Quartz | Level 8

## Time Series and Holts-Winters and February Monthly Forecasts

We have developed some time series (ARIMA) and smoothing models (Holt-Winters) that forecast monthly air traffic revenues. These flows are quite large on a daily basis, with monthly aggregates being accordingly large.

These models seem to work very well on a quarterly and annual basis. When using monthly values, however, we get issues with February. The extra few days the other months have make a huge difference in terms of \$ received.

It seems that the first February forecast after the end of historical data always has very large growth when comparing to February of the previous year. This settles down in the following February forecasts. Obviously this is masked in quarterly and annual forecasts. It does make some sense for the ARIMA models, which use AR components from months that have a few days more than January. Holt-Winters is also affected by this, especially in the level component.

So the question I have is should every February be adjusted for this discrepancy, or does SAS somehow account for the number of days in a month when doing a monthly forecast? It seems to me that if these methods will "bleed" growth from other months into February that never would have existed due to the shorter number of days, a February adjusted is needed given the large amount of flows. If such an adjustment is necessary, can you advise on an acceptable method? One I can see is simply normalizing the forecast base on days. For example, the average number of days in a month is 365/12=30.42 days. Now if February's forecast is too high, would we take forecast*(28days/30.42days).

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Pyrite | Level 9

## Re: Time Series and Holts-Winters and February Monthly Forecasts

you can try adjusting the series y_t by (number of days in an average month)/(number of days in month t). Forecast using the adjusted series as usual, and then adjust the forecast back. You will need to prepare the adjustment factors into the future as well. If you are using Forecast Studio, you can create the adjustment factor as a variable and use it in a project to pre and post adjust the series and forecasts.

alex