SUMMARY

The March 2005 release of the Transportation Services 

Index (TSI), an economic measure of freight and passenger movements,1

 marked the Bureau of Transportation Statistics’ (BTS’) entry into the company of federal 

statistical agencies that produce monthly U.S. economic 

indicators. The TSI consists of three component indexes: a 

freight index, a passenger index, and a combined (or total) 

index. Figure 1 shows the freight and passenger indexes 

as recently displayed on the BTS website.

The TSI is the broadest monthly measure of U.S. domestic 

transportation services and, as such, provides the best 

current measure available of these services. As an index, 

the TSI refl ects real monthly changes in freight and passenger services in the United States.

After development of the TSI, followed by additional research, it became clear the TSI moved in conjunction with 

other indicators of the national economy. Cycles of various 

kinds, depths, and durations occur frequently in the U.S. 

economy. Of these, the business cycles of recession and 

expansion, and the growth cycle are of particular interest 

to economists. The TSI, as presently published on the BTS 

website, spans the time period from 1990 to the present 

and covers two recessions. But, extending the TSI back 

to 1979 allows coverage of four recessions2

 and numerous growth cycles. By comparing the turning points in the 

extended TSI with other economic data series, it is possible to ascertain whether and how transportation services 

1

 USDOT press release, January 29, 2004, available at: http://www.bts.gov/press_

releases/2004/dot005_04/html/dot005_04.html.

2

 The National Bureau of Economic Research (NBER) declared recessions from 

January 1980 – July 1980, July 1981–November 1982, July 1990 – March 1991, 

and March 2001 – November 2001.

relate to movement in the overall economy. Quantitatively 

exploring the relationships between the turning points of 

the TSI and measures of the broader economy reveal 

some interesting results. 

One fi nding is that the freight component of the TSI, which 

encompasses fi ve modes of transportation, shows a strong 

leading relationship to the economy. When the accelerations and decelerations of the freight TSI (the turning 

points in the detrended series) are compared to the growth 

cycles of the economy, the freight measure leads by an average of approximately 4 to 5 months. The passenger TSI 

was identifi ed as a coincident indicator with the general 

economy.

Bureau of Transportation Statistics

Technical Report

U.S. Department of Transportation

Research and Innovative Technology Administration

December 2007

TR-002

Transportation Services Index and the Economy

by Peg Young, Ph.D.; Ken Notis; Gary Feuerberg, Ph.D.; and Long Nguyen

Figure 1: The Transportation Services Index, 

 January 1990 to June 2007

199019921994

1996

1998

2000200220042006

60

70

80

90

100

110

120

130

140

Chain-type index: year 2000=100

TSI—freight

TSI—passenger

SOURCE: U.S. Department of Transportation, Research and Innovative Technology 

Administration, Bureau of Transportation Statistics, http://www.bts.gov.
BTS Technical Report

2

BACKGROUND

In 2002, a team of academic researchers, under a grant 

from BTS, developed the Transportation Services Output Index (TSOI) to measure the economic activity of 

the transportation sector (Lahiri and Stekler, 2002). This 

monthly output index of for-hire U.S. transportation services represented passenger and freight movements. Their 

early research indicated a relationship between changes 

in the transportation services sector and the recessionary 

phase of the business cycles (Lahiri et al., 2003 and 2004).

Recognizing the potential importance of the TSOI to the 

transportation and economic communities, BTS developed 

what was initially an experimental version of the index, the 

Transportation Services Index, or TSI. It included an overall measure of transportation services and two additional 

indexes derived by separating the passenger and freight 

components. 

The sections that follow discuss the data components of 

the TSI along with the procedures for deseasonalizing, 

indexing, and weighting the data to create the indexes. 

This is followed by discussion of economic hypotheses on 

the nature of the relationships between the TSI measures 

and the recessions and growth cycles. Then, the discussion focuses on how the turning points are determined 

and analysis of the turns of the TSI against the turns in 

the business and growth cycles. The fi nal section provides 

conclusions as well as suggestions for future research. 

COMPONENTS OF THE TSI

Transportation services are employed to either move 

freight or move passengers. Given that the freight and 

passenger sectors are infl uenced by different forces in the 

economy and may exhibit different trends, the TSI is represented by three indexes: freight transportation services 

(freight TSI), passenger transportation services (passenger 

TSI), and total TSI, which is a combination of the freight 

and passenger data. 

The TSI includes only domestic “for-hire” transportation 

operated on behalf of or by a company that provides transport services to an external company for a fee. Not included in the for-hire population is transportation in vehicles 

owned by private fi rms providing services to that fi rm, taxi 

and intercity bus services, and noncommercial passenger 

transportation (e.g., trips in the family car). According to 

a prior BTS report, “Transportation Satellite Accounts: a 

New Way of Measuring Transportation Service in America” 

(Washington, D.C., February 1999), the for-hire transportation services component constitutes approximately 50 

percent of total transportation services.

Analyses of the TSI were initially constrained by the limited 

duration of the published index, which covers the period 

from January 1990 to the present. For research purposes, 

BTS extended the index back to 1979. This allowed BTS 

to determine how the TSI behaves in relation to the U.S. 

economy by comparing the turning points in its cycles 

against those of key national economic variables. Table 1 

provides a synopsis of the data sources. What follows is 

a discussion of the data utilized in the TSI, along with the 

methodology employed to aggregate the data.3

Freight

Domestically, goods are moved by road, air, rail, waterway, 

or pipeline as described below. Over the duration of the 

TSI’s history, the share of goods moved by each mode 

changed (based on weight and value); however, trucking 

has consistently represented the largest share of for-hire 

freight transportation. The fastest growing share of freight 

transportation is by air, but it remains the smallest in terms 

of ton-miles.

