Bureau of Transportation Statistics

Technical Report

U.S. Department of Transportation

Research and Innovative Technology Administration TR-003

May 2008

Uncovering Trends in Seasonal Transportation Data

New tool analyzes airline revenue passenger-mile trend data

by Gary Feuerberg, Ph.D.

Transportation activity often varies appreciably from 

month to month and season to season, making it diffi cult 

to discern from the data whether the overall trend for the 

activity is increasing, unchanging, or decreasing. Traditionally, analysts adjust data to compensate for these fl uctuations; however, conventional methods of “controlling” 

seasonal factors can be limiting—particularly when viewing trends over many years or months. But by eliminating

the seasonal infl uence, rather than simply controlling for 

it, decades of data can be grasped at a glance. In October 2004, the Bureau of Transportation Statistics (BTS) 

began to remove the seasonal fl uctuation in the data used 

in its monthly Transportation Services Index (TSI)1

. And, 

although the approach for removing seasonal factors from 

airline revenue passenger-miles (RPMs) is examined here, 

this same approach can be used for most data series that 

show strong seasonal variation. 

Two recent events caused signifi cant declines in airline 

RPMs—the terrorist attacks of September 11th, 2001, and 

the SARS (Severe Acute Respiratory Syndrome) outbreak 

in Asia that occurred in late 2002 and early 2003. The effects of 9/11 are readily apparent to the casual observer 

even in the raw data, but the impact of the SARS scare 

on the data is masked by seasonal fl uctuations. Although 

obvious at the time to the airlines that lost revenue and to 

the passengers who cancelled fl ights, the impact of the 

SARS epidemic on RPMs only becomes clear in the data 

once the seasonal infl uence is removed. 

Typically, holiday and winter recreational travel steadily 

declines after the fi rst of the year. So, the decline in traffi c 

that occurred from January though April 2003 was not 

unexpected. But when the seasonal effects are removed 

from the data, the underlying decline, coincident with the 

SARS epidemic, is revealed—the number of RPMs was 

lower than expected. 

1

 The Transportation Services Index (TSI) combines available data on freight traffi c 

and passenger travel, drawing on the various modes: air, trucking, rail, waterborne, 

transit, and pipeline. The data from 10 transportation services are each seasonally 

adjusted and combined to yield a monthly measure of transportation services 

output. See www.bts.gov for a full explanation.

The method usually employed to investigate airline data 

trends is to compare data for a particular month from 

one year to the next. For example, the March 2007 RPM 

value can be compared with the March 2006 value, or 

with that same month going back any number of years for 

which data are available. In this way the seasonal factor 

is “controlled” and comparisons can be made year by year 

by matching up the same months. Using this traditional 

method, one must summarize the changes for each of 

the 12 months of the calendar and then synthesize the 

monthly results in order to generalize to the year. However, 

this method is clumsy when viewing trends occurring over 

many months or years over the period examined.

The technique BTS adopted to remove distracting seasonal factors in the airline data can be applied to other transportation modes. This report describes BTS’ fi rst use of the 

tool and its potential for supporting analysis. 

Adjusting RPM Data To Remove Seasonality

RPMs are one indicator of how the airline industry is 

performing. Like many transportation variables, RPMs are 

subject to sizeable fl uctuations. No doubt the seasons and 

holidays have a strong effect on RPMs and can explain 

most of the variance. But unless measures are undertaken 

to either control or eliminate the seasonal factors, any 

underlying trends in the airline data won’t become apparent. To clearly see the trends in RPMs, the data must 

be adjusted to remove seasonal effects. This is called 

deseasonalizing the data. 

The method that BTS employs to adjust the time series 

data components of the TSI is called X-12 ARIMA, Release 0.2, and is discussed in box A.

Figure 1 displays the raw aviation passenger data that 

have not been adjusted. The consistent fl uctuations that 

repeat each year in the unadjusted line of raw data are a 

strong indication that the data are highly seasonal. 
BTS Technical Report

2

Box A: Seasonal Adjustment Methodology

The method discussed in this report to deseasonalize and subsequently smooth time series data has 

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.” The name, X-12, means there were 11 variations preceding it. The program was automated by 1965 and is used around the world along with several other 

procedures. As the most widely used method in seasonal adjustment, BTS adopted it for the TSI 

based on its acceptance by time series analysts and forecasters. 

Fundamentally, X-12 (without ARIMA) is a robust nonparametric1

 method that 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. Statistical properties of the estimators, 

such as confi dence intervals, are lacking. 

