficient between the overnight return at the opening (RU0931) and the 45-min.
return from 09:45 to 10:30 is –0.0401 with a t-statistic of 2.54, the p-value of which is 1.1%, indicatinga significantly negative correlation. As in Tokyo, this may also imply that the investors in the NYSE
give a second thought to the rise at and immediately after the day’s opening.

9

Table 4 gives summary statistics for these and other daily returns. 13 Again the normality isoverwhelmingly rejected, thus not shown therein. Unlike the TOPIX, the S&P500 tends to rise during
the trading hours (significantly positive open-to-close return, RUOC). Most of this rise during thedaytime occurs in the afternoon (significantly positive afternoon return from 13:01 to 16:00, RUAN).
The volatility is high when the market opens, as indicated by a high standard deviation of RU0931, but
it declines gradually over time. 14 Unlike Tokyo, there is no increase in volatility toward the end of theday. Serial correlation is also present at and immediately following the opening or for daily returns such
as RUCC.
Mean absolute one-minute returns are plotted in Figure 4 to check for volatility. It is very high at themarket opening, but it dissipates very rapidly and then gradually decline toward the middle and thenagain very slowly increases toward the closing of the market. The graph does not show a typicalU-shaped pattern, but it is more like reverse J-shaped which is also pointed out by Goodhart and O’Hara(1997, p. 86).

3. How quickly does one market react to the other?
3.1 Correlation coefficients
Since it is well known that the two stock markets affect each other, our primary focus here is on
determining how rapidly this influence is absorbed after the opening of a market. As a preliminary

13

There is a slight discrepancy in the data for S&P500. The S&P500 price level at 16:00 is not precisely
equal to the closing value as reported by the TickWrite, software provided by the data vendor (TickData) toretrieve data points at desired frequency. It turns out that the original tick data contain values at a few minutes
after 16:00. The last value for the day is reported as the closing price. A similar discrepancy occurs with the
opening price. If two or more data points exist between 09:30 and 09:31, the last value is reported as the priceat 09:31, but the very first value is reported as the opening price on a daily frequency. In empirical analyses
below, the daily close-to-close or open-to-close returns (RUCC and RUOC) and the like are based on true
opening and closing values. However, the difference is extremely small and the results are almost identicaleven if the values at 09:31 and 16:00 are treated as the opening and closing prices.
14
If the length of the overnight nontrading is taken into account, the standard deviation of RU0901 becomes
0.005775 ( = 0.18713/ 1050 ) and this appears to be too small compared with the following one-minutereturns.

10

investigation, we compute correlation coefficients between the previous day’s daily return in New Yorkand each one-minute return in Tokyo. We denote by RUCC the daily close-to-close return in New Yorkon the previous day. 15
These correlation coefficients are displayed with 95% confidence bands derived from the null ofzero correlation in Figure 5. They are positive and of no small magnitude until 09:21. Namely,
correlations with preceding RUCCt–1 persist for about twenty minutes after the opening of the TSE.
There are spikes at 09:01, 09:06, 09:11, 09:16 and 09:21, but they disappear when the sample period isrestricted to before March 1997. Thus, these spikes are most likely related to five-minute periodicity in
autocorrelation coefficients which Tsutsui et al. (2007) ascribe to the automatic updating of special
quotes. 16 After 09:21 correlation coefficients are roughly close to zero, except at and for several
minutes after 12:31 (opening of the afternoon session) when they are significantly negative. Thus far,the pattern is similar to that of mean returns of Figure 1. A notable difference exists toward the end of
the day. While mean returns indicate that stock prices rise toward the end of the day, they are totally
uncorrelated with previous day’s movements in New York.
Next we reverse the direction and compute correlation coefficients between each one-minuteS&P500 return and the preceding daily close-to-close return observed in Tokyo (RJCC). In this instance,
the daily return in Tokyo is the one observed on the same calendar date as New York because the closeof Tokyo at 15:00 JST is 01:00 EST (Eastern Standard Time) in New York and the NYSE opens its
trading eight and a half hours later on the same day. These coefficients are plotted in Figure 6. There are
significantly positive correlations in the first fifteen minutes (until 09:45), but their magnitude is far less

15

Although this daily close-to-close return in New York is recorded on the previous calendar date, it isobserved only three hours before the opening of the Tokyo market since 16:00 in New York is 06:00 the next
day in Tokyo.
16‘Special quotes’ are arranged by the TSE and issued whenever the next equilibrium price is likely to
exceed a certain prescribed limit in order to bring market participants’ attention to a likely jump in stock
price. If an announcement of a special quote fails to cause a successful trade, the next special quote at a
one-notch higher or lower price is announced automatically at a five-minute interval, which seems to cause a
serial correlation in stock price index at these intervals.

11

than that of Tokyo. After the initial responses, coefficients seem to be random around zero.
In both Tokyo and New York, the responses to the other’s daily movements dissipate within the first
fifteen to twenty minutes of daily trades. Thus, information from the other market seems to be rather
quickly absorbed.

3.2 Regression analysis: effect of New York on Tokyo
The main purpose of this paper is to determine how the other market affects one-minute returns of
the day and especially how rapidly the effects are dissipated at the opening of daily trades. In order toinvestigate this effect, regression analysis taking into account other effects on the stock returns may be
more appropriate than computing simple correlation coefficients.
One-minute returns averaged across days as plotted in Figures 1 and 3 exhibit non–random behavior
immediately after the opening and toward the closing of the day. In Tokyo, the returns are significantly
negative at and after the opening of the afternoon session. This pattern may be evidence of serial
correlation that persists for a few minutes. In addition, as discussed above, returns are correlated withthe same values of the previous day, indicating a daily periodicity. A model of this influence should take
into account both short-run serial correlation and daily periodicity.
Thus, our model of one-minute TOPIX returns is specified as follows:
5i
RJhhmm t = α hhmm + ∑ β hhmm
RJ ( hhmm − i ) t + γ hhmm RJhhmm t −1 + δ hhmm RUCC t −1 + u t ,

(3)

i =1

where hhmm refers to a time of the day in hours and minutes and hhmm–i indicates the time i minutes
prior to hhmm. In the case of TOPIX returns, hhmm takes the values from 0901 and 1100 for themorning session and from 1231 to 1500 for the afternoon session (from 1301 to 1500 before April 26,
1991 due to a longer lunch break). Therefore, (1000–3) refers to 09:57. However, (0901–1) and(0901–2) indicate 15:00 and 14:59 of the previous day respectively. Likewise, (1231–1) denotes 11:00