Trucking (fi gure 2)

Because monthly truck ton-miles data are not available 

through a federal agency, data are obtained from the 

American Trucking Associations (ATA). Data on movements by truck are provided through a truck tonnage index, 

calculated by the ATA; this index is a relative measure of 

the total tonnage transported by the motor carrier industry 

for a given month. For the most recent data, BTS employs 

a preliminary value of the truck tonnage index (provided by 

ATA); when the offi cial data become available, the preliminary values are replaced. 

3

 For further detail regarding the data sources, the reader can refer to the TSI 

webpage on the BTS website: http://www.bts.gov/programs/economics_and_fi nance/

transportation_services_index/html/source_and_documentation_and_data_quality.html.

Table 1: Data Sources for the Transportation 

 Services Index (TSI)

Mode Source Measure

Freight

Trucking American Trucking Associations Index of 

tonnage

Air Bureau of Transportation Statistics and carrier websitesFreight 

ton-miles

Rail Association of American Railroads Carloads & 

Intermodal 

units

Federal Railroad Administration Quarterly 

ton-miles

Water U.S. Army Corps of Engineers Tons

Pipeline Energy Information Administration Thousands 

of barrels, 

billion 

cubic feet

Passenger

Air Bureau of Transportation Statistics and carrier websitesRevenue 

passengermiles

Rail Federal Railroad Administration Revenue 

passengermiles

Transit American Public Transportation 

Association

Unlinked

trips

SOURCE: U.S. Department of Transportation, Research and Innovative Technology Administration, Bureau of Transportation Statistics, http://www.bts.gov.
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BTS Technical Report

Figure 2: Truck Tonnage Index, 

 January 1979 to September 2005

0

30

60

90

120

150

1979

1981

1983

1985

198719891991199319951997

19992001

2003

2005

Index: year 2000 = 100

SOURCE: American Trucking Associations, http://www.truckline.com.

Figure 3: Air Ton-Miles, 

 January 1979 to September 2005

0

1

2

3

4

1979198119831985198719891991

1993

1995

1997

1999

200120032005

Million ton-miles

SOURCE: U.S. Department of Transportation, Research and Innovative Technology Administration, Bureau of Transportation Statistics, http://www.bts.gov.

Figure 4: Quarterly Rail Ton-Miles,

 1st Qtr 1979 to 4th Qtr 2001

197919811983

1985

198719891991

19931995

1997

19992001

0

200

400

600

800

1,000

1,200

Million ton-miles

SOURCE: U.S. Department of Transportation, Federal Rail Administration, 

http://www.fra.dot.gov.

Figure 5: Rail Carloads and Intermodal Units,

 January 1979 to September 2005

0

400

800

1,200

1,600

2,000

1990

1992

1994199619982000

20022004

Thousand rail carloads and intermodals units

Carloads

Intermodal units

SOURCE: Association of American Railroads, http://www.aar.org.

Air (fi gure 3)

U.S. air carriers operating between airports located within 

the boundaries of the United States and its territories 

report freight ton-miles monthly to BTS. As with the air revenue passenger-miles, the ton-mile data are drawn from 

air carrier reports to BTS on Form 41 Schedule T-100. See 

section on air passenger-miles for details.

Rail (fi gure 4 & 5)

The rail freight data from 1990 to 2005 are derived from 

monthly carloads and intermodal units made available by 

the Association of American Railroads (AAR). These data 

are not a direct measure of ton-miles, but their monthly 

behavior is assumed to be similar to monthly ton-miles. 

For data prior to 1990, monthly data were not available, 

so BTS used quarterly rail ton-mile data taken from the 

Federal Railroad Administration (FRA). These quarterly 

values are then interpolated, using a quadratic polynomial 

to expand to monthly values.4

 Figure 4 provides a graph 

that includes the quarterly data used to estimate monthly 

data prior to 1990; fi gure 5 illustrates the monthly data series used to approximate rail ton-miles from January 1990 

to September 2005. 

Water (fi gure 6)

Waterborne freight includes ton and ton-mile data, collected by the U.S. Army Corp of Engineers (USACE), for 

4

 The quadratic polynomial interpolation procedure, which takes sets of three 

adjacent quarterly values and fi ts a quadratic curve to estimate the monthly values, 

allows for potential cyclical patterns in the data.
BTS Technical Report

4

internal U.S. waterways. All maritime vessels are required 

by law to report freight and tonnage to the USACE, with 

the exceptions of the following: military cargo on military 

vessels; cargo carried on general ferries; fuel products, 

such as coal and petroleum, loaded from shore facilities 

directly into vessel bunkers; and insignifi cant amounts of 

government materials.

Pipeline (fi gure 7)

Petroleum supply data are collected by the Petroleum Division in the Offi ce of Oil and Gas of the Energy Information 

Administration (EIA), U.S. Department of Energy (DOE). 

The data in the TSI, which consist of the monthly sum of 

natural gas consumption, Alaska petroleum production, 

and the movement between PADDs (Petroleum Administration for Defense Districts), approximate the movement 

of natural gas and petroleum. 5

Passenger

The passenger TSI encompasses three modes of travel: air, 

rail, and transit. The passenger TSI does not include movement by personal automobile because the index refl ects 

service for-hire. Also not included in the passenger index are 

taxi and intercity bus services due to the lack of available data.

