A Time Series Analysis of Domestic Air Seat and Passenger Miles

A Time Series Analysis of Domestic Air Seat and Passenger Miles

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Air passenger mobility can be studied by analyzing seat and passenger miles. Available seat-miles for an individual flight are the number of seats multiplied by the distance traveled; this measure can represent overall capacity. Revenue passenger-miles are a measure of the volume of air passenger transportation; a revenue passenger-mile is equal to one paying passenger carried one mile. Unused seat-miles are the difference between available seat-miles and revenue passenger miles; the unused seat-miles are used as a measure of airline capacity utilization. Figure 1 displays the monthly time series of these three measures from January 1992 through April 2002.

Figure 1 - Domestic Air Seat and Passenger Miles

Analyses follow on the available seat miles, revenue passenger miles and unused seat miles. The trends, once separated from the seasonality, will be extracted and compared.

Available Seat-Miles
Available seat-miles is used as a measure of airline capacity. As seen in detail in Figure 2, this measure has experienced strong growth, until September 2001. Strong seasonality is also apparent in the repetitive peaks and troughs from year to year.

Figure 2 - Domestic Air Available Seat Miles

To review the underlying trend and seasonality, we separate these components. Figure 3 provides a graphical summary of the impact of seasonality.

Figure 3 - Seasonal Factors for Available Seat Miles

As expected, the summer months of June, July and August experience the higher values of available seat-miles. January hold the lowest seasonality, followed by November.

Figure 4 now shows the underlying trend of available seat-miles. As expected, the growth upward is strong, until September 2001. A strong drop in that month is followed by a level shift downward as well as a slow exponential return towards that new level of growth. This new underlying level has produced a 7.6 billion drop in the trend. And, at present, there is no indication as to if and when that level will return to pre-September 2001 strength.

Figure 4 - Available Seat Miles With Underlying Trend

Also shown with the underlying trend are three outliers that proved to be significant: September 1998, December 2000 and January 2001. The September 1998 and the December 2000 were unexpectedly low; the January 2001 was unexpectedly high. The dip in 1998 may be due to the strike at Northwest Airlines from August to September 1998, and the fact that Christmas 2000 and New Year's Day 2001 both fell on Mondays may have resulted in more vacation days being taken in January and less in December.

Revenue Passenger Miles
Figure 5 shows that revenue passenger miles experience even stronger seasonality over the available seat-miles, but the underlying trend seems to be similar. When we separate the components, we note that seasonality is stronger, as shown in Figure 6.

Figure 5 - Domestic Air Revenue Passenger Miles

Figure 6 - Seasonal Factors for Revenue Passenger Miles

The pattern is comparable to that in Figure 3, but note that the scale is wider. If we show both sets of seasonality on the same graph, we see the variability between the two. The peaks and troughs for the revenue passenger miles range between 4.5 billion miles; the available seat miles swing between 2 billion miles.

Figure 7 - Comparison of Seasonality

Now that seasonality has been separated, we can view the underlying trend; see Figure 8. This series experiences the same drop in September 2001, with a similar level drop and underlying exponential return to that new level. In this case, the new underlying level represents a drop of approximately 4.8 billion revenue passenger miles. There is no strong evidence, as of the April 2002 data, if and when the trend will return to its previous level of growth. Also shown in Figure 8 are two significant interventions: a step increase / decrease from June 1992 through October 1992, and a temporary one-month drop in November 1996. This drop in November 1996 may be due to Thanksgiving being so late in the month in 1996; Thanksgiving fell on November 28 with the following Sunday on December 1.

Unused Seat-Miles
Figure 9 shows the time series pattern of the unused seat-miles, which is the difference between available and revenue miles. Since available and revenue miles have similar slopes, the unused data appear to not exhibit any long term slope.

Figure 8 - Revenue Passenger Miles With Underlying Trend

Rather it represents a relatively constant level of capacity utilization.

Figure 9 - Domestic Air Unused Seat Miles

Since unused seat miles are the difference between available and revenue miles, the trend of unused miles is represented in following graph by the difference of trends (Figure 10).

Figure 10 - Unused Seat Miles With Underlying Trend

The level prior to September 2001 was approximately 18 billion miles; after October 2001 the level dropped to approximately 16 billion miles.

Final Trends
The three resultant trends are provided in Figure 11. Since the short term rise and fall in 1992 for the revenue passenger miles was not apparently exhibited in the available seat miles, the differencing of the two trends results in a fall and rise in unused seat miles in 1992. Both available and revenue miles exhibit comparable slopes, with the expected declines after September 2001.

Figure 11 shows the trends without the actual data; Figure 12 portrays the actual and the trend data together.

Figure 11 - Trends of Domestic Air Seat and Passenger Miles

Figure 12 - Domestic Air Seat and Passenger Miles With Underlying Trends