The Society for Economic Studies
The University of Kitakyushu
Working Paper Series No.2012-13(accepted in March 25, 2013)1

Re-evaluating the Tobin Tax
New evidence from tick-by-tick quotation data on twelve currency pairs
Hiroyuki Ono
Toyo University
hiroono@toyo.jp
Minoru Hayashida
The University of Kitakyushu
hayasida@kitakyu-u.ac.jp
Preliminary
Do Not Quote
Abstract
This paper attempts to reevaluate the Tobin Tax’s capability to stabilize
the foreign exchange market and to raise revenues, using tick-by-tick
quotation data from twelve currencies with an ARFIMA model. The
results are that the coefficients for the transaction costs are of thepositive sign and highly significant in the model using exchange rate
volatility as an objective variable across all currency pairs. However,
the results for volume are mixed and do not form a clear picture, while
the elasticity is less than unity in absolute value even in cases where
negative and significant coefficients are obtained. These imply that the
Tobin Tax would not contribute to market stability, but may be useful inraising revenues.

2

1. IntroductionMore than three decades ago, James Tobin (1978) proposed taxing foreignexchange transactions; the proposal is now known as the Tobin Tax. The rationale
for such a tax was twofold. First, by raising transaction costs, it would penalize
so-called “noise traders,” thereby stabilizing the currency market. Second, the tax
would raise necessary revenues for international organizations, which arechronically in budgetary shortage. The tax could therefore promote various
programs considered publicly beneficial across national borders, addressing matterssuch as global warming and development aid, carried out by the organizations.
After its cool, if not antagonistic reception for more than a decade, Tobin’s (1978)
proposal has gradually gained serious attention among professional economists andpolicymakers, while remaining just an idea, rather than a policy option, andwithout igniting much enthusiasm to date1.
In the face of very volatile and unpredictable foreign exchange markets,
however, the Tobin Tax has received renewed interest in recent years. After thebankruptcy of Lehman Brothers, the US Dollar depreciated more than 17% against
the Japanese Yen in just 4 months2. Less than a year and half later, the Euro
started to depreciate against major currencies after Greece announced its budget
problems. Within 6 months, the Euro depreciated 18.5% against the Japanese Yen
and 15.8% against the US Dollar3. Further, after the great earthquake on March 11,
2011, while most people predicted that the Japanese Yen would depreciate against
other currencies, it in fact appreciated 7.7% against the US Dollar and 8.2% against
the Euro within 6 months.
In view of such developments in foreign exchange markets, in recent years
several political leaders have openly talked about the Tobin Tax4. Some economists
have echoed them5, and the IMF has responded with a proposal for new taxes6. In
Europe, real actions toward a financial transaction tax have been pushed forward.
Tobin (1996) himself writes how his idea has been received since the proposal.
The rate was 107.92 on September 12, 2008, and dropped to 89.13 on January 12, 2009 at the Tokyo
market closing.
3 The rates are from January 15 through June 30, 2011.
http://www.oanda.com/lang/ja/currency/historical-rates/
4 Angela Merkel, Nicolas Sarközy and Gordon Brown reportedly mentioned it around the time of the
G20 Summit meeting in Pittsburgh in 2009.
5 For instance, economists from all over the United States co-signed “An Open Letter from Economists
in Support of Financial Transaction Taxes”, in December 2009, which was made public through theCenter for Economic Policy Research
6 The IMF published Global Financial Stability Report: Meeting New Challenges to Stability and
Building a Safer System right before the G8 Summit meeting in Toronto in 2010.
1
2

3

According to the European Commission7:
As from September 2012 the European Commission received requests of eleven
Member States asking it to submit a proposal for a Council Decision to authorize
enhanced cooperation. Its objectives and scope were requested to be based on theoriginal Commission FTT proposal. The Commission's analysis provided a positive
outcome. On 23 October 2012 the Commission proposed to the Council to authorize
the enhanced cooperation in the area of financial transaction tax. The European
Parliament gave its consent to the latter proposal on 12 December 2012 and on 22
January 2013 the EU Council adopted a decision authorizing eleven Member States
to go ahead with enhanced cooperation on a common system of financial transaction
tax (FTT).

Although the proposal does not cover currency transactions, it may lay some groundto cover them if actually made into law in those countries8.
Since there has been no country that ever taxed currency transactions, rigorous
empirical research on the Tobin Tax per se has been very limited; the research on
the effects of transaction taxes is largely limited to the stock market. However, afew exceptions indicate a positive relationship between the transaction costs andvolatility in the foreign exchange markets. Although not explicitly focusing on thetransaction tax, a large volume of literature also offers some implications for
currency transactions; most such studies suggest that the bid-ask spread as a proxyof transaction costs and measures of volatility are positively correlated; theevidence for the relationship between the spread and trading activities is mixed andremains unclear.
In view of this, the present paper reinvestigates whether the Tobin Tax, if
implemented, would stabilize the market and raise necessary revenues, adding
another clinical data point on these issues. To do so, the paper employs an
Auto-Regressive Fractionally Integrated Moving Average (referred to as ARFIMA
hereinafter) model, using high-frequency, tick-by-tick quotation data across twelve
currency pairs. The main conclusions of the paper are that the tax would notcontribute to stability; it would rather decrease it. However, the tax may contributeto the raising of revenue.
The rest of the paper is organized as follows. The next section reviews previous
literature. Section 3 discusses data and methodology. Section 4 and 5 present
estimation results for exchange rate volatility and trading activities, respectively.
The final section concludes the paper, with summary, caveats, and venues for future
Excerpt from the European Commission website:
http://ec.europa.eu/taxation_customs/taxation/other_taxes/financial_sector/index_en.htm
8 These eleven countries are Belgium, Germany, Estonia, Greece, Spain, France, Italy, Austria,
Portugal, Slovenia, and Slovakia.
7

4extensions.
2. Literature Review
While the issue of whether a transaction tax enhances market stability has
been largely explored in the context of stock trading 9 , research focusing ontransaction taxes in currency trading has been very scarce. Among the few
exceptions, Aliber et al. (2003) examine the relationship between transaction costs
measured by the average bid-ask spread, on the one hand, and volatility of
exchange rate returns and trading volume, on the other. Using monthly data,
constructed from daily futures data from January 1, 1977 to December 31, 1999,
they find that volatility is positively associated, while trading volume is negatively
associated, with the transaction costs for three major currencies — British Pound,
Japanese Yen, and Swiss Franc — against the US Dollar10.
Improving on some methodological issues in Aliber et al. (2003), Lanne andVesala (2006) investigate the problem, using HFDF93 data on the German Markand Japanese Yen against the US Dollar. First, having constructed daily realized
variances, by computing the percentage differences of the logarithmic bid and ask
prices closest to the end of five-minute intervals, they regress the variances on thetransaction cost measures together with a one-period lagged objective variable,
Friday dummy, and Holiday dummy. They found a positive correlation between thetransaction cost and volatility of exchange rate returns for both currencies. Second,
they use the five-minute returns directly and conduct the Flexible Fourier form(FFF) regressions [e.g. Gallant (1981, 1982), and Andersen and Bollerslev (1997)],
and confirm the results above.
Away from the focus on the transaction tax, several other papers also haveinvestigated the relationship between the bid-ask spread as a proxy of transaction
costs and exchange rate volatility. Boothe (1988) finds evidence for a positive
correlation between them for seven major currencies over the period 1980 to 1981.
Bollerslev and Melvin (1994), using over 300,000 quotations in the Deutsche Mark /US Dollar interbank market, present evidence that the size of the bid-ask spread is
positively related to the underlying exchange rate uncertainty. Bessembinder(1994) shows evidence that the spread and forecast return variance are positively
There are numerous studies empirically examining the relationship between the transaction tax andstock return volatility. They include, to name a few, Umlauf (1993), Hu (1997), Hayashida and Ono(2010).
10 They could not find the same relationship for the German Mark, however.
95