Figures 8 through 10 show the monthly data for each passenger mode. 

Air (fi gure 8)

The largest component of the passenger TSI is aviation. Aviation data are collected and compiled from two sources: Form 

41, Schedule T-100 data submitted to BTS’ Offi ce of Airline 

Information (OAI) and from airline websites. The primary 

source of data, the T-100 dataset, contains extensive information on passenger air travel as well as freight movement by air. 

The TSI passenger index uses revenue passenger-miles data 

from the T-100 dataset. 

In those instances where the current data may not yet be 

available in the T-100 database, BTS uses the carriers’ web 

site postings of current passenger-miles. When T-100 data 

become available, these website values are replaced with the 

offi cial data in the T-100. 

5

 The pipeline data are only available back to 1980. This means that, for 1979, 

the freight component of the index does NOT include pipeline data. Rather, this 

component of freight was introduced into the index in 1980.

Figure 6: Waterborne Tonnage,

 January 1979 to August 2005

0

10

20

30

40

50

60

70

19791981198319851987198919911993

1995

1997

1999

2001

20032005

Tons

SOURCE: U.S. Army Corps of Engineers, Waterborne Commerce Statistics 

Center, http://www.usace.army.mil.

Figure 7: Natural Gas Consumption, Alaska 

 Petroleum Production, and PADD to 

 PADD movement, January 1980 to 

 March 2006

19801982198419861988199019921994199619982000200220042006

0

1

2

3

4

5

Quadrillion British thermal units (Btu)

SOURCE: U.S. Department of Energy, Energy Information Administration, 

http://www.eia.doe.gov.

Figure 8: Air Revenue Passenger-Miles (RPMs),

 January 1979 to September 2005 

0

20

40

60

80

100

19791981198319851987198919911993

1995

19971999

20012003

2005

Million RPMs

SOURCE: U.S. Department of Transportation, Research and Innovative Technology Administration, Bureau of Transportation Statistics, http://www.bts.gov.
5

BTS Technical Report

Rail (fi gure 9)

Rail revenue passenger-miles are compiled from the U.S. 

Department of Transportation, Federal Railroad Administration (FRA) data series for Amtrak and the Alaskan Railroad Corp. Commuter rail is not included in this measure 

because it is covered in the transit data. 

Transit (fi gure 10)

The fi nal component of the TSI passenger index is transit. 

Monthly transit data, primarily from heavy rail and trolleybus agencies as well as nearly all light rail and commuter 

rail agencies, are collected by the American Public Transportation Association (APTA). Historic monthly revenue 

passenger-miles were not available for public transit from 

a federal agency; so the index uses APTA’s monthly measure of unlinked trips.6

 Figure 10 provides a graph of the 

transit data used in the TSI.

CALCULATION OF THE TSI

After the data on the individual passenger and freight components have been collected (or estimated), these data 

series are seasonally adjusted and indexed.

Seasonal Adjustment, Indexing, Weighting, 

and Chaining

The previous fi gures illustrate the seasonal nature of the 

data. In order to portray real growth, BTS used a method 

called X-12-ARIMA to deseasonalize the data7. In applying 

the X-12 methodology to the transportation services timeseries data, BTS noted quantitatively that each time series 

component of the TSI displays strong seasonal patterns. 

(Appendix A provides details on the X-12 ARIMA seasonal 

adjustment procedure.)

After the individual data series are deseasonalized, the 

data are indexed using the 12-month average of data from 

the year 2000 as the base. Each modal series is indexed 

individually. Then weights for each transportation mode are 

created using Gross Domestic Product (GDP) value-added 

– as reported each year in the November issue of the Survey of Current Business, issued by the U.S. Department 

of Commerce’s Bureau of Economic Analysis. Inputs to 

transportation, which are already counted in measures of 

other sectors, are not included. The index thereby acts as 

a measure of the economic activity added by the transportation sector itself. 

These annual weights are “smoothed” to remove the 

abrupt end-of-year changes from December to January. 

The weights are then applied to integrate the individual 

modal indexes into combined freight, passenger, and 

overall transportation indexes. Figure 11 provides a graph 

of the relative impacts, represented in billions of dollars for 

a single year, to illustrate the relative weightings. 

The Fischer Ideal methodology (see Lent, 2004) is used 

to combine the indexes. Chaining is also used to generate 

period-to-period changes that are independent of the base 

year, because period-to-period changes are the focus of 

the index. When the indexing, weighting, and chaining 

have been completed, the fi nal three indexes can be created: the total TSI, the passenger TSI, and the freight TSI. 

As can be seen in fi gure 1, the TSI has experienced 

upwards growth throughout most of the reference period. 

6

 The Federal Transit Administration began producing monthly data in January 2003 

after the TSI was launched.

7

 For a reference on X-12-ARIMA, see Ladiray and Quenneville (2001).

Figure 9: Rail Passenger-Miles (PMs)

 January 1979 to July 2005

0

100

200

300

400

500

600

700

197919811983

1985

19871989199119931995

1997

19992001

20032005

Million rail PMs

SOURCE: U.S. Department of Transportation, Federal Rail Administration (FRA), 

Offi ce of Safety Analysis, http://www.fra.dot.gov.

Figure 10: Transit Unlinked Trips 

 January 1979 to June 2005

0

200

400

600

800

1,000

1979198119831985198719891991

1993

1995

19971999

20012003

2005

Thousand trips

SOURCE: American Public Transportation Association (APTA), 

http://www.apta.com.
BTS Technical Report

6

Occasional dips and drops are obvious, and the impact of 

the terrorist attacks of September 11, 2001, is pronounced. 