12due to the lunch break. The subscript t denotes a date during our sample. The second term on theright-hand side of equation (3), RJ ( hhmm − i ) t , captures serial correlation that lasts a few minutes.
Due to the five-minute periodicity reported in Tsutsui, et al. (2007), the lag order is set at five for thisterm. The third term RJhhmmt −1 , is inserted to account for daily periodicity. RUCCt–1 is the
explanatory variable that is the focus of this exercise and is a daily close-to-close S&P500 returnobserved just prior to the opening of daily trades in Tokyo. δ hhmm captures the effect of the previous
day’s close-to-close return in New York on each one-minute return in Tokyo.
Since the Tokyo Stock Exchange is open for four and a half hours each day, there are 270
one-minute returns every day, and we ran 270 regressions for each return and obtained as manycoefficient estimates for δ hhmm . The sample period is from January 5, 1988 to November 27, 2003, andthe number of observations is 2,374 for returns from 12:31 to 13:00 and 3,001 to 3,034 for others. 17
Estimation results of equation (3) at 9:01, 12:31, and 14:00 are presented in Table 5. The result for
14:00 (RJ1400) is given as a typical example of all other regressions. Figure 7 plots 270 regression
estimates of δ hhmm together with their 95% confidence bands. It shows that δ 0901 is about 0.18 and thatthe coefficients decline rapidly. Most of the coefficients after 09:06 are trifling in magnitude and are notsignificantly different from zero. In other words, the Tokyo Stock Exchange reacts to the previous day’s
movements in New York within the first six minutes after opening. This reaction speed is much fasterthan that indicated by the correlation coefficients of Figure 5 which exhibit positive correlation with
RUCCt–1 up to around 09:21. These correlation coefficients only capture the pairwise relation between
each one-minute return and RUCCt–1, hence they do not account for the lagged effects of immediate past
returns. However, the regression equation takes serial correlation into account by adding lagged
one-minute returns (the second term on the right-hand side of equation (3)). In fact, these lagged series
17

The slight difference in the number of observations is due to: 1. a few missing values, 2. a peculiar
convention in the TSE whereby only morning sessions are held on the last and first day of the year, 3. during
the earlier part of the sample period (before February 1989), two or three Saturdays per month were open fortrading, but were only for the morning session.

13

are significantly positive in most regression equations.
Another interesting finding from the regressions is that, while returns in the past few minutes
usually have a positive effect on the subsequent returns (see right columns of Table 5), the last return ofthe day (RJ1500) has a significantly negative effect on RJ0901 (see left columns of Table 5). Its
coefficient is –0.202 with a p-value of 0.000005%.
Another remarkable fact shown in the middle columns of Table 5 is that the coefficient for RUCCt–1
is significantly negative in a regression for RJ1231, which means that the opening price of the afternoon
session reverses the reaction at the opening of the morning session. Furthermore, just as RJ0901 reacts
negatively to the previous day’s closing (RJ1500-1), RJ1231 reacts negatively to the closing of themorning session (RJ1100). The coefficient on RJ1100 in a regression for RJ1231 is –0.207 with ap-value of 0.000004%.
Just one example of all other mundane results is given by the regression for RJ1400, in which
RUCCt–1 is not significant. Three out of five lagged one-minute returns are significant, but theindependent variable lagged one day is not.
One may wonder whether our results are valid, when intraday seasonality is removed. Indeed,seasonal adjustment on the first moment does not change the results at all except for the constant term as
far as the seasonal factors are constant during the season, because our regression equation (3) essentiallyhas daily frequency, which is estimated for every minute. 18 We did run regressions with seasonally18

Suppose we use a regression approach to achieve this. We first run a regression of a long one-minute stock
return series on 270 dummy variables each of which represents a specific time during the day. A dummy
variable for 09:01 is equal to unity at this time of day, but is zero for all other minutes. A 09:02 dummy takes
the value of unity at 09:02, but is zero otherwise, etc. One can easily ascertain that the estimated coefficienton each hhmm dummy is equal to the average of associated one-minute return across days. Hence, denoting
such a mean by μ hhmm , the deseasonalized series is simply RJhhmm t − μ hhmm , which implies the adjusted series

has a zero mean. Therefore, the above equation (3) now becomes,
5′′i [RJ ( hhmm − i ) t − μ hhmm − i ] + γ hhmm
′ ( RJhhmm t −1 − μ hhmm ) + δ hhmm
′ RUCC t − 1 + u t ,RJhhmm t − μ hhmm = α hhmm
+ ∑ β hhmm

but,

this

′ + ∑ β hhmm
′i [RJ (hhmm − i)t − μhhmm−i ] + γ hhmm
′ ( RJhhmmt −1 − μhhmm ) + δ hhmm
′ RUCCt −1 + ut
RJhhmmt − μhhmm = α hhmm

.This

i =1

simplifies

to

5

i =1

14

adjusted data, and we confirmed the above proposition.
How about seasonal adjustment for the second moment? The price volatility in the beginningof a market is well known to be high, as was confirmed in Figure 2. One of the causes for this is therevelations of new information during the nontrading hours and the closing price at the NYSE isprobably the single most important factor. 19 If we make seasonal adjustment for the variance, e.g.
applying the method of Andersen and Bollerslev (1997), to get rid of the high volatility, it will dampen
the effect of New York’s closing price on the NIKKEI at the beginning. 20 We are trying to determine thecause of high volatility at the market opening, and therefore, adjusting the seasonality in intraday
volatility is incompatible with what we are trying to estimate in the sense that the magnitude of the
response of Tokyo to New York is altered. However, since the t-value of the estimated coefficient does
not change, how fast Tokyo absorbs the effect of New York’s closing price is not altered.
The importance of New York to Tokyo’s market opening can be shown by simple arithmetic. The
standard deviation of RJ0901 is 0.30 (Table 1). The regression of RJ0901 on RUCC gives an estimatedcoefficient of 0.178 (Table 5). When we multiply the standard deviation of RUCC (=1.04 according toTable 4) by this coefficient, the product becomes 0.18 approximately. More than half of the standard

equation differs from (3) only in the constant term. Other explanatory variables are exactly the same as in(3).
19
The importance of New York to Tokyo’s market opening can be shown by simple arithmetic. The standard
deviation of RJ0901 is 0.30 (Table 1). The regression of RJ0901 on RUCC gives an estimated coefficient of0.178 (Table 5). When we multiply the standard deviation of RUCC (=1.04 according to Table 4) by thiscoefficient, the product becomes 0.18 approximately. More than half of the standard deviation of RJ0901 is
explained by the effect of RUCC.
20
Andersen and Bollerslev (1997) analyze intraday seasonality in volatility as follows. The high-frequency
return on day t, period n is denoted by Rt ,n and they assume a decomposition, R t , n = N − 1 / 2 σ t s n Z t , n , where N
is the number of periods per day, σ t is the volatility level for a specific day, sn is the seasonal intraday
volatility component, and Z t , n is an i.i.d. mean zero, unit variance error term. Intraday seasonal volatility is
estimated by applying the flexible Fourier form and the original return series is divided by estimated ŝ n togive a seasonal-volatility adjusted series. If we applied this adjustment to our one-minute returns, theestimated coefficient in equation (3) would be divided by this factor, ŝn . However, because the standard
error is also divided by this factor, the t-value is unaffected.

15

deviation of RJ0901 is explained by the effect of RUCC. All this shows the importance of New York’s
closing price in explaining a high volatility at the market open in Tokyo. Intraday seasonality in stock
price volatility is partly a result of influences from New York.

