## A TIME SERIES ANALYSIS OF AIRLINE DELAY

## A TIME SERIES ANALYSIS OF AIRLINE DELAY

The issue of airline delays, as measured by the number of late arrivals as a percent of total operations, has been of increasing importance in recent years as more of the U.S. population chooses air travel as a preferred mode of transportation. The actions on September 11, 2001 may have temporarily lessened the desire to travel by air, so this analysis takes a look at airline delay as it is impacted by September 11, 2001.

Figure 1, which shows a time plot of the number of late arrivals over the past 13 years, brings to the forefront the problem of characterizing such delays. This monthly data set obviously exhibits strong seasonal variation, which makes it difficult to view an underlying trend. The purpose of this project is to clarify these time series characteristics of airline delay, by decomposing quantitatively the time series behavior into seasonal components, trend and interventions.

Figure 1 - Number of Flights Arriving Late as a Percent of Operations.

The time series for late arrivals, as noted in Figure 1, does highlight three significant interventions that have occurred since 1987: January 1996, December 2000, and September 2001. Statistically, the September 2001 impact has significantly more impact than the previous two interventions, particularly when taking into consideration that the level of airline delays had been decreasing over the past year.

Figure 2 provides the underlying trend for airline delays. There is no significant long term slope over the last 13 years. After the three extreme interventions have been removed (as noted in the previous graph), the long term trend tends to drift around the overall level equal to approximately 21% late arrivals over this period of time.

Figure 2 - Underlying Local Trend for Late Arrivals

We may eventually see a more long term impact on airline delay due to events in September, but the present analysis only uses data through October 2001; the addition of more recent data to the analysis will hopefully reveal more on the long term impact on delays.

But we can also look at the impact of September 2001 on another aspect of on-time performance: cancellations. Figure 3 provides a graph of the number of flights cancelled as a percent of operations. As is obvious from the graph, the percent of flights cancelled in September 2001 far exceeds any other month over this 13 year period.

September 2001 is not the only significant intervention in the cancellation time series; it is, however, three times larger than any other intervention during this time period. After the large interventions have been accounted for, the underlying trend for the cancellation rate becomes relatively level, as shown in Figure 4.

Figure 3 - Number of Flights Cancelled as a Percent of Operations

Figure 4 - Underlying Trend for Flights Cancelled

Figure 4 does highlight one key point: Once the seasonality has been removed from the data, the underlying trend does indicate a long term increase in percent of cancelled flights. This long term trend is calculated after the significant interventions have been removed, so this increase cannot be attributed to these occasional spikes. This slope is not large (approximately 0.15% per year), but it is significant.

A final note is made regarding the seasonality of the two time series. The seasonality for flight delays changes over time; Figure 5 provides the seasonal pattern for the four months that change the most over time. January, June and April all exhibit increasing delays over time, whereas March shows a decided decline. For cancellations, however, the seasonality is relatively stable over time. The average monthly deviation is shown in Figure 6. As expected, winter experiences the highest cancellations.

Figure 5 - Seasonal Deviations for Flight Delays

Figure 6 - Average Seasonal Deviation in Flight Cancellations