Figure 12 shows the extended history of the TSI back to 

1979. Discussed next is whether the changes in direction of the TSI measures can be related to the changes in 

direction of the economy. 

BUSINESS CYCLES AND THE TSI

Transportation services involve the movement of people, 

goods, and services. All transportation freight services, 

and many transportation passenger services, are undertaken to support other economic activities. Freight services 

move the products produced by the mining, agricultural, 

and manufacturing sectors of the economy; connect 

manufacturers to their sources of raw materials, intermediate goods, and spare parts; and provide the goods sold by 

wholesalers and retailers. Many passenger transportation 

services are used by business travelers whose travel is 

directly connected to economic activity. 

Therefore, one would expect a measure of transportation 

services to have some relationship to other measures of 

economic activity, and perhaps track macroeconomic cycles. Indeed, GDP has been identifi ed in the transportation 

economics literature as one of the main drivers of demand 

for freight transportation services (Wilson, 1980).

A measure of the output of the transportation sector, such 

as freight, might be even more valuable if it leads the other 

economic measures as it could then be used in forecasting 

those measures as well as macroeconomic cycles. There 

are a priori reasons to expect transportation to be a precursor of economic activity. Freight transportation activity, 

in particular, is directly tied to the supply chain and to the 

build-up and maintenance of inventories, and so transportation of fi nished goods may anticipate growth in sales 

at the retail and wholesale levels. A signifi cant portion of 

freight volume consists of raw materials and other intermediate goods, which may be ordered in anticipation of 

growing activity in the manufacturing sector. Alternatively, 

a decline in freight shipments may result from anticipations 

of declines in economic activity in the downstream sectors. 

The build-up and decline of inventories probably explains 

why rail traffi c fi gures have historically been used as a 

general economic indicator (Page and Wirtz, 2003). 

Figure 12: Three TSI’s: Total, Freight, and Passenger, January 1979 to May 2006

30

50

70

90

110

130

Index: year 2000 = 100

TSI freight

TSI passenger

TSI total

197919821985

1988

19911994

1997

200020032006

SOURCE: U.S. Department of Transportation, Research and Innovative Technology Administration, Bureau of Transportation Statistics, http://

www.bts.gov.

Figure 11: Value-Added for TSI Components, 2002

Railroad transportation 

(freight)

Railroad transportation 

(passenger)

Local and interurban 

passenger transit

Trucking and

warehousing

Water transportation

Transportation by 

air (freight)

Transportation by 

air (passenger)

Pipelines, except 

natural gas

Pipeline transportation 

of natural gas

0

20

40

60

80

100

120 Billions $

SOURCE: U.S. Department of Transportation, Research and Innovative Technology 

Administration, Bureau of Transportation Statistics, http://www.bts.gov.
7

BTS Technical Report

These a priori reasons indicate that the transportation sector overall could be strongly related to the general economy. Individual transportation modes have been used in the 

past as indicators of the business cycle. However, there 

is reason to expect a multimodal measure of transportation to be superior to any single mode as an indicator of 

the overall economy, aside from the well-known statistical 

fact that indexes of several factors are nearly always more 

stable than single factors. A multimodal measure should 

be superior as an indicator because, by incorporating all 

modes, it “absorbs” the competition among the modes, and 

refl ects the overall economic change more accurately than 

a single measure. Railroad carloads, for instance, could 

decrease if there were a change in the economic situation 

facing railroad customers and their logistics patterns due to 

problems in the economy, or the carloads could decrease 

due to a shift in traffi c to waterborne transportation or to 

trucks. By contrast, an index that incorporates all modes is 

less subject to such vicissitudes in modal share. 

Hence, it is reasonable to expect that changes in a multimodal index are more likely to represent the infl uence of 

macroeconomic factors. The TSI freight index works especially well in this regard because “for-hire” freight makes 

up a large portion of all freight movement. By contrast, 

the “for-hire” passenger TSI only includes a small portion 

of passenger transportation because travel by the private 

automobile is excluded.

RECESSIONS AND GROWTH-CYCLES

The majority of cycle research in economics focuses on the 

business cycle, in which recessions and expansions are 

identifi ed. In recent years, the U.S. economy has experienced fairly long time periods between recessions. Macroeconomists have identifi ed growth cycles that occur within 

the larger business cycle. Growth cycles represent the 

cyclical changes in the economy once the long-term trend 

has been removed. Therefore, growth cycles highlight the 

accelerations and decelerations in the economy. 

If downturns in the TSI also signal downturns in the growth 

cycle, then looking only at the business cycle and ignoring the growth cycle would cause the TSI to appear to 

generate “false positives,” i.e., to indicate a change in the 

business cycle when no such change followed. This would 

make the TSI an imprecise indicator, even if all recessions 

were preceded by TSI downturns. By adding growth cycle 

slowdowns to the relatively few recessions, BTS can more 

completely test the relationship of the TSI to the economy. 

No particular reason exists to expect the TSI to have a different relationship to growth slowdowns, which likely impact 

inventory levels, ordering processes, and other transportation related supply chain factors, than to recessions.

IDENTIFICATION OF TURNING POINTS

In 1946 Arthur Burns and Wesley Mitchell wrote the fi rst 

major paper on business cycle turning points in the American economy. Turning points signal a shift from recession 

to expansion or expansion to recession, and are found at 

the trough or the peak of a business cycle. Using hundreds 

of historic data series, Burns and Mitchell identifi ed clusters 

of turning points in the overall business cycle. (Burns and 

Mitchell, 1946)

The fundamental components of the business cycle described by Burns and Mitchell are still used today. However, 

because it is often not clear which observation is the “true” 

low or high point of a cycle until much later, methodologies 

for recognizing turning points have been refi ned frequently 

during the past 60 years.