3.3 Regression analysis: effect of Tokyo on New York
Next, we examine the effects of the Tokyo stock market on New York. We regress each of RUhhmmt(one-minute returns of S&P500 at each minute of the day t) on a constant, lagged one-minute returns of
the preceding three minutes, the return at the same time the day before, and a daily close-to-close returnobserved in Tokyo prior to the opening of the NYSE:

3i
RUhhmmt = α hhmm + ∑ β hhmm
RU ( hhmm − i ) t + γ hhmm RUhhmmt −1 + δ hhmm RJCCt + ut ,

(4)

i =1

where RJCCt is the daily close-to-close return of the TOPIX observed eight and a half hours before theopening of the New York stock market. As in equation (3), we include lagged one-minute returns (thesecond term on the right-hand side of (4)), but the lag order is three, which seems to be enough tocapture the very short-run serial correlation in RUhhmm.
Estimation results at 09:31 and 15:00 are presented in left and middle columns of Table 6. When the
NYSE opens in the morning, RJCCt has a significantly positive and the lagged dependent variable(RU0931t–1) a significantly negative effect on RU0931. But the previous day’s final one-minute return at
the closing has no effect.
The result for RU1500 is displayed as a typical example of all other regressions, where RJCCt has noeffect. Of the three lagged one-minute returns, only that of one minute previously is significant. The
dependent variable lagged one day is not significant either.
The estimated coefficients on δ hhmm are presented in Figure 8. Comparing Figure 8 with Figure 7,
we initially notice that the first several coefficients in Figure 6 are significant but that they are much16

smaller in magnitude than those in Figure 7. Thus, the effect of the Tokyo stock market on the New York
market is far weaker than the reverse effect. There are possibly two reasons for the small effect of Tokyoon New York. First, the U.S. economy is apparently more important to the Japanese economy than theother way round. In fact, the dominant effect of the U.S. stock prices on other countries’ stock prices iswell documented in many studies (e.g., Eun and Shim 1989). Second, although New York is the nearest
predecessor to Tokyo, closing right before Tokyo opens, the NYSE opens eight and a half hours after theTSE closes. In the meantime Frankfurt and London start their daily trading before New York. Tsutsuiand Hirayama (2004a) analyze these four countries using daily closing prices and report a finding thatthe market which closes immediately before one market has the largest effect. In light of this finding, it
would be natural to have a small effect of Tokyo on New York due to the intervening effects of Frankfurt
and London.
To account for these effects, we include the daily close-to-close return in FAZ Index of Frankfurt
Stock Exchange (RGCCt) in the regression equation:
3i
RUhhmmt = α hhmm + ∑ β hhmm
RU ( hhmm − i ) t
i =1

(5)

+ γ hhmm RUhhmmt −1 + δ hhmm RJCCt + ε hhmm RGCCt + ut ,where ε hhmm captures the effect of Frankfurt on New York. The effect of London’s daily closing cannot
be incorporated, because London’s closing time is later than the opening of the NYSE. London closes
its daily trading at 16:30 GMT, which is 11:30 EST in New York. Namely, when New York opens at
09:30 local time, London’s closing value is not yet known. Thus, we had to drop London’s dailyclose-to-close return variable. 21 The Frankfurt Stock Exchange, on the other hand, is open for trading
between 10:30 and 13:30 local time. This closing time is two hours before opening of New York.
Frankfurt’s daily close-to-close return is known to New York, the effect of which is captured by ε hhmm
21

If we had intra-day data of London, we could compute a return up to the time of New York’s opening tocapture the effect of London on New York. Unfortunately we could obtain only daily closing prices for
London and Frankfurt, which compelled us to disregard this effect of London.

17

in equation (5) above.
We ran a regression for this equation and the estimated ε 0931 is about 0.042 (see the right columnsof Table 6) which is greater than δ 0931 = 0.028 in equation (4) (see the left columns of Table 6). 22
However, it is only one-quarter of the effect of New York on Tokyo (see the left columns of Table 5
and 0.178 ÷ 4 ≈ 0.045 ). The result seems to vindicate our two conjectures above offered as an
explanation for the small effect of Tokyo on New York. Though this smallness is partly caused by theintervening market in Frankfurt, Frankfurt’s effect on New York is also very small compared with theeffect of New York on Tokyo, which implies a dominant influence of New York on other markets.
We report, in passing, the estimated δ 0931 , the coefficient on the first one-minute return after
opening, in equation (5). It is now 0.015, which is roughly half that in equation (4). δ 0932 is alsosignificantly positive, but not after these first two minutes. This reduction implies that about half ofTokyo’s effect on New York as measured by equation (4) is absorbed by Frankfurt.
Next, in Figure 8, coefficients up to RU0944 tend to be significant, which means it takes the NYSE
about fourteen minutes to absorb new information from Tokyo. Closer inspection reveals that eight out
of fourteen coefficients on RJCCt are statistically significant. When we examine the effect of Frankfurt
on New York in equation (5), it is significant for most of the first fifteen minutes after 09:31. 23 Since thereaction time is six minutes in Tokyo, the reaction time of New York is longer than that of Tokyo.
This difference in reaction time does not necessarily reflect differences in efficiency. It may be
explained by the fact that the opening price of the Tokyo Stock Exchange is formed by a batch process(itayose, see Footnote 4), in which trading orders are accepted during sixty minutes prior to the market
opening at 09:00. However, in the New York Stock Exchange, the usual continuous trading process
determines the opening price. Another reason for this difference may be due to different degree of
nonsynchronous trading.
22
23This coefficient of 0.042 does not change much even if RJCCt is excluded from equation (5).
This result is basically unaltered even if RJCCt is dropped from equation (5).

18

3.4 What returns do the markets react to?
In the previous section, we assume that the markets react to daily close-to-close returns. Since themedia, such as TV and newspapers, regularly announce this return, this assumption is reasonable. In thissubsection, we will investigate whether the markets react to the information from more specific periods
than the close-to-close return.
The close-to-close return of the TOPIX (RJCC) can be divided into a close-to-open return(RJ0901; nontrading-hours return) and an open-to-close return (RJOC; trading-hours return). RJOC canfurther be divided into a morning return (RJMN; 9:01 to 12:31) and an afternoon return (RJAN; 12:31 to
15:00).
Likewise, the close-to-close return of S&P500, RUCC, is divided into a close-to-open return,
RUCO, an open-to-close return, RUOC, a morning return, RUMN, and an afternoon return, RUAN,
where morning means 9:31 to 13:00 and afternoon is 13:01 to 16:00. 24
Let us first look at correlations between these returns. While RUOC highly correlates with
RUCC (coefficient is 0.995), the correlation coefficient between RUCO and RUCC is only 0.28.
Actually, RUOC is almost identical to RUCC, which can also be ascertained by their means andstandard deviations in Table 4. This fact leads us to expect that the Tokyo market reacts to RUOC justthe same way as to RUCC in equation (3). Indeed, replacing RUCC with RUOC in regression equation(3) yields nearly the same result. The same applies to RJOC and RJCC in equation (4).
In order to find out which return the markets react to, we compare the explanatory power of the
returns in equation (3) or in equation (4). For the ease of exposition, let us refer to equation (3) as Model
A and the equation in which RUCC is replaced with RUOC, RUCO, RUMN or RUAN as Model B.
Construction of these models requires a non-nested test, because neither is a subset of the other model.
24

RUCO is the close-to-open overnight return, which is slightly different from RU0931 that is defined as thereturn between 16:00 in the previous day and 09:31. See Footnote 13.