ARIMA modeling was added in 1975. ARIMA, which stands for Auto-Regressive Integrated Moving Average, was introduced to model the time series data in order to produce forecasts. These 

forecasts are then used to extend the data series before it undergoes adjustments and smoothings. 

The subsequent seasonal adjustments are found to be more reliable.2

1

 Nonparametric techniques refer to a branch of applied statistics in which no assumptions are made regarding the underlying form of the 

data, i.e., “distribution free.”

2

 Dominique Ladiray and Benoit Quenneville (2001), Seasonal Adjustment with the X-11 Method, Springer-Verlag, New York, p. 9.

Decline of RPMs During the 2nd Quarter 2003

After the aviation RPM data are adjusted to take out the 

seasonal fl uctuation, possible trends are easier to fi nd. 

Figure 2 shows that the aviation RPM value is generally 

increasing, suggesting that people are traveling more or 

further. But a closer look reveals that at least two extended 

periods of decline occurred within the general tendency of 

increasing RPMs. 

In order to take out all—or nearly all—of the RPM fl uctuation, one can use X-12 ARIMA to smooth the deseasonalized data, using the moving average2

 of contiguous data 

points. The default in X-12 ARIMA for the moving average 

is 13 months, but it can be set to a different number of 

months where appropriate. 

Note that the smoothed line cannot be precisely defi ned 

and graphed. There is no correct “solution” or defi nitive 

formula for smoothing data. With more data points, the 

smoothing will usually “hide” more fl uctuation in the data 

and smooth it out more. On the other hand, with a shorter 

moving average, the smoothed line will appear jagged and 

display the smaller changes in the data.

Figure 3 shows the deseasonalized data after it has been 

smoothed and linked by a line that makes it easier to see 

trends in the data. Instead of using the default of a mov2

 Henderson moving averages are used in X-12 to extract the trend. See Dominique 

Ladiray and Benoit Quenneville (2001), Seasonal Adjustment with the X-11 Method, 

Springer-Verlag, New York, pp. 36–37.

ing average of 13 data points, this line uses 5 data points 

to better pinpoint where the changes lie. Declining periods emerge around the time of the attack of 9/11 in the 

year 2001 and around the second quarter of 2003, from 

December 2002 to April 2003. During these four months, 

there is a continuous drop in the deseasonalized RPM 

data. Recovery begins in May 2003. Other abrupt changes 

in the deseasonalized data are shorter in length and can 

be attributed to the “irregular” component of the model.

The fi rst decline, which is the more dramatic, was apparent 

even in the raw data (see fi gure 1) and was expected as a 

result of the widespread public fear of fl ying after the 9/11 

attacks. But the second decline, the SARS decline, was 

masked when viewing the raw data because of the seasonal fl uctuations discussed below.

Analysis of Regional Routes

The BTS database containing aviation data, TranStats,3

provides six distinct codes under “region”: Atlantic, Domestic, International, Latin America, Pacifi c, and System. 

Airlines generally fl y in one or two of these regions. This 

analysis will focus on Pacifi c region traffi c and compare 

it with traffi c in the other regions. But “region” is a term 

developed by the commercial airlines and lacks scientifi c 

precision. The region names are not mutually exclusive and 

some traffi c can logically fall into more than one category. 

This problem is particularly evident in the minor category 

3

 TranStats is a BTS database found at: http://www.transtats.bts.gov.
3

BTS Technical Report

Figure 1: Aviation Revenue Passenger-Miles, Raw Data, 1994–2006

1994

1995

1996

19971998

19992000200120022003

2004

2005

2006

0

10

20

30

40

50

60

70

Revenue passenger-miles (millions)

NOTE: RPM = Revenue Passenger-Miles

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

Bureau of Transportation Statistics, available at http://www.transtats.bts.gov/

Figure 2: Aviation Revenue Passenger-Miles, Seasonal Infl uences 

 Removed, 1994–2006

0

10

20

30

40

50

60

1994

1995

1996

19971998

19992000200120022003

2004

2005

2006

Revenue passenger-miles (millions)

Periods of decline

NOTE: RPM = Revenue Passenger-Miles

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

Bureau of Transportation Statistics, available at http://www.transtats.bts.gov/

Figure 3: “Smoothed” Airline RPM Data Showing Two Distinct Declines:

 September to November 2001 and December 2002 to April 2003

0

10

20

30

40

50

60

19941995199619971998

1999

2000

2001

2002

2003

2004

2005

2006

Revenue passenger-miles (millions)

NOTE: RPM = Revenue Passenger-Miles

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

of Transportation Statistics, available at http://www.transtats.bts.gov/
BTS Technical Report

4

Table 1: RPMs by Carrier Region, December 2002 to April 2003

 (in millions)

Region

December

2002/2003

January

2002/2003

February

2002/2003

March

2002/2003

April

2002/2003

Percent change 

12/2002 to 04/2003

Atlantic 6,007 5,481 4,717 5,784 5,465 -9.0

Domestic 42,410 37,206 35,101 42,911 40,371 -4.8

International 513 673 694 834 580 13.1

Latin America 3,355 3,365 2,885 3,348 2,935 -12.5

Pacifi c 4,372 4,472 3,647 3,898 2,513 -42.5

 Total 56,658 51,196 47,044 56,776 51,865 -8.4

NOTES: Totals do not add due to rounding. RPMs = Revenue Passenger-Miles.

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

Bureau of Transportation Statistics, based on data available at http://www.transtats.bts.gov/

of region, International.4 However, for the most part, the 

region categories are accurately descriptive. Note that the 

sixth code, “system,” is used very infrequently and is not 

applicable to this analysis. 

From December 2002 to April 2003, the 42.5 percent 

decline in the Pacifi c region (see table 1, right column) 

was quite dramatic compared to declines in the Atlantic, 

Domestic, and Latin America regions. The overall decline 

of all regions during this period was 8.4 percent, which 

becomes the basis to compare traffi c changes for each 

region. With the exception of the residual category of 

“international,” the other regional declines were within 

about 4 percent of the overall decline, and thus much 

smaller than Pacifi c’s 42.4 percent decline.

Individual Airlines Analyzed

The BTS database on individual airlines was analyzed 

in two ways. One method examined the trend of all the 

airlines, de-seasonalized, while the other method focused 

only on airlines that declined and determined whether this 

pattern manifested for travel in the Pacifi c region. 

1. Time series analysis of the RPM trend of the individual airline.

Of the approximately 120 airlines reporting data in the 

United States in 2003, the top 18 airlines generated threefourths of total RPMs5

. These airlines’ monthly RPM data 

were deseasonalized, except for Comair, which was missing too much data. The aim was to see whether a decline 

in the period December 2002 to April 2003 occurs after the 

seasonality is removed. Table 2 shows the results.

A trend line of seasonally adjusted data for each airline 

found that eight of the top airlines showed an unmistak4

 International refers to a residual region category for traffi c to destinations outside 

the United States reported by carriers that are not required to designate Atlantic, 

Pacifi c, or Latin America entities. Not all carriers are assigned Atlantic, Pacifi c, or 

Latin America entities, especially when they do not have scheduled fl ights in those 

regions.

5

 The number one airline for RPMs in 2002 was American Airlines at 121 billion 

revenue passenger-miles. The 18th carrier was Frontier with 3.4 billion revenue 

passenger-miles.

able decline in the December 2002 to April 2003 period. 

Another eight showed no decline. The trend for American 

Eagle Airlines was unclear, and Comair reported incomplete data6

. 

Of the eight major airlines that exhibited the pattern of 

decline in the 2nd quarter of 2003 (table 2, column 1), only 

America West Airlines and US Airways did not fl y in the 

Pacifi c region. Moreover, of the airlines that showed no 

decline, none fl ew in the Pacifi c region (table 2, column 

2). Hence, whether an airline fl ew in the Pacifi c region is 

a good predictor in the deseasonalized data of when the 

airline RPMs declined during the second quarter 2003.

2. Comparison of RPM totals the year before and the 

year after the “decline” period. 

Carefully examining the raw data also supports the trends 

found in the deseasonalized data, which are easier to 

detect after the data undergoes deseasonalization. The 

“Pacifi c” group of six airlines discussed above exhibited a 

pattern of decline when comparing the same period one 

year before (December 2001 to April 2002), and then a 

recovery one year after the period (December 2003 to 

April 2004). See table 3. Continental Micronesia Airlines, a 

smaller airline not in the top 18 but affi liated with Continental, fl ies frequently in the Pacifi c region—more than Delta 

or Hawaiian. It showed the same pattern of decline and 

recovery during this period.