Recession Defi ned by NBER

The Business Cycle Dating Committee of the National Bureau of Economic Research (NBER) is regarded as the authority on identifying the turning points in business cycles. 

A recession is often considered a period of two consecutive quarters of decline in Gross Domestic Product. The 

Committee defi nes a recession as “a signifi cant decline 

in economic activity spread across the economy, lasting 

more than a few months, normally visible in real GDP, real 

income, employment, industrial production, and wholesaleretail sales,” and determines peaks and troughs based on 

multiple sources, but requires no set methodology. 

During the period from 1980 to the present, the Committee found four recessions. However, these shifts in the 

business cycle were not identifi ed by NBER in real time; 

each of these recessions was identifi ed several months, or 

years, after its conclusion. As a result of this time delay, as 

well as its lack of a formal methodology for duplication, the 

NBER process cannot be used to make real-time declarations about the economic conditions of the country. This 

delay in recognizing the cyclical turning points exists not 

only for the business cycle, but for the growth cycles as 

well, which are discussed next.

Growth-Cycles Determined

Economists have determined that the growth cycles within 

a business cycle also have turning points. Turning points 

may signal the end points of expansions and recessions, 

or they may signal the endpoints of growth cycles. A 

growth cycle is a general slowdown in growth around a 

trend that continues to grow. As noted by Zarnowitz and 

Ozyildirim (2001), “growth cycles are generally shorter, 

more frequent, and much more nearly symmetrical than 

business cycles.” Unlike business cycles, growth cycles 

are not declared by NBER. Various end points of growth 

cycles have been identifi ed and are available in academic 

literature. For this analysis, the TSI team used the growth 

cycles as identifi ed by Zarnowitz and Ozyildirim; their 

research utilized the composite index of coincident indicators (CCI), as defi ned and maintained by the NBER, to 

identify the economy’s growth cycles. See table 2 for dates 

of these cycles.
BTS Technical Report

8

Academics have developed procedures that formalize the 

identifi cation of turning points for business cycles. One 

technique used as a starting point for many methodologies 

is an algorithm developed by Bry and Boschan (B&B) in 

1971. Application of the B&B algorithm is also the fi rst step 

in many growth cycle analyses. Two of the most widely 

used and academically vetted methodologies, the PhaseAverage Trend and the Hodrick-Prescott fi lter, use the B&B 

technique to prepare the cycle for more in-depth analysis. 

The basic procedure for the B&B approach to identifying 

turning points, summarized in Appendix B8

, can be used to 

measure the turning points in other cycles, e.g., the TSI.

CALCULATIONS OF TSI TURNING POINTS 

TSI and recession cycles

Utilizing the B&B procedure, BTS fi rst took a 12-month 

moving average of the TSI data and then applied the 13-

point Spencer curve9 to all three series. The 12-month centered moving average allowed identifi cation of the general 

location of the turns, whereas the Spencer curve helped 

pinpoint the date. Then, by referring back to the original 

data, BTS selected the peaks and troughs indicated by the 

moving average and Spencer curve. To see the impact of 

the moving average, BTS illustrates the freight and passenger indexes against their 12-month moving averages in 

fi gures 13 and 14.

After identifying the general dates of the peaks and 

troughs, BTS eliminated inappropriate turns, as specifi ed 

in appendix B. The peaks and troughs in the two indexes 

were then compared to the turning points in the recessions, 

as identifi ed by the NBER. The TSI results are displayed 

in table 3, along with the dates of the recessions. In fi gure 15 the smoothed freight and passenger time lines are 

compared graphically to the turning points of the business 

cycles (the shaded areas within the graph represent the 

recessionary periods).

The freight index tends to signal well the NBER declared 

recessions, but the changes in direction between the 

recessions raise the possibility of the freight index being 

8

 Taken from Bry and Boschan (1971), table I, page 21.

9

 The Spencer curve is a smoothing formula that uses simple averages to 

approximate more complex quadratic equations. For further information, see Kendall 

and Ord (1990).

too sensitive a measure. The passenger index, in contrast, 

shows little consistency regarding the lead / lag relationship. Unlike the freight index, the passenger index does not 

appear to be sensitive enough to relate to turns in the economy. The question suggested by fi gure 15 is why the freight 

index over-signals recessions. Studying the growth cycles 

helps explain the relationship found between the freight TSI 

and recessions.

TSI and Growth Cycles

As noted in Zarnowitz and Ozyildirim (2001), recession 

turning points are not the only changes of interest in economic time series: the turning points affi liated with growth 

cycles also are of interest. This was fi rst suggested in the 

original TSOI research performed by Lahiri et al. (2003). 

In order to specify the growth curve turns, the data need 

to be detrended and, in its research, BTS chose to use the 

H-P, or Hodrick-Prescott, fi lter to remove the trend in the 

values in the time series.10 The smoothed and detrended 

data for the two series are provided in fi gure 16.

The resultant time series are specifi ed in fi gure 17, along 

with the turning points of the Composite Coincident Index, 

or CCI, which indicate turns in the growth cycle of the economy as calculated by Zarnowitz and Ozyildirim (2001).11

10 The HP fi lter used an alpha of 108,000 as suggested by Zarnowitz and Ozyildirim 

(2001) and by Lahiri et al. (2003).