19

In this paper we apply Deaton’s F test (Deaton 1982). In this test, we compare Model A and B, and focus
on the variables that are not included in the other model. In the test of Model A (equation 3) vs. Model B(RUxx replaces RUCC in equation 3), equation (3) is run first; then we add the alternative return
variable and test the explanatory power of this variable by a standard F test (equivalent to a t test, since
there is only one additional variable). If the additional variable is statistically significant, Model B isselected over Model A. In the test of Model B vs. Model A, Model B is run first; then we add RUCC andtest the explanatory power of RUCC. If RUCC is significant, Model A is selected over Model B.
Naturally, a pair of these tests may not produce an unequivocal result.
P-values of the test for the first seven minutes of TOPIX returns are presented in Table 7, since
the first six minutes are the time the Tokyo market significantly reacts to New York. In the left columns,
we compare additional explanatory power of RUOC and RUCC. When RUOC is added to equation (3)(Model A), RUOC is significant at a 10% level for three cases out of seven (see the second column). 25
The third column shows the results when RUCC is added to Model B. Three cases out of seven cases are
significant, implying RUOC and RUCC have almost the same explanatory power. The result isreasonable because RUOC and RUCC are almost identical series.
Comparing RUCO and RUCC, while RUCC is significant in six cases, RUCO is significant onlyin two cases. This implies that the close-to-close return is more important and is the one focused on by
Japanese investors. Similar results are obtained for the morning return (RUMN) and the afternoon return(RUAN). In summary, Table 7 suggests that the Tokyo market watches the close-to-close return (RUCC)
more than other returns, probably because this is what the media usually reports. RUOC has strong
explanatory power simply because it is almost identical to RUCC.
The same procedure is applied to equation (4) to compare the explanatory power of RJCC withother returns such as RJOC and the results for the first fifteen minutes are shown in Table 8. In the first25

We also provide the number of significant cases at a 5% level in the Table, which leads to the sameconclusions.

20

pair, RJOC is significant in four cases at a 10% level, while RJCC is significant in six cases. RJ0901 is
significant in four cases, and RJCC in eleven cases. RJMN is insignificant in all cases and RJAN issignificant only in one case. RJCC is significant in eight and seven cases in the last two pairs of tests inTable 8. These results suggest the same conclusion as the Tokyo market: the close-to-close return of
TOPIX is what the U.S. investors focus on.

4. Changes in the linkage over sub-periods
In order to examine whether the response pattern has changed during our sample period, we
divide the whole sample into three subperiods and conduct the same analysis of the previous section.
We examined the daily closing prices of S&P500 and TOPIX for our sample period and divided thewhole period into the following three subperiods 26 : Period I: January 5, 1988 to December 31, 1989
when stock prices exhibited an upward trend in both the U.S. and Japan. Period II: January 4, 1990 to
October 15, 1998, when stock prices in the U.S. exhibited an upward trend, while those in Japan fellsignificantly at first and were stagnant thereafter. Period III: October 16, 1998 to November 27, 2003,
when stock prices in both countries moved in a similar fashion, exhibiting an inverted U-shaped pattern.
We regress equation (3) by OLS and the sum of coefficients on RUCCt–1 in regressions for
RJhhmm cumulated over each one-minute interval is depicted in Figure 9 for the Tokyo stock market.
Thus, the graph shows cumulative effects of the S&P500 on the TOPIX during the course of a day’s
trading. Individual coefficients are statistically significant only at the beginning of the day. Others are
seldom significant, thus rendering the cumulative sums statistically not very meaningful. However,even though they are not different from zero statistically, whenever they tend to be positive over26

We should ideally search for break points by conducting structural break tests. However, equation (3)consists of 270 regression equations and each one of them has to be subjected to such a test. We will thenhave 270 sets of break points. There is no established method to aggregate those into a single set. Namely it
seems quite difficult to specify break points uniquely with these tests. Hence we give these points
exogenously.

21

successive minutes the cumulative sum tends to rise, which does imply that the effect from the othermarket is cumulatively positive. Thus, aside from strict statistical significance, we can infer a general
direction of the other market’s influence during the day from this graph. Figure 9, which plots thesecumulative sums for three subperiods, reveals the following: 1)The length of reaction time has
decreased over the sixteen-year period. In Period I, positive responses continue until around 09:30 andthereafter negative responses follow during the morning session. In Period II, positive responses
dissipate by around 09:15 and the decline afterwards is much smaller. Period III exhibits a rapid
increase after the opening and the peak is observed at 09:06.

2) The magnitude of the cumulative

reaction has become greater, from around 0.1 for Period I to 0.3 for Period III. Two reasons can beoffered. One is that the increase reflects intensified economic integration between the U.S. and Japan.
The other is that the relative size of the Tokyo stock market to the New York stock market, as measured
by annual turnover, has declined over the period. Tokyo’s turnover exceeded that of New York in 1988
and 1989. However, the Japanese stock prices have declined and stagnated since then, whereas the New
York market has seen a spectacular rise in the 1990s. Thus, the U.S. turnover has grown tremendously,
dwarfing that of Tokyo. 3) A negative response at the opening of the afternoon session is visible in all
three subperiods. 27
Cumulative sums of coefficients on RJCC in regression equation (4) for the New York stock market
are displayed in Figure 10. The speed of reaction has become greater from Period I to Period II.
Specifically, positive responses, small in magnitude, continue for about two hours after the opening in
Period I, but in Periods II and III initial positive responses abate in about fifteen minutes after opening.
The overall magnitude of cumulative responses is much higher in Period III than in Period I or II.
However, it is much smaller than that of Tokyo. This is probably due to the relative importance of theeconomy.

27

In Period I when the afternoon session started at 13:00 this negative response is observed at 13:01.

22

5. Is there asymmetry in the reaction as the other market rises or falls?
In order to see if there is asymmetry in responses to the other market’s rise or fall, we regress
Japanese returns on positive RUCCt–1 and on negative RUCCt–1 separately. Although the regression
equation is equation (3), we divide the observations into one group where RUCCt −1 is positive andanother where RUCCt–1 is negative. Thus, we ran two sets of regressions. The resultant estimates are
displayed in Figure 11, in which cumulative sums of coefficients are shown. The cumulative responses
to the positive and negative RUCCt–1 are remarkably similar.
Likewise, estimating equation (4) with positive and negative RJCCt separately, we compute thecumulative sums of coefficients for the New York stock market reacting to positive and negative RJCCt
values which are depicted in Figure 12. Unlike Tokyo, New York exhibits clear asymmetry in reaction.
Bad news from Japan has a considerably stronger effect on New York than good news. The magnitudeof the response in New York to a fall in Tokyo is roughly double that of a rise. The response pattern isalso different: when Tokyo has advanced, responses in New York are spread over a longer period, about
one and a half hours, but when Tokyo has fallen, positive responses swiftly reach a peak within about
fourteen minutes. This asymmetry in reaction to a rise or fall in Tokyo is in contrast to the finding ofTokyo’s symmetric responses to New York. 28
This asymmetry in New York might be strongly influenced by the rapid declines in the TOPIX
during the period from January 1990 to July 1992. To check on this possibility, we divided the sample
into three subperiods as above and ran the same regressions. We again obtained asymmetric responses
in New York to a rise or fall in Japan in all three subperiods, indicating asymmetry throughout the
sixteen-year period. Why investors in New York are more sensitive about the fall in Tokyo is anotheragenda for future research.
28

Analyzing the daily stock price index data from 1975 to 1995 for the U.S., the U.K., Germany, and Japan,
Hirayama and Tsutsui (1998b) found that negative large changes have a clearer effect than positive ones.

23

6. Conclusions
This paper explores how rapidly the Tokyo and New York stock markets respond to the
movements of the stock price index of the other market using high-frequency data over the period fromJanuary 5, 1988 to November 27, 2003. Estimating the reactions of one-minute returns of one country to
the preceding daily return of the other country, we find that:
1) A positive response of the Tokyo stock market dissipates within six minutes, while that of New
York dissipates within fourteen minutes. The TSE is more efficient in absorbing the impact at the
opening than NYSE, possibly because TSE employs a batch process called itayose for forming
the opening price, in which trading orders are accepted during one hour prior to opening.
2) The magnitude of the response is around 0.054 (cumulative sum for the first fourteen minutes) for
the New York stock market and 0.22 (cumulative sum for the first six minutes) for Tokyo. Thus,
the effect of New York on Tokyo is over four times greater than the reverse effect.
3) The response time has shortened over the period. The magnitude of the response has grown for
the Tokyo stock market over the three periods, while that of the New York stock market has
grown between the first and the second period.