associated11. Defining volatility as the log first difference of the middle and closing
rates, Hartmann (1999) finds a positive correlation between the spread andpredicted return volatility for daily JPY/USD data from December 1989 to January
1995. In contrast to these studies, with data provided by EBS Co. Ltd, for JPY/USD
and EUR/USD from 1 January 1999 to 31 December 2001, Ito and Hashimoto(2006) find a negative correlation between the spread and volatility, defined as
average absolute one-minute change in the log of the midpoint, bid-ask quotes.
However, using the same data but in lower frequency (15 minutes) intervals, Huaand Li (2011) estimated PGARCH models and found evidence that bid–ask
spreads12 are positively associated with exchange rate volatility for the JPY/USD
rate13.
On the relationship between the spread and trading activities, however, theempirical evidence is much more mixed, despite market microstructure theories’
predicting a negative correlation. While Glassman (1987) finds a positive
relationship, Bessembinder (1994) and Hartman (1999) show that the relationshipis different, whether the volume is expected or not; the expected volume isnegatively associated with the spread, while the reverse relationship is found forthe unexpected volume. While Lyons (1995) reveals a positive correlation between
the dealers’ order size and the bid–ask spread, Ding (2007) finds that spreads are
independent of order sizes in the inter-dealer market, but that they are negatively
correlated in the customer market. Ito and Hashimoto (2006) find that the width ofbid-ask spread is negatively correlated with the number of deals during businesshours. Hua and Li (2011) also find a negative correlation of the width of bid-ask
spread with the number of deals as well as the number of quotation changes.
All in all, the existing literature largely, if not unequivocally, suggests a positive
correlation between the spread and volatility, but the evidence for trading activities
remains unclear. This motivates the present paper. In comparison with thesestudies, the paper distinguishes itself in the following manners. First, it covers awider range of currency exchange rates. Second, in view of a long memory propertyof the variables in question, the paper employs ARFIMA models. Third, the paper
uses tick-by-tick quotation data recorded in the frequency of 1/100th of a second.

The forecast return variance here is a one-step-ahead conditional return variance estimated from a
GARCH(1,1) specification.
12 Defined here to be the difference between the last quoted ask and bid in each interval, and thus
different from Ito and Hashimoto’s (2006) definition.
13 Exchange rates are defined to be the (last) ask quotes in each interval, and their variances withineach interval are used for the volatility measure.
1163. Data and Methodology
3-1 Data
The data used in this study are on a tick-by-tick quotation basis, drawn from
Thompson Reuters’ Tick History©. There are eleven series for each pair of foreignexchanges in the data set on the GMT basis: price, volume, bid price, bid size, ask
price, ask size, open, high, low, accumulated volume, and turnover. Among these,bid price, bid size, ask price, and ask size are recorded whenever new orders are
made, while price, volume, and turnover are recorded every time deals are made,timed to 1/100th of a second. Accumulated volume is the sum of turnover oftransactions made up to the point. Turnover is the product of the price and volume.
Open is the opening price of the day. High and Low are the highest and lowest
prices of the day up to the point.

A sample for JPY/USD is shown in Table A-1 in

the Appendix.
The data to analyze are the following twelve pairs of foreign exchange rates: (1)
EUR/USD, (2) JPY/USD, (3) GBP/USD, (4) CHF/USD, (5) EUR/JPY, (6) EUR/GBP,(7) EUR/AUD, (8) EUR/CHF, (9) GBP/JPY, (10) AUD/JPY, (11) ZAR/JPY and (12)
GBP/AUD14. There are roughly 140,000 data points for each of these pairs15. The
period for the analysis is from April 25, 2010 to August 31, 2011.
To date, no country has ever taxed currency transactions, so there are no actual
data for a transaction tax on currency exchange. However, it is an establishedpractice to treat the bid-ask spread as a measure of transaction costs [e.g. Glassman(1987), Boothe (1988), and Lanne and Vesala (2006)], and to view it as a proxy forthe transaction tax. The rationale behind this is that, once the tax is levied, traders
would include the amount to be taxed away in bid and ask prices when offering
them; so, the bid-ask spread would increase when the tax is imposed. We employ
this strategy. More specifically, the transaction cost, referred to as COST, is definedas:
COST =𝐴𝑆𝐾 − 𝐵𝐼𝐷
𝐴𝑆𝐾 + 𝐵𝐼𝐷

Here, ASK and BID refer to the arithmetic means of quoted ask and bid prices ineach five-minute interval, respectively. The volatility measure, referred to as VOL,
The abbreviation for each currency is as follows. USD: the United States Dollar, EUR: Euro, JPY:
the Japanese Yen, GBP: the Great Britain Pound, CHF: Swiss Franc, AUD: the Australian Dollar, andZAR: the South African Rand.
15 In executing ARFIMA estimations, we delete missing data, i.e. intervals in which there is noobservation of at least one of these four variables; therefore, the total number of observations used in
the actual estimation is smaller.
147