11 The turning points for the growth curves as specifi ed by Zarnowitz and Ozyildirim 

(2001) only go up to June 2000. To estimate the trough of the fi nal cycle noted by 

Zarnowitz and Ozyildirim, BTS applied the B&B turning point procedure to the recent 

Composite Coincident Index data. We did not attempt to estimate additional growth 

cycles, which do appear on the graph to be “in process.”

Table 3: Dates of Turning Points of TSI Freight 

 and Passenger Against the Recessions

Turning points in the economy, TSI freight, and TSI passenger

Economy TSI freight TSI passenger

Peak Jan-80 NA NA

Trough Jul-80 Jul-80 Mar-81

Peak Jul-81 Feb-81 

Trough Nov-82 Nov-82

Peak Apr-84 

Trough Jul-85

Peak Dec-88 

Trough Jul-89

Peak Jul-90 Aug-90 Oct-90

Trough Mar-91 Mar-91 Mar-91

Peak Dec-94 

Trough Jan-96

Peak Mar-01 Dec-99 Sep-00

Trough Nov-01 Oct-01 Sep-01

SOURCE: U.S. Department of Transportation, Research and Innovative Technology Administration, Bureau of Transportation Statistics, http://www.bts.gov.

NOTE: This table shows the comparative patterns of peaks and troughs (i.e., 

turning points) in the economy and the two TSI indexes over time, and is meant 

to illustrate the comparative patterns among the series while providing information on the exact dates of the peaks and troughs. Not every peak or trough in 

any one series has a corresponding turning point in the other series.

Table 2: Dates of Business and Growth Cycles

Business cycles 

(peak-trough-peak)

Growth cycles 

(peak-trough-peak)

Jan-80 – Jul-80 – Jul-81

Jul-81 – Nov-82 – Jul-90

Jul-90 – Mar-91 – Mar-01

Mar-79 – Jul-80 – Jul-81

Jul-81 – Dec-82 – Sep-84

Sep-84 – Jan-87 – Jan-89

Jan-89 – Dec-91 – Jan-95

Jan-95 – Jan-96 – Jun-00

SOURCE: Zarnowitz and Ozyildirim (2001).
9

BTS Technical Report

Figure 13: Freight TSI and 12-Month Moving 

 Average, January 1979 to May 2006

197919821985

19881991

1994

1997

200020032006

40

50

60

70

80

90

100

110

120 Index

TSI freight

Moving average

SOURCE: U.S. Department of Transportation, Research and Innovative Technology Administration, Bureau of Transportation Statistics, http://www.bts.gov.

Figure 15: TSI Matched Against the Recessions,

 January 1979 to August 2005

1979

1981

1983

1985

1987

1989

199119931995

19971999

2001

2003

2005

35

45

55

65

75

85

95

105

115

TSI passenger

TSI freight

Index

 indicates recession

SOURCE: U.S. Department of Transportation, Research and Innovative Technology Administration, Bureau of Transportation Statistics, http://www.bts.gov.

Figure 16: H-P fi ltered TSI, 

 January 1979 to July 2005

197919821985

1988

1991

19941997200020032006

-15

-10

-5

0

5

10

15

Index

TSI freight - H-P

TSI passenger - HP

SOURCE: U.S. Department of Transportation, Research and Innovative Technology Administration, Bureau of Transportation Statistics, http://www.bts.gov.

Figure 14: Passenger TSI and 12-Month Moving 

 Average, January 1979 to May 2006

197919821985

198819911994

1997

200020032006

35

45

55

65

75

85

95

105

115 Index

TSI passenger

Moving average

SOURCE: U.S. Department of Transportation, Research and Innovative Technology Administration, Bureau of Transportation Statistics, http://www.bts.gov.

Figure 17: Smoothed TSI Freight and Passenger Against the Growth Cycles, 

 January 1979 to August 2005

1979

1981

1983

19851987

19891991

1993

1995

19971999

2001

20032005

-9

-6

-3

0

3

6

9

Index

TSI freight - HP

TSI passenger - HP

 indicates downturn in growth cycle

SOURCE: U.S. Department of Transportation, Research and Innovative Technology Administration, Bureau of Transportation Statistics, http://www.bts.gov.
BTS Technical Report

10

As indicated in the fi gure, the turns in the freight component track more closely with the turns in the growth cycle. 

The passenger cycles are still not clear; this result might 

be attributable to the inclusion of only “for-hire” modes in 

the index, which thus lacks a very large component – automotive vehicle miles traveled (VMT). Consequently, BTS 

chose to examine further only the relationship of the freight 

index to the turns in the growth cycle.

Employing the same rules to eliminate spurious turns and 

then referring back to the original to pinpoint actual months 

in which the turns occurred, BTS compared the dates of 

the peaks and troughs against the turns in the growth 

cycle in the table 4. (Note that, although a downturn in the 

growth cycle may be occurring, as well as in the freight TSI 

in 2004 or 2005, BTS chose not to portray that potential 

turn so close to the endpoint of a time series.)

The TSI freight tends to lead the identifi ed growth cycles at 

the peaks as well as at the troughs. To quantify the degree 

of lead, the fi nal column in the table provides the number 

of months of lead or lag. On average, the TSI freight leads 

by 4 to 5 months for the troughs and 4 to 5 months for the 

peaks. The range of the degree of lead for the troughs is 

wider than the lead for the peaks, possibly indicating a 

more consistent relationship between the freight TSI and 

the peaks, or downturns, of the growth cycle. Only two 

false cycles occurred in the TSI freight – the fi rst with a 

peak at July 1989 and a trough at March 1990, and the 

second with a peak at July 1992 and a trough at July 1993. 