Its reason is probably increased market

integration and changes in the relative size of the two markets
4) The response of the Tokyo stock market is symmetric in terms of a fall or rise in New York, while
the response of the New York stock market to a fall in Tokyo is twice as great as that to a rise.
5) The opening price of the afternoon session of the Tokyo stock market negatively responds to theprevious movement in New York.
6) The fact that daily stock price movements of New York and Tokyo exert positive influences oneach other at the market opening tends to increase price volatility and more than half of thestandard deviation of RJ0901 is explained by the daily close-to-close return in New York. This24

can be interpreted as one of the causes of intraday seasonality in volatility.
Determining the causes of interesting findings 4) and 5) remains an agenda for future research. We
suggested, however, that 5) is the result of giving a second thought over lunch to the excessive responseat the opening of the day.
The reaction time is on the average six minutes for Japan and fourteen minutes for the U.S. This isconsistent with the findings on stock price reactions to earnings and dividend announcements which are
typically ten to fifteen minutes (Patell and Wolfson, 1984). The difference in the response time may not
imply difference in market efficiency. It may be explained by the market microstructure. One relevant
feature was the itayose process at the market opening in Tokyo. Another candidate is nonsynchronoustrading. Different behavioral patterns may also be a part of the picture, but we await research inbehavioral finance comparing the two markets’ participants. 29

29

According to a questionnaire survey of stock investors in both Japan and the U.S. reported in Shiller et al.
(1996), wishful thinking distinctly characterizes Japanese investors.

25

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Tsutsui, Y., K. Hirayama, T. Tanaka, and N. Uesugi, “Can we make money with fifth-order
autocorrelation in Japanese stock prices?” Asian Economic Journal, Vol. 21, No. 4, (2007) ,369-389.

27

Table 1. Summary Statistics of Selected TOPIX Returns
RJCC
RJOC
RJMN
RJAN

Mean
–0.005414–0.028921–0.061056
0.027906Max.
9.544252
9.535624
4.928397
4.986915

Min.
–7.099952–7.077842–7.383014–4.181279

S.D.
1.241356
1.120321
0.848256
0.651292

LB Q(5)0.000000
0.000000
0.000000
0.000000

N. Obs.
3946
3946
3878
3882

RJ0901
RJ0902
RJ0903
RJ0904
RJ0905
RJ0906
RJ0907
RJ0908
RJ0909
RJ0910
RJ0911
RJ0912
RJ0913
RJ0914
RJ09150.022538
0.009977
0.002953
0.002050–0.000182
0.005068–0.000177–0.000180–0.002076–0.001682–0.000919–0.001643–0.002397–0.001593–0.000664

1.290985
0.531608
0.313808
0.335886
0.304305
0.8741800.372772
0.293806
0.287059
0.257447
0.628561
0.338236
0.225850
0.265057
0.331735–1.384551–0.467999–0.370573–0.307720–0.259738–0.837865–0.415340–0.294364–0.336252–0.231399–0.678866–0.303619–0.258847–0.300950–0.263754

0.300236
0.122559
0.066933
0.053931
0.049527
0.129583
0.054780
0.048681
0.046205
0.042652
0.070972
0.043420
0.041816
0.0411000.040282

0.000002
0.000664
0.137623
0.284805
0.015789
0.000777
0.021402
0.200642
0.040822
0.040816
0.000000
0.150820
0.393895
0.539881
0.189326

3946
3946
3946
3946
3946
3946
3946
3946
3946
3946
3946
3946
3946
3946
3946

RJ1058
RJ1059RJ11000.000893
0.000958
0.000383

0.253167
0.270980
0.624921-0.203527-0.231672-0.343656

0.003117
0.003779
0.013196

0.460764
0.544917
0.000000

3946
3946
3946

RJ1231
RJ1232
RJ1233–0.020839–0.006396–0.004164

0.495607
0.374045
0.233465–0.512869–0.272433–0.237738

0.110544
0.053161
0.036479

0.000000
0.000549
0.192422

3080
3080
3080

RJ1456
RJ1457
RJ1458RJ1459
RJ15000.002471
0.002008
0.006019
0.007532
0.031975

0.336507
0.295976
0.310071
0.429410
0.881639–0.223676–0.361518–0.434954–0.331767–0.613469

0.042856
0.044994
0.050495
0.053642
0.142120

0.811288
0.758851
0.506295
0.152021
0.000000

3891
3891
3891
3891
3891

Notes: Variables are TOPIX returns (in percent). RJOC is daily open-to-close return, RJMN morning returnfrom 09:01 to 12:31 (opening of the afternoon session), RJAN afternoon return from 12:31 to 15:00. RJhhmm
where hhmm is 0902, …, 1500 is a one-minute return except RJ0901 which is daily close-to-open(overnight) return and RJ1231 which is a 91-min. return over the lunch break. S.D. is the standard deviation.
LB Q(5) is the Diebold’s heteroscedasticity-adjusted Ljung–Box Q statistic which tests the null hypothesisthat every autocorrelation coefficient up to the fifth order is zero. p-values are shown in this column. The
sample period is from January 5, 1988 to November 27, 2003. See Footnote 15 for the reasons for different
numbers of observations.

28

Table 2. Correlation Coefficients between Selected TOPIX Returns
RJ0901
RJ45M1000
RJ1231

RJ09011.0000–0.0288–0.0348

RJ45M1000 RJ1231
1.00000.05541.0000Notes: RJ0901 is the overnight return from the previous day’s close to the opening,
RJ45M1000 is the 45-min. return from 09:15 to 10:00, and RJ1231 is the
one-and-a-half hour return during the lunch break. The sample period is from April
30, 1991 to November 27, 2003.

Table 3. OLS Regressions to Explain RJ1231
Variable
Constant
RJ0901
RJ45M1000
RJ1100
RJ1059RJ1058
RJ1057
RJ1056
RJ1231–1
R2
p-value of F test
Num. of Obs.

Eq. (i)Coeff. p-val.
–0.018 0.000–0.013 0.149–0.2050.103
0.066–0.011
0.101
0.082
0.023
0.000
2371

Eq. (ii)
Coeff.
p-val.
–0.0200.000–0.011
0.145
0.016
0.028

0.000
0.121
0.411
0.898
0.197
0.002
0.004
0.025
3077

Eq. (iii)
Coeff.
p-val.
–0.0170.000–0.011
0.216
0.019
0.024
–0.208
0.000
0.096
0.142
0.064
0.425
–0.012
0.888
0.099
0.204
0.083
0.002
0.026
0.000
2371

Notes: The dependent variable is RJ1231, over-lunch return from 11:00 to 12:31. RJ0901 is
the overnight return from the previous day’s close to the opening price at 09:01. RJ45M1000
is the 45-min. return from 09:15 to 10:00. RJhhmm, where hhmm is 1056, …,1100, is the
one-minute return up to hhmm. The subscript, –1, denotes a one-day lag. The sample period isfrom April 30, 1991 to November 27, 2003. The sample size is reduced in equations (i) and(iii) relative to equation (ii) due to the lagged dependent variable on the right-hand side.
p-values are calculated based on the White’s robust standard errors.