is the standard deviation of prices within the five-minute intervals16. The data on
volume itself is used and summed over the same five-minute intervals. It is referred
to as TO.
Descriptive statistics are presented in Table 1 below. Together, the results of
the unit root (ADF) tests are presented. For all of the twelve pairs, VOL, COST, andTO are stationary.
Table 1: Descriptive Statistics(1) EUR/USD
VOL
SPREADTO
Mean
0.000228 0.000142 7.765375
Median0.000196
0.00014 4.428571
Maximum 0.004809 0.001233
500
Minimum
0-0.000261SD
0.000166 0.0000374 14.75503
ADF-41.4763 -30.32089 -38.4352
lag
9
27
14
P-value000VOL0.013001
0.01077
0.424939
00.009423-34.5766180(2) JPY/USD
SPREADTO
0.014463 12.22432
0.013893 8.444444
0.23686502-0.024273
10.004408 15.61478-24.90011 -55.5144
221700.0001VOL
0.000263
0.000212
0.00311400.000219-121.923
00.0001(3) GBP/USD
SPREADTO
0.000247 5.397821
0.000239
2
0.002667 300.3333-0.000313
10.0000715 12.75667-28.46215 179.4821
25000.0001VOL
0.000223
0.000173
0.00473800.00022-72.9373
00.0001(4) CHF/USD
SPREADTO
0.000273 4.948259
0.0002620.005575500-0.0000809
10.0000868 11.03716-33.34474 -130.811
25
000.0001(5) EUR/JPY
VOL
SPREADTO
Mean
0.024358 0.023552 8.854247
Median0.020226 0.022816 6.494426
Maximum 0.593169 0.300952 536.3333
Minimum
0 -0.034089
1SD
0.016932 0.006754 10.46026
ADF-29.5156 -19.36188 -58.4789
lag
18
33
15
P-value
000.0001VOL
0.000158
0.000141
0.00274800.000162-3.4869420.009(6) EUR/GBPSPREADTO
0.000179 4.992337
0.0001731
0.001741
400-0.0000627
1
0.0000491 15.69498-32.13199 -84.6066
20
0
0
0.0001(7) EUR/CHF
VOL
SPREADTO
0.000326 0.000334 4.700905
0.000252 0.000321 1.690476
0.006904
0.0041300
0 -0.000137
10.000341 0.000105 10.5778-53.7253 -35.73439 -34.6322
021
2
0.000100VOL0.000255
0.000207
0.0051200.000267-58.0225
00.0001(8) EUR/AUD
SPREADTO
0.000257 5.491593
0.000235 1.571429
0.005234550-0.000112
10.0001 13.19215-13.68827 -101.985
36
000.0001(9) JPY/GBP(10) JPY/AUD
VOL
SPREADTOVOL
SPREADTO
Mean
0.028519 0.032722 7.741521 0.02081
0.022182 10.10834
Median0.024133 0.031506 5.433333 0.017187
0.021475
7.75
Maximum 0.782366 0.537027
500 0.546718
0.471613
261.5
Minimum
0 -0.019401
1
0-0.026091
1SD
0.019518 0.010272 10.21529 0.014034
0.007288 9.074758
ADF-17.1669 -38.47533 -68.1296 -12.863-35.84689 -27.1738
lag
35
17
11
59
19
36
P-value
000.0001000(11) JPY/ZAR
VOL
SPREADTO
0.00643 0.017729 4.25709
0.006124 0.015983 2.230769
0.132952
0.235
210
0 -0.006335
1
0.005184 0.008221 6.314362-21.3316 -40.74617 -100.739
9
15
3
0
0
0.0001VOL
0.000338
0.000265
0.00550800.000353-0.35819
140.8962(12) GBP/AUD
SPREADTO
0.000431 3.967701
0.000381
10.007842290-0.0000749
1
0.000158 10.35992-18.28017 -102.075
27
00

3-2 Methodology
It is well known that volatility has a long memory. In such cases, ARFIMA
models are now widely used. ARFIMA(p,d,q) is in general defined to be:Φ(𝐿)(1 − 𝐿)𝑑 (𝑦𝑡 − 𝜇) = Η(𝐿)𝑢𝑡 ,𝑢𝑡 ~𝑊𝑁(0, 𝜎𝑢2 )where Φ(𝐿) and Η(𝐿) are polynomial equations of lag operator 𝐿 with dimensions
p and q respectively, and absolute values of roots of characteristic equations arelarger than 1. 𝑊𝑁(0, 𝜎𝑢2 ) is white noise with mean zero variance 𝜎𝑢2 , and 𝑑 is adifference parameter to take fractional values. Note that∞𝑑(1 − 𝐿) = 1 + ∑
𝑘=1
16

𝑑(𝑑 − 1) ⋯ (𝑑 − 𝑘 + 1)(−𝐿)𝑘 .
𝑘!

There is a period of roughly 10 minutes where there are no data for every date.

8

1

1

1

If 0 < 𝑑 < 2, 𝑦𝑡 has a long memory; if 𝑑 < 2, 𝑦𝑡 is stationary; and if 𝑑 > − 2, 𝑦𝑡 isinvertible.
As shown in Table A-2 in the Appendix, both VOL and TO exhibit a longmemory property for all twelve pairs, justifying the use of the ARFIMA model. In
the analyses below, we set p = q = 0 as a first approximation for the current paper.
For the exchange rate volatility as an objective variable, we estimate two models:
one with constant and transaction cost only (Model 1) as explanatory variables, andone with volume and linear time trend in addition (Model 2). For the turnover as an
objective variable, Model 1 is the same, but Model 2 only adds linear time trend.

4. Transaction Costs and Exchange Rate Volatility
It is shown in Table 2 that, across twelve currency pairs, the estimatedcoefficients of COST are of the positive sign and highly significant; the P-values areless than 1% in all cases. The d-parameter falls between 0 and 1/2, confirming thestationary property in Table 1. This is true for both Model 1 and Model 2. Thisimplies, in line with much of the literature, that transaction cost increases withexchange rate volatility.
Table 2: Transaction Costs and Exchange Rate Volatility

9(Note) The lower entries for the d-parameter, a constant, COST and time trend are P-values associatedwith the estimated coefficients in the upper entry.

It is worth investigating whether the above results remained the same before
the earthquake on March 11, 2011. As mentioned earlier, most people predicted theJapanese Yen would depreciate against major currencies in the aftermath of theearthquake, but in fact it appreciated. This may suggest some anomaly in the
movement of exchange rates involving the Japanese Yen after the earthquake.
Therefore, for those exchange rates, the models are also estimated with the sample
before March 11. The results are shown in Table 3. There is not much difference
between the results in Table 2 and Table 3. Therefore, the above conclusion holds:
an increase in transaction costs would increase exchange rate volatility.
Table 3: Transaction Costs and Exchange Rate Volatility(Currency Pairs involving the Japanese Yen before March 11, 2011)(Notes) See the notes in Table 2.

As mentioned before, the tax on transactions would increase the bid-ask spread,as traders would include the amount to be taxed away in bid and ask prices when
proposing them. In so much as it is true, the above results imply that the Tobin Tax
would increase, not decrease, the foreign exchange volatility.

5. Transaction Cost and Trading Volume
The results in the previous section suggest that the Tobin Tax, raisingtransaction costs, would not contribute to the stability of foreign exchange rates, as
Tobin (1978) and his proponents expected. That does not mean that the tax is
10

useless, however, because another case for the tax is that it may raise revenue to be
used for various international programs, such as global warming or development
aid. Whether the tax is a good revenue source is the subject of this section.
To examine that, an ARFIMA model is estimated as before, because TO also
exhibits a long memory, as Table A-2 in the Appendix shows. The results arereported in Table X. As is the case with previous studies, the results are mixed, andshow no clear-cut picture. The estimated coefficients for COST are: negative andsignificant for EUR/AUD and GBP/JPY, positive and significant for JPY/USD,
AUD/JPY, and ZAR/JPY, and insignificant for the other seven currency pairs. It isdifficult to draw any conclusive statements from these results.
Table 4: Transaction Costs and Trading Volume(Note) The lower entries for the d-parameter, a constant, COST and time trend are P-values associatedwith the estimated coefficients in the upper entry.

It should be reminded that the period after March 11, 2011 could be anomalous
for the Japanese Yen. That may be seen in that the coefficient is positive andsignificant for three out of five pairs involving the currency, despite themicrostructure literature expectation of a negative relation. So it is worth
investigating, as before, excluding data after the earthquake. The results are shownin Table 5. There is not much difference between the results in Table 4 and Table 5.