CONCLUSIONS AND FUTURE RESEARCH

The historical freight index anticipated the four NBER declared recessions in the 1979 – 2006 time period, but other 

turns in the index did not precede full-blown recessions 

or expansions. The passenger index showed little consistency regarding the lead / lag relationship with recessions. 

The fi nal comparison of the turning points in the freight TSI 

against the turning points in the growth cycles, however, 

proved to be a strong relationship: the freight TSI tends to 

lead the growth cycle, both at the peaks as well as at the 

troughs, at least for the time periods from 1979 to the present. Economic theory provides justifi cation of this leading 

characteristic. 

While the above conclusion regarding the history of the 

TSI can be ascertained, it should be noted that it may be 

diffi cult to use this information in real-time to predict changes in the economy through turns in the TSI. Because the 

employed procedures utilize moving averages, 6 months 

of the most recent data are lost in the analysis. By our calculations, the freight TSI leads by less than that amount, 

thereby making it diffi cult to use the index as a predictor in 

real-time. In addition, several months of data after the turning point are needed to ascertain if the change in direction 

is more than just local variation; the usual rule-of-thumb 

is a change of direction that is maintained for at least 3 

months. This additional requirement for monthly data further limits the ability to use the TSI as a real-time predictor 

of turning points in the economy, but it does not weaken 

the fi ndings in the historical data. Transportation services, 

freight in particular, appear to lead the economy. The forhire passenger TSI did not prove to be as predictive. But, 

again, this may be due to the fact that personal automotive VMT was not included in this index. By expanding the 

passenger TSI to include automotive VMT in the future, a 

more complete passenger travel index would be available 

for evaluation. 

References

Burns A. and W. Mitchell. 1946. Measuring Business Cycles. New 

York, NY: National Bureau of Economic Research.

Bry, G. and C. Boshan. 1971. Cyclical Analysis of Time Series: Selected Procedures and Computer Programs, NBER Technical Paper 20. Cambridge, MA: National Bureau of Economic Research.

Kendall, M. and K. Ord. 1990. Time Series, 3rd ed. London, UK: 

Edward Arnold.

Lahiri, K and H. Stekler. 2002. The Theoretical Development, 

Selection, and Testing of Economic Indicators for the Transportation Industry, BTS Research Grant fi nal report. Washington, DC: 

Bureau of Transportation Statistics.

Lahiri, K., H. Stekler, W. Yao and P. Young. 2003. Monthly Output 

for the U.S. Transportation Sector. Journal of Transportation and 

Statistics 6(2/3), 1-28.

Lahiri, K., W. Yao and P. Young. 2004. Transportation and the 

Economy: Linkages at Business-Cycle Frequencies. TransportaTable 4: HP-fi ltered TSI Turning Points Against 

 the CCI Growth Cycles 

Growth Cycle Turning Points in the Coincident Index and TSI freight

Economy

TSI freight - HP 

fi ltered

Lead / Lag of 

TSI in months

Peak Mar-79

Trough Jul-80 Jul-80 0

Peak Jul-81 Jan-81 +6

Trough Dec-82 Nov-82 +1

Peak Sep-84 Apr-84 +6

Trough Jan-87 Oct-85 +13

Peak Jan-89 Jun-88 +7

Trough Jul-89 --

Peak Mar-90 --

Trough Dec-91 Mar-91 +9

Peak Jul-92 --

Trough Jul-93 --

Peak Jan-95 Dec-94 +1

Trough Jan-96 Jan-96 0

Peak Jun-00 Nov-99 +2

Trough Feb-02 Sep-01 +5

Peak Trough

Average lead 

in months +4.4 +4.7

Range in 

months 1 to 7 0 to 13

SOURCE: U.S. Department of Transportation, Research and Innovative Technology Administration, Bureau of Transportation Statistics, http://www.bts.gov.
11

BTS Technical Report

Table A-1: Time Series Characteristics of TSI Data Components

Mode ARIMA model Moving seasonality? MCD1

Model2: additive 

or multiplicative? Trading days (TD) & Holidays (H)3 

Rail passenger (011) (011) No 5 M No TD; all H

Rail freight

 Carloads No valid model yet No 5 A TD, No H

 Intermodals (011) (011) No 3 A No TD; Easter & Thanksgiving

Trucking (011) (011) No 3 A TD; Easter 

Waterborne (011) (011) No 12 A TD; No H

Transit (011) (011) No 4 A TD; No H

Aviation

 Freight (011) (011) No 3 M TD and Easter & Thanksgiving

 Passenger (011) (011) Yes, at 1% level 4 M No TD, All 3 H

Pipeline

 Natural gas (012) (011) No 7 M TD; No H

 Petroleum (011) (011) No 5 M TD, No H

SOURCE: U.S. Department of Transportation, Research and Innovative Technology Administration, Bureau of Transportation Statistics, http://www.bts.gov.

1

 

1

 MCD=Months to cyclical dominance. 3 months is normal for the trend to equal and surpass the irregularity; higher than 3 shows irregularity too high 2

 M=Multiplicative Model A=Additive Model

3

 TD=Trading Days. H=(Moving) Holidays: Easter, Labor Day, and Thanksgiving. Beginning January 27, 2005, Thanksgiving uses -3 for value, Easter is set at 2 for 

Trucking; otherwise, equals 7; Labor Day is always set at 4.

tion Research Record: Journal of the Transportation Research 

Board, No. 1864, 103-111.