Continental, Delta Airlines, United Airlines, and Continental 

Micronesia fi t this pattern of decline and recovery. Hawaiian plummeted from 61 million RPMs during the period 

one year before to 22 million RPMs. It failed to recover by 

the following year, however. There was very little change 

in RPMs for Northwest Airlines. Only American Airlines 

contradicted the pattern.

This pattern of decline and recovery only fi t the Pacifi c region for these particular airlines and not any other region. 

6

 These airline submissions have occasional missing data. In the case of Comair, 

the amount of missing data precluded further analysis. Three airlines (Frontier 

Airlines, American Eagle, and Hawaiian) were missing one data point and estimates 

had to be interpolated.
5

BTS Technical Report

SARS Scares Travelers Away

The few airlines that regularly fl ew to the Pacifi c were also 

the airlines with RPM declines during the 2nd quarter of 

2003. The RPM decline suffered by the few airlines serving the Pacifi c region coincided with news of the SARS 

outbreak in China, establishing a likely causal connection. 

The connection with SARS was supported by the lack of 

a drop in other regions, except for a smaller decline in the 

Atlantic region. 

Travelers to Asia were apparently scared away by the 

outbreak. The World Health Organization (WHO)7 reported 

in October 2004:

“The fi rst known cases of SARS occurred in Guangdong 

province, China, in November 2002 and WHO reported 

that the last human chain of transmission of SARS in that 

epidemic had been broken on 5 July 2003.” 

 and

“Severe Acute Respiratory Syndrome (SARS) was fi rst 

recognized as a global threat in mid-March 2003....

By July 2003, the international spread of [SARS] resulted 

in 8,098 SARS cases in 26 countries, with 774 deaths.”

7

 Guidelines for a Surveillance of Severe Acute Respiratory Syndrome (SARS), 

October 2004.

According to the WHO report, the SARS news discouraged 

some travelers from fl ying to Asia. The report included the 

following statement about the effect that the SARS scare 

had on travel:

“The epidemic caused signifi cant social and economic disruption in areas with sustained local transmission of SARS 

and on the travel industry internationally in addition to the 

impact on health services directly.”

It was only by applying deseasonalization to the airline 

data that the SARS impact became clear. The trend patterns in the data came into full view when the fl uctuating 

seasonal factors were removed, showing the RPM decline 

during the second quarter of 2003.

Potential for Further Application

Data deseasonalization has great potential for improving 

analysis of transportation time series data. The approaches outlined in this paper for seasonal adjustment, the application of X-12 ARIMA to airline data, can be used for other 

transportation data as well. BTS is trying the technique 

with transportation data pertaining to pipelines, transit, 

passenger trains, waterborne freight, and air freight.

Table 2: Airlines With and Without Decline in RPMs, 

 December 2002 to April 2003 

Declined No decline Indefi nite results/missing data

American Air Tran American Eagle

America West Alaska Comair

Continental ATA

Delta Express Jet

Hawaiian Frontier

Northwest Jet Blue

United Southwest

US Airway Spirit Air

NOTE: RPM = Revenue Passenger-Miles

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

Administration, Bureau of Transportation Statistics, available at http://www.transtats.bts.gov/

Table 3: Comparison of Pacifi c Region RPM Totals (in millions)

Delta Northwest United American Continental Hawaiian

Continental 

Micronesia

Before (Dec. 2001 to Apr. 2002) 424 7,581 8,830 1,102 1,011 61 1,014

Study period 

(Dec. 2002 to Apr. 2003) 360 7,700 7,837 1,208 914 22 831

After (Dec. 2003 to Apr. 2004) 453 7,593 9,218 1,552 1,253 19 1,055

NOTE: RPM = Revenue Passenger-Miles

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

available at http://www.transtats.bts.gov/
This report was prepared by 

Gary Feuerberg, Mathematical 

Statistician, of the Bureau of 

Transportation Statistics (BTS). 

BTS is a component of DOT’s 

Research and Innovative 

Technology Administration.

About this Report For related BTS data and publications

For questions about this or other BTS 

reports, call 1-800-853-1351, email 

answers@bts.gov, or visit www.bts.gov

Data — 

• U.S. Department of Transportation, 

Bureau of Transportation Statistics, 

online: “TranStats” (http://www.transtats.bts.gov/).

• U.S. Department of Transportation, 

Bureau of Transportation Statistics, 

Offi ce of Airline Information, Air Carrier Traffi c Statistics (Green Book) 6, 

no. 2/3, 2003.