11

Therefore, the above conclusion holds: no conclusive statements are drawn17.
Table 5: Transaction Costs and Trading Volume(Currency Pairs involving the Japanese Yen before March 11, 2011)(Notes) See the notes in Table 4

Taken at face value, the above results imply that, since an increase intransaction costs through a transaction tax does not reduce the trading volume, thetax would certainly raise revenues for the 10 cases, except for EUR/AUD and
GBP/YEN. It is of interest, in these two cases where the negative and significant
coefficients are estimated, to calculate the tax elasticity of trading volume. Even if
the coefficient is negative and significant, the tax may be a good revenue source ifelasticity is less than unity in the absolute value. Here, because the transaction cost
is approximated by the spread, our linear elasticity measure, η, is defined:η=(𝑉𝑂𝑡 − 𝑉𝑂𝑡−1 )/𝑉𝑂𝑡−1
𝑌𝑡=(𝑆𝑃𝑅𝐸𝐴𝐷𝑡 − 𝑆𝑃𝑅𝐸𝐴𝐷𝑡−1 )/𝑆𝑃𝑅𝐸𝐴𝐷𝑡−1 𝑋𝑡

Here, Yt  (VOt  VOt 1 ) / VOt and X t  ( SPREAD t  SPREAD t 1 ) / SPREAD t . The estimate
for  is obtained by regressing Y on X with a constant.
The results are the following:[EUR/AUD]Yˆt  1.709699  0.302522 X t(0.0000) (0.1864)
N=18,705
R2=0.000040[GBP/JPY]Yˆt  0.750683(0.0000) 0.030664 X t(0.1436)

The reasons for these mixed results would require further scrutiny, but are left for future
investigations.
1712

N=94,423

R2=0.000012

The figures in the parenthesis are the P values associated with the estimatedcoefficients above them. In both cases, the estimated η is of the negative sign andless than unity in absolute value. This implies that, even in these two cases where
the transaction costs are negatively correlated with trading volume, the transaction
tax would still be a useful vehicle for raising revenues.
6. Concluding remarks
This paper investigates whether the Tobin Tax would contribute to the stabilityof foreign exchange markets and would be capable of raising revenues. The data
used are tick-by-tick quotation data for 12 currency pairs drawn from Thompson
Reuters’ Tick History © for the period from April 25, 2010 to August 31, 2011. Since
the Tobin Tax would increase transaction costs, which are approximated by theaverage bid-ask spread over five-minute intervals, average bid-ask spread serves as
our “hypothetical” rate of the Tobin Tax. The market stability is measured bystandard deviation of deal prices over the same intervals. Given that both thestability measure and the average of the deal volumes in the same intervals exhibit
a long-memory property, the paper employs ARFIMA models.
The results are that coefficients for the transaction costs are positive and highly
significant unanimously in the models with the stability measure as an objective
variable. This would imply that the Tobin Tax would damage market stability,
rather than ameliorate it. However, in the models with trading volumes as an
objective variable, the results do not show any uniform tendency one way or theother: out of 12 cases, the coefficients for the transaction costs are negative andsignificant for 2 cases, positive and significant for 3 cases, and insignificant for 7
cases. If the tax would not affect or increase the trading volume, it would raise
revenues, but if the tax decreases the volume, the degree to which it does so matters.
If elasticity is greater than unity in absolute value, the tax revenue, which is the
product of the tax rate and volume, would not be raised. In the two cases where thecoefficients were negative and significant, the elasticity is calculated to be less thanunity in absolute value. Therefore, taking these results at face value, they imply
that the Tobin Tax would be useful in raising revenues, even if it does not contributeto stability.
In concluding the paper, it is worth mentioning some caveats and future
extensions. This paper defines the stability of the market as that of the price level
13and examines the volatility of deal prices, but a number of studies examine thevolatility of price return. To see the robustness of the present results, it may be
useful to examine return volatility as well. Also, the paper takes deal volume as anindicator for market activity, but the number of deals within the five-minuteinterval and other related variables, subject to availability, are worth investigating.
This paper use five minutes as a frequency of estimation, but it may be interesting
to examine how the results change when the frequency is altered to, say, one minuteor thirty minutes. Further, if the twelve foreign exchange markets under study
should be viewed as closely interrelated, estimating them independently may beinappropriate; the Seemingly Unrelated Estimation (SURE) may be necessary toobtain efficient estimates. These are all interesting topics to explore, but are left to
future investigations.
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23, 801–24.
Hu, S. Y. (1998). The effects of the stock transaction tax on the stock market:
experiences from Asian markets. Pacific Basin Finance Journal, 6, 347-364.
Hua, M. and Li, C.Y. (2011) The intraday bid-ask spread behavior of the JPY/USD
exchange rate in the EBS electronic brokerage system, Applied Economics, 43,
2003-2013.
Ito, T. and Hashimoto, Y. (2006) Intraday seasonality in activities of the foreignexchange markets: evidence from the electronic broking system, Journal of theJapanese and International Economies, 20, 637–64.
Lanne, M, and Vesala, T. (2006) The effect of a transaction tax on exchange rate
volatility, Bank of Finland Research Discussion Papers, 11, 2006.
Lyons, R. K. (1995) Tests of microstructural hypotheses in the foreign exchange
market, Journal of Financial Economics, 39, 321–51.
Tobin, J. (1978) A proposal for international monetary reform, Eastern Economic

Journal, 4, 153-159.
Tobin, J. (1996) Prologue, in Haq, M, Kaul, I. and Grunberg, I. eds: The Tobin tax:

coping with financial volatility, Oxford University Press.
Umlauf, S. R. (1993) Transaction taxes and the behavior of the Swedish stock
market, Journal of Financial Economics, 33, 227-240.

15

APPENDIX
Table A-1: Sample of the original data

16

Table A-2: Long memory property of VOL and TO(1) EUR/USD
VO
VOL
AC PAC Q-Stat Prob AC PAC Q-Stat Prob AC
1 0.338 0.338 8794.2 0
2 0.293 0.202 15410 0
3 0.269 0.143 20974 0
4 0.251 0.108 25822 0
5 0.24 0.09 30268 0
6 0.225 0.067 34159 0
7 0.208 0.049 37495 0
8 0.205 0.051 40726 0
9 0.198 0.044 43735 0
10 0.188 0.034 46446 0
11 0.175 0.023 48808 0
12 0.177 0.033 51219 0
13 0.166 0.021 53345 0
14 0.159 0.018 55294 0
15 0.158 0.023 57229 0
16 0.152 0.018 59019 0
17 0.148 0.016 60708 0
18 0.145 0.016 62324 0
19 0.138 0.011 63793 0
20 0.132 0.008 65128 0
21 0.134 0.016 66506 0
22 0.126 0.007 67726 0
23 0.122 0.007 68868 0
24 0.117 0.006 69932 0
25 0.115 0.007 70944 0
26 0.111 0.006 71902 0
27 0.112 0.01 72869 0
28 0.105 0.004 73724 0
29 0.102 0.004 74532 0
30 0.098 0.002 75274 0
31 0.095 0.003 75977 0
32 0.093 0.004 76645 0
33 0.091 0.003 77277 0
34 0.086 0.001 77847 0
35 0.083 0.001 78383 0
36 0.087 0.009 78965 00.097 0.097 807.79 0
0.088 0.079 1469.7 00.056 0.041 1737.5 0
0.072 0.058 2189.2 00.054 0.036 2444.7 0
0.055 0.036 2701.3 0
0.054 0.035 2951.6 0
0.042 0.021 3101.9 0
0.06 0.041 3414.6 0
0.047 0.025 3607.6 0
0.035 0.012 3715.6 0
0.04 0.02 3852.1 0
0.044 0.023 4016.1 0
0.052 0.031 4248 00.051 0.029 4475.1 0
0.04 0.016 4616.6 0
0.036 0.013 4729.6 0
0.042 0.019 4880.5 0
0.038 0.014 5004.9 0
0.037 0.014 5120.9 0
0.024 0.001 5170.3 0
0.036 0.015 5281 00.033 0.012 5374.9 0
0.034 0.012 5474.9 0
0.026 0.005 5533.6 0
0.032 0.012 5622.3 0
0.025 0.004 5676.8 0
0.028 0.008 5746.3 0
0.021 0.001 5783.1 0
0.024 0.005 5831.6 0
0.026 0.008 5890.1 0
0.025 0.006 5943.4 0
0.027 0.009 6005.6 0
0.026 0.008 6064 0
0.021 0.003 6102.3 00.014 -0.004 6118.7 0