Ladiray, D. and B. Quenneville. 2001. Seasonal Adjustment with 

X-11 Method. New York, NY: Springer.

Lent, J. 2004. Effects of Extreme Values in Price Indexes: The 

Case of the Air Travel Price Index. Journal of Transportation and 

Statistics 7(2/3), 41-52.

Page, D. and R. Wirtz. 2003. Wrong Side of the Tracks. Fedgazette, Federal Reserve Bank of Minneapolis, November 2003.

Shiskin, J., A. Young and J. Musgrave. 1967. The X-11 Variant 

of the Census Method II Seasonal Adjustment Program, Bureau 

of the Census Technical Paper No. 15. Washington, DC, U.S. 

Department of Commerce, February 1967.

Wilson, G. 1980. Economic Analysis of Intercity Freight Transportation. Bloomington, Indiana: Indiana University Press.

Vandaele, W. 1983. Applied Time Series and Box-Jenkins Models. San Diego, CA: Academic Press, Inc.

Zarnowitz, V. and A. Ozyildirim. 2001. Time Series Decomposition and Measurement of Business Cycles, Trends and Growth 

Cycles, Economics Program Working Paper #01-04. New York, 

NY: The Conference Board.

APPENDIX A: DETAILS ON SEASONAL 

ADJUSTMENT

The data used for the Transportation Services Index are 

seasonally adjusted by a method that evolved over many 

decades starting in the 1950s at the U.S. Bureau of Census. 

Called X-12-ARIMA, Release 0.2, this procedure recently 

evolved out of the “X-11 Variant of the Census Method II 

Seasonal Adjustment Program.” (Shishkin et al., 1967) The 

name, X-11, means 11 variations precede it. 

Fundamentally, X-12 (without ARIMA) is a robust nonparametric method, which achieves its estimates through a 

series of iterative steps. As such, it is an “empirical” approach as distinguished from a “model-based” approach to 

seasonal adjustment. Although seasonal adjustments of the 

transportation series used in the TSI have been relatively 

small, statistical properties of the estimators, such as confi -

dence intervals, are lacking.

ARIMA modeling was added to X-11 methods in 1975, 

thereby providing a popular statistical component to an 

iterative approach of successive smoothings. The ARIMA 

was introduced to model the data to produce forecasts that 

are used to extend the data series before undergoing the 

adjustments and smoothings. The seasonal adjustments 

were then found to be more reliable as measured by the reductions in revisions of estimates near the end of the series. 

With the exception of transit, all time series used in the 

published TSI begin at January 1990. Table A-1 summarizes 

the characteristics of each of the 10 transportation time 

series employed in constituting the TSI. Note that with the 

exception of natural gas, the Auto-Regressive Integrated 

Moving Average (ARIMA) model that best suits the data can 

be specifi ed as the Box-Jenkins “airline model,” otherwise 

known as an ARIMA(011) (011)12 . Note, too, that no suitable ARIMA model has been found for the carloads component of rail freight. 

The longer historical time series data had the same distribution characteristics as the current data with one exception 

(trucking). For this reason, the decision was made to incorporate the same holidays in the historical time series models and to use the same parameter values for each holiday 

used in the current data. The pattern for historical data for 

trucking differed slightly with that in the published TSI; the 

historical data had to be modeled with a log transformation.
BTS Technical Report

12

The Bureau of Transportation Statistics is a component of DOT’s 

Research and Innovative 

Technology Administration.

This BTS Special Report presents 

research from the TSI research 

team: Peg Young, Ken Notis, Gary 

Feuerberg, and Long Nguyen.

About this Report For related BTS data and publications

For copies of the BTS Special Report or 

questions about this or other BTS reports, 

call 1-800-853-1351, email answers@bts.

gov, or visit www.bts.gov.

Data — 

• http://www.bts.gov/xml/tsi/src/index.

xml.

Publications — 

• K. Lahiri, H. Stekler, W. Yao, and P. 

Young. “Monthly Output Index for the 

U.S. Transportation Sector,” Journal 

of Transportation and Statistics, vol. 

6, no. 2/3, 2003.

APPENDIX B: BRY AND BOSCHAN 

PROCEDURE 

I. Determination of extremes and substitution of 

values.

II. Determination of cycles in 12-month moving 

average (extremes replaced).

a. Identifi cation of points higher (or lower) 

than 5 months on either side.

b. Enforcement of alternation of turns by 

selecting highest of multiple peaks (or 

lowest of multiple troughs).

III. Determination of corresponding turns in Spencer 

 Curve (extremes replaced).

a. Identifi cation of highest (or lowest) value 

within ± 5 months of selected turn in 12-

month moving average.

b. Enforcement of minimum cycle duration of 

15 months by eliminating lower peaks and 

higher troughs of shorter cycles.

IV. Determination of corresponding turns in short-term 

 moving average of 3 to 6 months, depending on 

 MCD (months of cyclical dominance).

a. Identifi cation of highest (or lowest) value 

within ± 5 months of selected turn in 

Spencer curve.

V. Determination of turning points in unsmoothed 

 series.

a. Identifi cation of highest (or lowest) value 

within ± 4 months of selected turn in shortterm moving average.

b. Elimination of turns within 6 months of 

beginning and end of series.

c. Elimination of peaks (or troughs) at both 

ends of series which are lower (or higher) 

than values closer to end.

d. Elimination of cycles whose duration is 

less than 15 months.

e. Elimination of phases whose duration is 

less than 5 months.

VI. Statement of fi nal turning points.