29

Table 4. Summary Statistics of Selected S&P500 Returns
RUCC
RUOC
RUMN
RUAN

Mean
0.041675
0.036210–0.003487
0.039431

Max.
5.451431
6.205689
4.023462
5.018159

Min.
–6.865681–6.865681–4.341921–5.240286

S.D.
1.042395
1.017440
0.758387
0.637614

LB Q(5)0.023050
0.000000
0.000023
0.000000

N. Obs.
4014
4014
4014
4014

RU0931
RU0932
RU0933
RU0934
RU0935
RU0936
RU0937
RU0938
RU0939
RU0940
RU0941
RU0942
RU0943
RU0944
RU0945
RU0946
RU0947
RU0948
RU0949
RU09500.0082650.001432
0.003773
0.002902
0.001415
0.001634
0.001818
0.000900
0.000352–0.000672
0.000453–0.000378–0.000724–0.000625–0.001040–0.000456–0.000024–0.000946–0.000868–0.001124

1.401524
0.886300
0.677632
0.602593
0.434428
0.566342
0.371824
0.367519
0.369199
0.975905
1.419375
0.273372
0.333264
0.845680
0.622440
1.035158
0.295632
0.498991
0.312094
0.318218–1.649356–0.591704–0.487086–1.214823–0.502196–0.269207–0.587030–0.950650–0.588413–1.347478–0.320305–0.920964–0.375926–0.402200–0.374209–0.320899–0.401757–0.415385–0.381088–0.412264

0.1871300.079346
0.071638
0.070406
0.061016
0.056813
0.053691
0.054016
0.050169
0.056239
0.048864
0.048071
0.043056
0.044064
0.042680
0.042752
0.042440
0.042172
0.041142
0.041282

0.000000
0.000046
0.000000
0.000023
0.489507
0.008811
0.010972
0.036028
0.089316
0.012362
0.228744
0.118769
0.016551
0.189585
0.145902
0.075415
0.281982
0.015185
0.786378
0.007237

4014
4014
4014
4014
4014
4014
4014
4014
4014
4014
4014
4014
4014
4014
4014
4014
4014
4014
4014
4014

RU1556
RU1557
RU1558
RU1559
RU16000.000446
0.000957
0.001198
0.002425
0.001906

0.225533
0.223683
0.132838
0.224797
0.189216–0.161202–0.170993–0.212960–0.189719–0.231702

0.026527
0.026275
0.025592
0.026541
0.026650

0.5191190.484659
0.063213
0.184533
0.122381

4014
4014
4014
4014
4014

Notes: Variables are several S&P500 returns. RUCC is daily close-to-close return, RUOC daily
open-to-close return, RUMN morning return from 09:31 to 13:00, and RUAN afternoon return from 13:01 to
16:00. RUhhmm where hhmm is 0932, …, 1600 is a one-minute return except RU0931 which is
close-to-open (overnight) return. S.D. is the standard deviation. LB Q(5) is Diebold’sheteroscedasticity-adjusted Ljung-Box Q statistic which tests the null hypothesis that every autocorrelation
coefficient up to the fifth order is zero. p-values are shown in this column. The sample period is from January
5, 1988 to November 27, 2003.

30

Table 5. Selected Estimation Results of Eq. (3)RJ0901
Variable
Coeff.
Constant
0.017
RUCC–1
0.178
RJ1500–1 –0.202
RJ1459–1 –0.049
RJ1458–1
0.039
RJ1457–1 –0.012
RJ1456–1
0.145
RJ0901–1
0.025
2
0.369
R
p-val. of F
0.000
Num. Obs.
3034

p-val.
0.000
0.000
0.000
0.587
0.667
0.906
0.201
0.292

RJ1231
Variable
Coeff.
Constant–0.017
RUCC–1–0.010–0.207
RJ11000.088
RJ10590.060
RJ1058–0.004
RJ10570.097
RJ1056
RJ1231–1
0.085
2
0.031
R
p-val. of F
0.000
Num. Obs.
2374

p-val.
0.000
0.000
0.000
0.174
0.449
0.960
0.211
0.001

RJ1400
Variable
Coeff.
Constant
0.000
RUCC–1–0.001
0.098
RJ13590.054
RJ13580.050
RJ13570.020
RJ13560.022
RJ1355
RJ1400–1–0.0040.017
R2p-val. of F
0.000
Num. Obs.
3001

p-val.
0.468
0.231
0.001
0.039
0.040
0.402
0.346
0.845

Notes: OLS estimation results of eq. (3) for RJ0901, RJ1231, and RJ1400 only are displayed above. The subscript –1 indicates a one-day lag. The
sample period is from January 5, 1988 to November 27, 2003. ‘p-val.’ is the p-value of a t-statistic on each explanatory variable, which is calculated
based on the White’s robust standard errors. ‘p-val. of F’ is the p-value of the F test for the entire regression. For different numbers of observations see
Footnote 12. The number of observations for RJ1231 is particularly small because 12:31 was in the middle of a lunch break before April 26, 1991.

31

Table 6. Selected Estimation Results of Equations (4) and (5)eq. (4) RU0931
Variable
Coeff.
Constant 0.010
RJCC 0.028
RU1600–1 0.003
RU1559–1 0.125
RU1558–1 0.250
RU0931–1 –0.170
0.049
R2p-val. of F
0.000
Num. Obs.
3148

p-val.
0.003
0.000
0.986
0.524
0.193
0.000

eq. (4) RU1500
Variable
Coeff.
Constant
0.001
RJCC –0.0002
RU1459RU1458RU1457
RU1500–1

R2
p-val. of F
Num. Obs.

0.327
0.002
–0.019
0.014
0.112
0.000
3148

p-val.
0.143
0.631
0.000
0.960
0.544
0.584

eq. (5) RU0931
Variable
Coeff.
Constant 0.010
RJCC 0.015
RGCC 0.042
RU1600–1 –0.106
RU1559–1 0.072
RU1558–1 0.094
RU0931–1 –0.192
0.135
R2p-val. of F
0.000
Num. Obs.
3085

p-val.
0.002
0.000
0.000
0.544
0.702
0.612
0.000

Notes: OLS estimation results of eq. (4) for RU0931, RU1500 and of eq. (5) for RU0931 are displayed above. The subscript , –1, indicates a one-day lag.
Sample period is from January 5, 1988 to November 27, 2003. ‘p-val.’ is the p-value of a t-statistic on each explanatory variable, which is calculated
based on the White’s robust standard errors. ‘p-val. of F’ is the p-value of the F test for the entire regression.

32

Table 7. Explanatory Power of RUCC and Other Returns: Deaton’s F-tests

RJ0901
RJ0902
RJ0903
RJ0904
RJ0905
RJ0906
RJ0907
10% signif.
5% signif.