0.504
0.407
0.371
0.347
0.325
0.317
0.305
0.292
0.276
0.276
0.269
0.263
0.251
0.242
0.24
0.236
0.233
0.236
0.232
0.221
0.218
0.216
0.211
0.206
0.2
0.198
0.199
0.201
0.195
0.196
0.191
0.184
0.18
0.182
0.179
0.181

(2) JPY/USD
VOL
PAC Q-Stat Prob AC
0.504 24303 00.205 40124 0
0.147 53327 00.108 64822 00.081 74926 00.078 84548 00.061 93456 00.049 101638 00.034 108947 00.047 116247 00.037 123191 0
0.033 129791 00.021 135829 00.019 141442 00.025 146947 00.023 152276 00.023 157470 00.03 162794 00.022 167935 00.01 172609 00.016 177166 00.017 181650 00.012 185924 00.01 190000 00.006 193821 00.01 197555 00.017 201360 0
0.019 205238 00.008 208886 00.015 212564 00.008 216057 00.003 219303 0
0.004 222411 00.011 225580 00.007 228639 00.014 231783 0

VO
PAC Q-Stat Prob AC

0.14 0.14 1880.3 0
0.076 0.058 2440.5 00.059 0.042 2779.4 0
0.048 0.032 3005.8 0
0.042 0.026 3173.9 0
0.037 0.022 3309.4 0
0.035 0.02 3426 00.03 0.016 3513 00.029 0.015 3591.8 0
0.026 0.013 3657.4 0
0.031 0.019 3748.5 0
0.026 0.012 3812.6 0
0.029 0.017 3894.2 0
0.031 0.018 3987.6 0
0.028 0.014 4064.1 0
0.025 0.011 4123.6 0
0.029 0.016 4206.8 0
0.028 0.014 4284.9 0
0.022 0.007 4329.5 00.028 0.015 4404.7 0
0.025 0.011 4463.4 0
0.019 0.005 4496.5 0
0.021 0.009 4538.5 0
0.02 0.008 4578.9 0
0.023 0.011 4630.5 0
0.021 0.008 4673 00.015 0.002 4694.8 0
0.021 0.01 4738.7 0
0.012 -0.001 4751.8 0
0.017 0.007 4778.2 0
0.018 0.007 4808.4 0
0.016 0.005 4832.1 0
0.015 0.005 4855.1 0
0.011 0.001 4867.2 0
0.015 0.005 4887.5 0
0.013 0.004 4905 0

17(3) GBP/USD
VO
VOLPAC Q-Stat Prob AC PAC Q-Stat Prob AC

0.134 0.134 614.21 00.106 0.09 1000.7 0
0.081 0.058 1227.7 0
0.068 0.044 1387.8 0
0.059 0.034 1505.1 0
0.057 0.033 1615.9 0
0.055 0.031 1719.7 0
0.05 0.025 1804.3 0
0.048 0.024 1882.8 0
0.039 0.016 1936.2 0
0.046 0.024 2008.4 0
0.043 0.02 2072.7 0
0.045 0.022 2141.2 0
0.047 0.024 2217.3 0
0.047 0.022 2292.9 0
0.034 0.009 2333.6 0
0.028 0.004 2360.6 0
0.038 0.017 2410.6 0
0.036 0.014 2455 00.028 0.005 2481 00.028 0.007 2507.8 0
0.027 0.007 2531.9 0
0.025 0.007 2554.2 0
0.023 0.004 2571.6 0
0.02 0.002 2585 00.019 0.002 2596.8 0
0.015 0 2604.9 0
0.022 0.008 2621.3 0
0.023 0.009 2639.9 0
0.025 0.01 2662.2 0
0.012 -0.004 2667.2 0
0.013 -0.001 2673 00.021 0.009 2687.9 0
0.023 0.01 2705.7 00.009 -0.006 2708.4 0
0.014 0.003 2715.4 0

0.076 0.076 323.5 0
0.055 0.049 493.19 00.037 0.029 568.78 00.037 0.03 646 00.033 0.025 706.88 00.024 0.016 738.92 0
0.027 0.02 779.73 00.023 0.015 808.75 00.026 0.019 846.96 0
0.017 0.009 863.89 0
0.013 0.006 874.02 0
0.018 0.011 891.81 00.021 0.014 915.62 00.017 0.01 932.79 0
0.018 0.011 951.61 00.012 0.005 960.21 00.021 0.015 984.77 00.018 0.01 1002.1 0
0.018 0.011 1020 00.01 0.002 1025.2 0
0.01 0.004 1031.1 0
0.013 0.007 1040.3 00.012 0.006 1048.3 0
0.018 0.012 1066.2 0
0.012 0.005 1073.7 0
0.005 -0.001 1075.2 0
0.006 0.001 1077.1 0
0.006 0.002 1079.5 00.005 0.001 1080.9 0
0.01 0.006 1087.1 0
0.005 0 1088.3 0
0 -0.004 1088.3 0
0.011 0.008 1095.3 0
0.016 0.012 1109.8 00.005 0 1111.5 0
0.01 0.006 1117.4 0(4) CHF/USD
VOL
PAC Q-Stat Prob AC

0.196 0.196 714.17 00.115 0.08 962 00.109 0.076 1185.3 0
0.105 0.067 1390.9 0
0.082 0.039 1516.1 0
0.068 0.029 1602.7 0
0.073 0.037 1701.7 0
0.075 0.037 1806 00.065 0.026 1885.8 0
0.051 0.013 1935.1 0
0.056 0.022 1993.5 0
0.044 0.009 2029.5 0
0.046 0.015 2068.5 00.054 0.025 2123.1 0
0.051 0.019 2172.3 00.039 0.006 2200.6 0
0.047 0.018 2241.4 0
0.054 0.024 2295.3 0
0.047 0.015 2337 00.045 0.015 2375.6 0
0.042 0.01 2407.9 0
0.034 0.003 2429.4 0
0.027 -0.001 2443.2 0
0.033 0.009 2463.7 0
0.033 0.007 2483.4 0
0.033 0.009 2504.3 0
0.027 0.002 2517.8 0
0.028 0.005 2532.3 0
0.028 0.005 2546.6 0
0.032 0.011 2565.2 0
0.031 0.009 2583.7 0
0.025 0.001 2595 00.023 0.002 2605.2 0
0.026 0.006 2618 00.038 0.018 2644.7 0
0.025 0.002 2656.8 0

VO
PAC Q-Stat Prob

0.041 0.041 65.969 00.066 0.065 234.12 0
0.021 0.016 251.79 0
0.046 0.041 334.65 00.023 0.018 355.63 0
0.015 0.008 364.44 00.009 0.004 367.57 00.017 0.013 378.74 00.013 0.009 385.1 0
0.021 0.017 402.59 00.023 0.019 422.12 0
0.014 0.009 430.14 0
0.027 0.021 457.59 00.018 0.013 470.76 00.022 0.015 488.98 00.009 0.003 491.98 0
0.017 0.011 503.61 00.011 0.006 508.1 0
0.015 0.009 516.86 00.014 0.009 524.03 0
0.013 0.008 530.78 00.018 0.013 543.24 00.012 0.006 548.48 0
0.002 -0.004 548.62 0
0.016 0.011 558.71 00.009 0.004 562.02 0
0.018 0.012 573.86 0
0.006 0.001 575.35 00.016 0.01 584.91 0
0.017 0.012 595.83 00.017 0.011 607.43 00.001 -0.006 607.45 00.008 0.003 610.1 0
0.006 0.002 611.54 0
0.008 0.003 613.84 0
0.01 0.006 617.85 0

(5) EUR/JPY

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36

(6) EUR/GBP

AC

VOL
PAC Q-Stat Prob AC

VO
PAC Q-Stat Prob AC

0.524
0.463
0.438
0.421
0.406
0.394
0.379
0.37
0.357
0.356
0.35
0.346
0.336
0.321
0.317
0.313
0.31
0.311
0.304
0.295
0.29
0.289
0.281
0.274
0.27
0.265
0.269
0.264
0.262
0.263
0.256
0.25
0.248
0.245
0.244
0.246

0.524 26200 00.26 46675 00.181 65004 00.137 81960 00.106 97752 00.085 112592 00.064 126352 00.057 139451 00.042 151626 00.052 163771 00.043 175482 00.042 186946 00.028 197716 00.013 207573 00.021 217201 0
0.021 226538 00.024 235752 00.029 244990 00.019 253832 00.01 262124 0
0.012 270163 00.017 278131 0
0.008 285679 00.005 292838 00.008 299817 00.007 306552 00.02 313483 00.01 320123 0
0.012 326662 00.018 333286 00.007 339573 00.003 345550 00.007 351446 00.007 357206 0
0.009 362896 00.015 368666 00.117 1317.8 0 0.053 0.053 20.901 00.043 1625.2 0 0.048 0.045 38.054 00.07 2245.6 0 0.029 0.025 44.449 00.036 2528.7 0 0.046 0.042 60.503 00.022 2668 0 0.031 0.025 67.88 00.017 2767.6 0 0.026 0.019 72.819 00.027 2923 0 0.018 0.011 75.269 00.02 3038 0 0 -0.006 75.269 00.012 3101.9 0 0.014 0.01 76.799 00.016 3181.2 0 0.015 0.011 78.493 00.015 3258 0 0.006 0.001 78.749 00.009 3300.7 0 0.009 0.006 79.391 00.017 3375.2 0 0.009 0.006 80.013 00.017 3456.3 0 0.015 0.012 81.754 00.01 3505.8 0 0.011 0.007 82.661 00.019 3595.4 0 0.007 0.003 82.985 00.025 3738.4 0 0.009 0.005 83.539 00.007 3786.9 0 0.002 -0.001 83.582 00.011 3844.1 0 0.001 -0.002 83.598 00.006 3883.3 0 0.004 0.002 83.741 00.011 3938.1 0 0.003 0.001 83.813 00.01 3989.5 0 0.003 0.002 83.899 00.005 4020.3 0 0.005 0.004 84.081 00.001 4037.9 0 -0.003 -0.005 84.146 0
0.005 4061.2 0 0.006 0.005 84.395 00.002 4076.4 0 0.009 0.007 84.952 00.013 4124.4 0 0.002 0 84.989 00.004 4145.2 0 -0.001 -0.002 84.995 00.009 4179.7 0 0 -0.002 84.997 00.006 4209.1 0 0.01 0.009 85.79 0
0.006 4236.4 0 0.004 0.002 85.901 00.004 4256.9 0 0.014 0.012 87.37 00.004 4276.5 0 0.014 0.012 88.771 00.004 4296.6 0 0.004 0.001 88.881 00 4306.5 0 0.013 0.01 90.125 00.007 4330.5 0 0.011 0.007 91.041 0

0.117
0.056
0.08
0.054
0.038
0.032
0.04
0.035
0.026
0.029
0.028
0.021
0.028
0.029
0.023
0.03
0.039
0.022
0.024
0.02
0.024
0.023
0.018
0.013
0.016
0.013
0.022
0.015
0.019
0.017
0.017
0.015
0.014
0.014
0.01
0.016

VOL
PAC Q-Stat Prob AC(7) EUR/AUD
VO
PAC Q-Stat Prob AC

0.04 0.04 37.41
0.033 0.031 62.161
0.032 0.029 85.324
0.029 0.026 104.54
0.017 0.013 111.37
0.027 0.023 127.62
0.014 0.009 132
0.022 0.019 143.58
0.013 0.008 147.35
0.015 0.011 152.68
0.023 0.019 164.46
0.015 0.01 169.44
0.012 0.008 173.01
0.008 0.003 174.49
0.009 0.005 176.4
0.008 0.004 177.85
0.007 0.003 178.93
0.011 0.007 181.47
0.017 0.013 187.84
0.011 0.007 190.57
0.01 0.007 193.08
0.007 0.003 194.17
0.004 0.001 194.62
0.01 0.006 196.73
0.013 0.01 200.85
0.01 0.006 202.92
0.019 0.015 211.11
0.013 0.009 215.21
0.012 0.007 218.45
0 -0.004 218.45
0.009 0.006 220.48
0.008 0.004 221.97
0.004 0 222.34
0.007 0.004 223.35
0.001 -0.003 223.37
0 -0.003 223.37