A vs. B
RUOC
0.00000
0.00000
0.37860
0.60801
0.37833
0.097280.53043
3
2

B vs. A
RUCC
0.00000
0.00000
0.79958
0.858290.609120.040360.48952
3
3

A vs. B
RUCO
0.00000
0.00000
0.376400.61052
0.38701
0.103640.53388
2
2

A vs. B
RUMN
0.000030.76067
0.01134
0.82851
0.40475
0.153770.35052
2
2

B vs. A
RUCC
0.00000
0.00000
0.00000
0.001020.001510.00008
0.63545
6
6

B vs. A
RUCC
0.00000
0.00000
0.00000
0.019070.005360.005210.82338
6
6

A vs. B
RUAN
0.00000
0.350820.00809
0.93536
0.32623
0.071800.30665
3
2

B vs. A
RUCC
0.00000
0.00001
0.019450.00818
0.062890.00004
0.29799
65

Notes: See notes to Table 4 for definition of the variables. P-values of the F tests, which are calculated based on the White’s robust standard errors, areshown in the Table. ‘A vs. B’ in Deaton’s F test takes Model A as given and inserts additional variables that appear in Model B. If the F test of thesevariables is not significant, these variables from Model B do not have additional explanatory power, which implies a rejection of Model B. In our tests,
only a single variable is added at a time, thus the F test is equivalent to a t test. ‘B vs. A’ reverses the procedure. ‘10% signif.’ stands for the number ofcases, out of seven trials, that the alternative variable is significant at a 10% level. ‘5% signif.’ is the same proportion at a 5% level. There are four pairsof Model A and B above: RUOC vs. RUCC, RUCO vs. RUCC, RUMN vs. RUCC, and RUAN vs. RUCC. Each row represents a regression equation
explaining the variable indicated by the first column.

33

Table 8. Explanatory Power of RJCC and Other Returns: Deaton’s F-tests

RU0931
RU0932
RU0933
RU0934
RU0935
RU0936
RU0937
RU0938
RU0939
RU0940
RU0941
RU0942
RU0943
RU0944
RU094510% signif.
5% signif.

A vs. B
RJOC
0.08701
0.00003
0.031310.050120.71204
0.416590.180160.82304
0.18934
0.769140.83856
0.344850.689440.76082
0.49733
4
3

B vs. A
RJCC
0.003070.002540.05086
0.01986
0.949450.615390.28604
0.367040.04452
0.892120.83646
0.54201
0.406230.21478
0.36807
5
4

A vs. B
RJ09010.080690.00003
0.031930.05255
0.71099
0.41858
0.194470.80526
0.19218
0.756450.849640.36746
0.692140.76204
0.48124
4
3

A vs. B
RJMN
0.526100.78705
0.791280.122250.50460
0.865850.79563
0.48304
0.98592
0.22794
0.461590.95438
0.42951
0.71530
0.677210
0

B vs. A
RJCC
0.00000
0.00000
0.08660
0.04582
0.142290.08971
0.07882
0.01586
0.00375
0.037410.054300.115160.100500.000900.45776
11
7

B vs. A
RJCC
0.00000
0.03987
0.486960.00170
0.14189
0.46992
0.67209
0.021450.00925
0.027220.55585
0.48926
0.047080.005960.25476
8
8

A vs. B
RJAN
0.588400.076460.170650.904450.437240.64979
0.62483
0.572070.38471
0.21665
0.53224
0.597440.624170.92634
0.98180
1
0

B vs. A
RJCC
0.00000
0.08030
0.81794
0.03189
0.59558
0.411880.657900.03806
0.00027
0.34106
0.055120.548440.180590.001260.350347
5

Notes: See notes to Table 1 for definition of the variables. P-values of the F tests, which are calculated based on the White’s robust standard errors, areshown in the Table. For the test procedure, see notes to Table 7. ‘10% signif.’ stands for the number of cases, out of fifteen trials, that the alternative
variable is significant at a 10% level. ‘5% signif.’ is the same based on a 5% level. There are four pairs of Model A and B above: RJOC vs. RJCC,
RJ0901 vs. RJCC, RJMN vs. RJCC, and RJAN vs. RJCC. Each row represents a regression equation explaining the variable indicated by the firstcolumn.

34

Figure 1 Daily Means of TOPIX One-Minute Returns
0.04

Mean

0.03

Upper Bound
Lower Bound

0.02

0.01

0.00

-0.01

-0.02

RJ1451

RJ1441

RJ1431

RJ1421

RJ1411

RJ1401

RJ1351

RJ1341

RJ1331

RJ1321

RJ1311

RJ1301

RJ1251

RJ1241

RJ1231

RJ1051

RJ1041

RJ1031

RJ1021

RJ1011

RJ1001

RJ0951

RJ0941

RJ0931

RJ0921

RJ0911

RJ0901-0.03

Notes: One-minute returns of TOPIX are averaged across days. The sample period is from January 5, 1988 to November 27, 2003. The sample size
varies between 3,080 and 3,946. See Table 1 for the differing sample sizes. 95% confidence bands are shown for the null of a zero mean.

35

Figure 2.

Daily Means of Absolute TOPIX One-Minnute Returns

0.25
Mean
0.2

0.15

0.1

0.05

RJ1451

RJ1441

RJ1431

RJ1421

RJ1411

RJ1401

RJ1351

RJ1341

RJ1331

RJ1321

RJ1311

RJ1301

RJ1251

RJ1241

RJ1231

RJ1051

RJ1041

RJ1031

RJ1021

RJ1011

RJ1001

RJ0951

RJ0941

RJ0931

RJ0921

RJ0911

RJ09010Notes: Absolute TOPIX one-minute returns are averaged across days. The sample period is from January 5, 1988 to November 27, 2003.
The sample size varies between 3,080 and 3,946. See Table 1 for the differing sample sizes.

36Figure 3 Daily Means of S&P500 One-Minute Returns
0.010
0.008

Mean

0.006

Upper Bound
Lower Bound

0.004
0.002
0.000
-0.002-0.004-0.006

RU0931
RU0941
RU0951
RU1001
RU1011
RU1021
RU1031
RU1041
RU1051
RU1101
RU1111
RU1121
RU1131
RU1141
RU1151
RU1201
RU1211
RU1221
RU1231
RU1241
RU1251
RU1301
RU1311
RU1321
RU1331
RU1341
RU1351
RU1401
RU1411
RU1421
RU1431
RU1441
RU1451
RU1501
RU1511
RU1521
RU1531
RU1541
RU1551-0.008Notes: One-minute returns of S&P500 are averaged across days. The sample period is from January 5, 1988 to November 27, 2003. The sample
size is 4014. 95% confidence bands are shown for the null of a zero mean.

37

Fig. 4 Daily Means of Absolute SP500 One-Minute Returns
0.120
Mean

0.100

0.080

0.060

0.040

0.020

RU0931
RU0941
RU0951
RU1001
RU1011
RU1021
RU1031
RU1041
RU1051
RU1101
RU1111
RU1121
RU1131
RU1141
RU1151
RU1201
RU1211
RU1221
RU1231
RU1241
RU1251
RU1301
RU1311
RU1321
RU1331
RU1341
RU1351
RU1401
RU1411
RU1421
RU1431
RU1441
RU1451
RU1501
RU1511
RU1521
RU1531
RU1541
RU15510.000

Notes: Absolute S&P500 one-minute returns are averaged across days. he sample period is from January 5, 1988 to November 27,
2003. The sample size is 4014.