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

18

VOL
PAC Q-Stat Prob AC

0.155 0.155 372.43
0.109 0.087 555.2
0.097 0.07 700.94
0.081 0.051 803.23
0.065 0.034 868.51
0.08 0.052 968.15
0.066 0.033 1035.1
0.054 0.022 1080.2
0.059 0.029 1134.7
0.048 0.017 1170.8
0.038 0.009 1192.8
0.037 0.011 1214
0.032 0.007 1229.8
0.045 0.024 1261.2
0.04 0.016 1286.5
0.043 0.019 1314.7
0.038 0.013 1337.3
0.042 0.018 1364.6
0.04 0.015 1389.4
0.041 0.016 1415.9
0.034 0.008 1433.7
0.03 0.005 1447.2
0.043 0.021 1475.9
0.026 0 1486.6
0.043 0.021 1515.2
0.032 0.006 1530.7
0.036 0.013 1551.1
0.034 0.01 1568.7
0.034 0.01 1586.4
0.042 0.019 1613.5
0.038 0.013 1635.8
0.029 0.003 1648.6
0.019 -0.005 1654.1
0.028 0.007 1666.4
0.022 0 1673.6
0.025 0.006 1683.4

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

(8) EUR/CHF
VO
PAC Q-Stat Prob AC

0.136 0.136 656.7 0
0.093 0.076 963.67 0
0.075 0.055 1164.9 0
0.081 0.06 1398 00.074 0.049 1594.7 0
0.057 0.03 1711 00.057 0.032 1827.3 0
0.057 0.031 1941.7 0
0.057 0.031 2058.8 00.047 0.019 2135.9 0
0.047 0.022 2215.7 0
0.033 0.007 2255.6 0
0.036 0.013 2301.9 0
0.032 0.009 2338.2 0
0.033 0.011 2376 00.035 0.014 2419.5 0
0.032 0.011 2456.2 0
0.032 0.012 2493.9 0
0.026 0.006 2518.2 0
0.032 0.013 2554 00.032 0.013 2591.2 0
0.036 0.017 2638.1 0
0.033 0.013 2677.4 0
0.027 0.007 2704.2 0
0.023 0.003 2722.4 0
0.022 0.003 2739 00.029 0.012 2769.2 0
0.017 -0.001 2780 00.02 0.004 2794 00.025 0.01 2816.2 0
0.026 0.01 2840.5 0
0.022 0.005 2857.5 0
0.021 0.005 2873.1 0
0.025 0.009 2895 00.018 0.002 2907 00.014 -0.001 2914.4 0

VOL
PAC Q-Stat Prob AC

0.233 0.233 617.15 0
0.153 0.104 882.33 00.152 0.102 1144.6 0
0.143 0.082 1375.9 0
0.132 0.067 1574.8 0
0.121 0.053 1741.6 0
0.107 0.038 1872.3 00.106 0.04 2001.1 0
0.111 0.045 2141 0
0.097 0.027 2248.3 0
0.101 0.035 2364 00.085 0.016 2446.9 0
0.077 0.013 2514.7 0
0.074 0.013 2577.8 0
0.088 0.03 2664.9 0
0.085 0.024 2746.2 0
0.081 0.021 2820.7 0
0.083 0.023 2898.8 0
0.078 0.016 2967.3 0
0.074 0.014 3030.1 0
0.064 0.004 3076.8 0
0.07 0.016 3133.2 0
0.062 0.005 3176.7 0
0.063 0.01 3221.8 0
0.063 0.011 3267.4 0
0.074 0.023 3329.2 0
0.064 0.009 3376.1 0
0.053 0 3408.4 0
0.053 0.004 3440.3 00.053 0.005 3472 00.05 0.003 3500.6 0
0.048 0.003 3527 00.052 0.009 3558.1 0
0.044 -0.001 3580.1 0
0.043 0.001 3601.1 0
0.043 0.002 3621.7 0

VO
PAC Q-Stat Prob

0.081 0.081 173.55 00.044 0.038 225.97 0
0.038 0.032 264.58 00.029 0.022 286.67 0
0.029 0.023 309.65 00.033 0.026 338.52 00.026 0.018 356.04 0
0.017 0.01 363.87 0
0.025 0.018 380.23 00.012 0.004 383.76 00.018 0.012 392.12 0
0.015 0.009 398.36 00.014 0.009 403.9 0
0.013 0.007 408.05 0
0.015 0.01 414.12 0
0.018 0.013 423 00.014 0.008 428.03 0
0.016 0.01 434.87 0
0.018 0.012 443.4 0
0.005 -0.001 444.17 0
0.006 0.001 445.1 0
0.016 0.012 452.07 0
0.013 0.007 456.34 00.012 0.006 459.97 00.011 0.006 463.38 00.007 0.002 464.75 00.006 0.001 465.7 0
0.007 0.002 466.91 0
0.009 0.005 469.12 0
0.012 0.007 472.77 00.012 0.007 476.54 0
0.007 0.002 477.78 00.004 0 478.22 00.009 0.006 480.59 00.009 0.005 482.81 00.017 0.012 490.13 0

(9) GBP/JPY(10) AUD/JPY(11) ZAR/JPY(12) GBP/AUD

VO
VO
VO
VO
VOL
VOL
VOL
VOL
AC PAC Q-Stat Prob AC PAC Q-Stat Prob AC PAC Q-Stat Prob AC PAC Q-Stat Prob AC PAC Q-Stat Prob AC PAC Q-Stat Prob AC PAC Q-Stat Prob AC PAC Q-Stat Prob
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36

0.507
0.44
0.418
0.397
0.384
0.381
0.369
0.361
0.343
0.341
0.336
0.334
0.326
0.314
0.312
0.306
0.305
0.302
0.3
0.291
0.285
0.285
0.283
0.272
0.27
0.262
0.265
0.264
0.263
0.268
0.254
0.252
0.25
0.246
0.246
0.248

0.507 24067
0.246 42149
0.179 58473
0.129 73232
0.104 87030
0.098 100608
0.074 113358
0.065 125579
0.039 136616
0.048 147494
0.044 158090
0.044 168540
0.032 178462
0.019 187671
0.028 196773
0.023 205552
0.027 214246
0.025 222809
0.024 231236
0.013 239166
0.011 246753
0.019 254347
0.017 261828
0.004 268743
0.01 275563
0.003 281999
0.016 288565
0.015 295076
0.016 301574
0.024 308275
0 314311
0.008 320272
0.007 326103
0.006 331776
0.009 337425
0.016 343194

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

0.117 0.117 1312 0
0.071 0.058 1798.5 0
0.046 0.031 1997.5 0
0.037 0.025 2128.3 0
0.038 0.028 2269.4 0
0.034 0.022 2378.4 0
0.026 0.015 2444.4 0
0.029 0.019 2523.5 0
0.031 0.02 2614 00.032 0.021 2711.4 0
0.022 0.01 2759.3 00.027 0.016 2827 00.02 0.009 2865.3 0
0.015 0.005 2888.1 0
0.02 0.011 2924.9 0
0.021 0.012 2966.1 0
0.018 0.009 2998.2 0
0.016 0.007 3024 0
0.015 0.006 3046 0
0.018 0.009 3075.4 0
0.016 0.007 3099.4 0
0.014 0.005 3118.1 0
0.02 0.012 3155.1 0
0.018 0.009 3186 00.01 0.001 3195.5 0
0.016 0.009 3220.7 0
0.01 0.001 3229.7 00.013 0.006 3245.5 00.014 0.007 3264.3 0
0.016 0.009 3289.5 00.013 0.005 3305.3 0
0.011 0.004 3317.7 0
0.009 0.002 3325.3 0
0.015 0.008 3346.5 0
0.015 0.007 3366.8 0
0.006 -0.002 3370 0

0.554
0.489
0.467
0.448
0.43
0.419
0.405
0.396
0.378
0.376
0.37
0.362
0.354
0.345
0.339
0.336
0.335
0.329
0.327
0.315
0.313
0.307
0.302
0.294
0.29
0.287
0.287
0.286
0.282
0.285
0.279
0.272
0.268
0.268
0.269
0.272

0.554 29627 00.263 52718 00.187 73708 00.138 93095 00.102 110965 00.085 127880 00.066 143725 00.058 158845 00.036 172654 00.047 186275 00.042 199502 00.034 212158 00.029 224276 00.022 235789 00.021 246847 00.025 257725 00.029 268526 00.022 278983 00.025 289320 00.007 298901 00.017 308380 0
0.01 317459 00.011 326270 00.004 334613 00.007 342716 00.011 350680 00.016 358639 00.016 366535 00.012 374231 00.021 382066 0
0.01 389597 00.003 396735 00.004 403664 00.011 410617 00.015 417612 00.02 424747 0

0.159
0.115
0.108
0.104
0.095
0.094
0.095
0.09
0.086
0.085
0.081
0.085
0.078
0.074
0.076
0.075
0.068
0.073
0.067
0.075
0.057
0.062
0.059
0.062
0.062
0.062
0.061
0.061
0.057
0.062
0.057
0.055
0.059
0.059
0.063
0.056

0.159 2452.9 0 0.246
0.091 3721.2 0 0.22
0.079 4839.2 0 0.198
0.07 5886.3 0 0.182
0.057 6767.9 0 0.178
0.054 7623.7 0 0.178
0.052 8489.6 0 0.177
0.044 9270.6 0 0.169
0.039 9980.4 0 0.154
0.037 10671 0 0.15
0.033 11309 0 0.156
0.036 12005 0 0.143
0.028 12599 0 0.14
0.024 13135 0 0.139
0.026 13688 0 0.142
0.025 14229 0 0.129
0.017 14670 0 0.128
0.024 15190 0 0.129
0.017 15626 0 0.123
0.026 16168 0 0.12
0.006 16486 0 0.12
0.014 16862 0 0.114
0.011 17201 0 0.112
0.015 17579 0 0.113
0.015 17953 0 0.11
0.015 18323 0 0.112
0.014 18686 0 0.103
0.014 19048 0 0.105
0.01 19361 0 0.108
0.016 19733 0 0.105
0.01 20045 0 0.11
0.009 20337 0 0.106
0.014 20670 0 0.105
0.013 21006 0 0.102
0.017 21387 0 0.098
0.008 21686 0 0.098

19

0.246 3502.9 0 0.067 0.067 341.87 0 0.118 0.118 161.94 0 0.087 0.087 226.18 00.169 6290.8 0 0.033 0.029 425.21 0 0.063 0.05 207.99 0 0.054 0.047 313.43 00.122 8549.6 0 0.029 0.025 490.59 0 0.041 0.029 227.7 0 0.06 0.052 419.92 0
0.094 10471 0 0.023 0.019 530.72 0 0.035 0.024 241.89 0 0.025 0.014 438.81 00.084 12301 0 0.022 0.018 568.95 0 0.042 0.033 262.8 0 0.044 0.036 497.36 00.079 14123 0 0.024 0.02 612.96 0 0.034 0.022 276.2 0 0.034 0.023 532.28 00.072 15923 0 0.02 0.015 642.56 0 0.028 0.017 285.52 0 0.018 0.008 541.64 00.059 17571 0 0.016 0.011 662.71 0 0.019 0.008 289.59 0 0.025 0.016 559.6 0
0.04 18933 0 0.005 0.001 664.73 0 0.025 0.017 297.13 0 0.025 0.016 577.81 00.038 20231 0 0.014 0.01 678.84 0 0.03 0.021 307.8 0 0.027 0.018 599.01 0
0.046 21630 0 0.007 0.003 682.86 0 0.017 0.006 311.35 0 0.021 0.011 611.51 00.03 22815 0 0.009 0.006 689.5 0 0.022 0.013 316.97 0 0.054 0.046 696.94 0
0.028 23952 0 0.011 0.007 697.94 0 0.018 0.009 320.57 0 0.02 0.006 708.27 0
0.028 25063 0 0.013 0.01 711.5 0 0.017 0.008 323.88 0 0.015 0.005 715.36 00.033 26225 0 0.011 0.008 721.2 0 0.023 0.015 329.97 0 0.025 0.015 734.18 0
0.017 27182 0 0.006 0.003 724.25 0 0.025 0.016 337.22 0 0.042 0.033 786.19 0
0.019 28123 0 0.006 0.003 726.64 0 0.021 0.011 342.35 0 0.004 -0.01 786.76 00.023 29087 0 0.009 0.007 733.21 0 0.016 0.006 345.26 0 0.023 0.014 802.3 0
0.017 29962 0 0.007 0.004 736.85 0 0.013 0.004 347.24 0 0.043 0.034 857.97 0
0.015 30794 0 0.014 0.011 750.96 0 0.023 0.016 353.48 0 0.041 0.029 907.18 0
0.017 31626 0 0.004 0 752.1 0 0.02 0.01 357.93 0 0.018 0.002 916.59 00.011 32375 0 0.005 0.003 754.11 0 0.013 0.003 359.96 0 0.022 0.01 931.44 00.012 33101 0 0.007 0.005 757.84 0 0.016 0.008 362.89 0 0.021 0.01 944.21 0
0.015 33840 0 0.009 0.007 764.53 0 0.015 0.007 365.61 0 0.018 0.005 953.39 0
0.012 34534 0 0.013 0.01 777.91 0 0.021 0.012 370.55 0 0.027 0.016 974.91 0
0.016 35259 0 0.008 0.005 783.14 0 0.01 0.001 371.77 0 0.015 0.003 981.22 0
0.006 35876 0 0.007 0.004 786.58 0 0.012 0.004 373.35 0 0.021 0.011 993.73 00.011 36507 0 0.011 0.008 795.77 0 0.02 0.013 377.99 0 0.038 0.025 1035.9 0
0.016 37180 0 0.006 0.003 798.69 0 0.013 0.004 379.82 0 0.009 -0.003 1038.5 0
0.012 37815 0 0.007 0.003 801.96 0 0.015 0.007 382.45 0 0.011 -0.001 1041.8 0
0.018 38509 0 0.007 0.004 806.03 0 0.01 0.002 383.65 0 0.014 0.002 1047.6 0
0.014 39164 0 0.005 0.002 807.7 0 0.014 0.007 385.97 0 0.009 -0.001 1050.2 0
0.012 39799 0 0.006 0.004 810.81 0 0.017 0.009 389.18 0 0.014 0.007 1056.3 0
0.009 40396 0 0.007 0.005 814.87 0 0.011 0.003 390.56 0 0.021 0.012 1069.9 0
0.007 40953 0 0.01 0.007 822.78 0 0.014 0.007 392.92 0 0.007 -0.004 1071.1 0
0.008 41508 0 0.001 -0.002 822.85 0 0.012 0.005 394.71 0 0.013 0.005 1076.4 0