38

Figure 5 Correlation Coefficient of TOPIX 1 Min-Returns
with Previous Day's Close-to-Close Daily Return of S&P500 (RUCC)
0.7
0.6

Correl. Coeff.
Upper Bound

0.5

Lower Bound

0.4
0.3
0.2
0.1
0
-0.1

RJ1451

RJ1441

RJ1431

RJ1421

RJ1411

RJ1401

RJ1351

RJ1341

RJ1331

RJ1321

RJ1311

RJ1301

RJ1251

RJ1241

RJ1231

RJ1051

RJ1041

RJ1031

RJ1021

RJ1011

RJ1001

RJ0951

RJ0941

RJ0931

RJ0921

RJ0911

RJ0901-0.2

Notes: RJhhmm, where hhmm is the hours and minutes of the time of day, is the one-minute return of TOPIX. Notice there is a lunch break between 11:00 and 12:30.
Correlation coefficients between each of RJhhmm and RUCCt-1 (previous day’s close-to-close daily return of S&P500) are plotted. The sample period is from January
5, 1988 to November 27, 2003. The sample size is 3080 for the half-hour duration from 12:31 to 13:00 due to a longer lunch break before April 26, 1991 and is between
3891 and 3946 for other times. See Footnote 15 for description of this difference in the sample size. Upper and lower bounds indicate 95% confidence bands for thenull of a zero correlation coefficient.

39

Figure 6 Corrrelation Coefficient of S&P500 1-Min. Returns with
Previous Day's Close-to-Close Daily Return of TOPIX (RJCC)
0.2

Corr. Coeff.
Upper Bound

0.15

Lower Bound
0.1

0.05

0

-0.05

RU0931
RU0941
RU0951
RU1001
RU1011
RU1021
RU1031
RU1041
RU1051
RU1101
RU1111
RU1121
RU1131
RU1141
RU1151
RU1201
RU1211
RU1221
RU1231
RU1241
RU1251
RU1301
RU1311
RU1321
RU1331
RU1341
RU1351
RU1401
RU1411
RU1421
RU1431
RU1441
RU1451
RU1501
RU1511
RU1521
RU1531
RU1541
RU1551-0.1

Note: RUhhmm, where hhmm is the hours and minutes of the time of day, is the one-minute return of S&P500. Correlation coefficients between
each of RUhhmm and RJCCt (previously observed close-to-close daily return of TOPIX) are plotted. The sample period is from January 5, 1988
to November 27, 2003. The sample size is 4014. Upper and lower bounds indicate 95% confidence bands for the null of a zero correlation
coefficient.

40

Figure 7 Regression Coefficients on RUCC

0.18
0.16

Coeff.
Upper Bound

0.14

Lower Bound
0.12
0.1
0.08
0.06
0.04
0.02
0

RJ1451

RJ1441

RJ1431

RJ1421

RJ1411

RJ1401

RJ1351

RJ1341

RJ1331

RJ1321

RJ1311

RJ1301

RJ1251

RJ1241

RJ1231

RJ1051

RJ1041

RJ1031

RJ1021

RJ1011

RJ1001

RJ0951

RJ0941

RJ0931

RJ0921

RJ0911

RJ0901-0.02

5i
Note: This plots regression coefficients on RUCCt-1 of equation (3), RJhhmm t = α hhmm + ∑ β hhmm
RJ ( hhmm − i ) t + γ hhmm RJhhmm t −1 + δ hhmm RUCC t −1 + ut , andi =1

their 95% confidence bands. They capture the effect of previous day’s close-to-close return of S&P500 on each of the TOPIX one-minute returns. See notes to Figure
5.

41Figure 8 Regression Coefficients on RJCC
0.04
0.035

Coeff.
Upper Bound

0.03

Lower Bound
0.025
0.02
0.015
0.01
0.005
0
-0.005

RU1551

RU1541

RU1531

RU1521

RU1511

RU1501

RU1451

RU1441

RU1431

RU1421

RU1411

RU1401

RU1351

RU1341

RU1331

RU1321

RU1311

RU1301

RU1251

RU1241

RU1231

RU1221

RU1211

RU1201

RU1151

RU1141

RU1131

RU1121

RU1111

RU1101

RU1051

RU1041

RU1031

RU1021

RU1011

RU1001

RU0951

RU0941

RU0931-0.01

3i
Note: This plots regression coefficients on RJCCt of equation (4) RUhhmm t = α hhmm + ∑ β hhmm
RU ( hhmm − i ) t + γ hhmm RUhhmm t −1 + δ hhmm RJCC t + u t , andi =1

their 95% confidence bands. They represent effects of the preceding close-to-close daily return of TOPIX on each one-minute return of S&P500. See notes to Figure
7.

42Figure 9 Cumulative Sum of Regression Coefficients on RUCC : Three Subperiods
0.35

Period I
Period II
Period III

0.3

0.25

0.2

0.15

0.1

0.05

RJ1451

RJ1441

RJ1431

RJ1421

RJ1411

RJ1401

RJ1351

RJ1341

RJ1331

RJ1321

RJ1311

RJ1301

RJ1251

RJ1241

RJ1231

RJ1051

RJ1041

RJ1031

RJ1021

RJ1011

RJ1001

RJ0951

RJ0941

RJ0931

RJ0921

RJ0911

RJ09010Note: Each line is a cumulative sum of regression coefficients on RUCCt-1 for three subperiods. Period I is from January 5, 1988 to December 21, 1989, Period II fromJanuary 4, 1990 to October 15, 1998, Period III from Oct. 16, 1998 to November 27, 2003. Notice that there do not actually exist regressions for RJ1231, …, RJ1300
for Period I because the lunch break was from 11:00 to 13:00 before April 26, 1991.

43

Figure 10 Cumulative Sum of Regression Coefficients on RJCC: Three Subperiods
0.1
Period I

Period II

0.09
Period III
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01

RU1551

RU1541

RU1531

RU1521

RU1511

RU1501

RU1451

RU1441

RU1431

RU1421

RU1411

RU1401

RU1351

RU1341

RU1331

RU1321

RU1311

RU1301

RU1251

RU1241

RU1231

RU1221

RU1211

RU1201

RU1151

RU1141

RU1131

RU1121

RU1111

RU1101

RU1051

RU1041

RU1031

RU1021

RU1011

RU1001

RU0951

RU0941

RU09310Note: Each line is a cumulative sum of regression coefficients on RJCCt in equation (4) for three subperiods. See also notes to Figure 9.

44

Figure 11 Cumulative Sum of Regression Coefficients on Positive
and Negative RUCC
0.3

0.25

0.2

Positve RUCC

0.15

Negative RUCC
0.1

0.05

Note: Regression equation (3) is estimated separately for positive and negative RUCCt-1.

45

RJ1451

RJ1441

RJ1431

RJ1421

RJ1411

RJ1401

RJ1351

RJ1341

RJ1331

RJ1321

RJ1311

RJ1301

RJ1251

RJ1241

RJ1231

RJ1051

RJ1041

RJ1031

RJ1021

RJ1011

RJ1001

RJ0951

RJ0941

RJ0931

RJ0921

RJ0911

RJ09010

RU0931
RU0941
RU0951
RU1001
RU1011
RU1021
RU1031
RU1041
RU1051
RU1101
RU1111
RU1121
RU1131
RU1141
RU1151
RU1201
RU1211
RU1221
RU1231
RU1241
RU1251
RU1301
RU1311
RU1321
RU1331
RU1341
RU1351
RU1401
RU1411
RU1421
RU1431
RU1441
RU1451
RU1501
RU1511
RU1521
RU1531
RU1541
RU1551Figure 12 Cumulative Sum of Regression Coefficientson Positive and Negative RJCC

0.3

Positive RJCC

0.25

Negative RJCC

0.2

0.15

0.1

0.05

0

Note: Regression equation (4) is estimated separately for positive and negative RJCCt.

46