Seasonality in Time Series Forecasting

6 Pages Posted: 21 Oct 2008

See all articles by Samuel E. Bodily

Samuel E. Bodily

University of Virginia - Darden School of Business

Larry Weatherford

University of Wyoming - College of Business

Multiple version iconThere are 2 versions of this paper


This note teaches the student how to account for seasonality in time-series data. All the necessary steps to (1) deseasonalize, (2) forecast with deseasonalized data, and then (3) reseasonalize the forecast are illustrated with examples from the coal industry.




When making forecasts using data from a time series (a sequence of observations spread evenly over time), one can often take advantage of seasonality. Seasonality comprises movements up and down in a pattern of constant length that repeats itself.

For example, if you were looking at monthly data on sales of ice cream, you would expect to see higher sales in the warmer months (June to August in the northern hemisphere) than in the winter months, year after year. The seasonal pattern would be 12 months long. If we used weekly data, the seasonal pattern would repeat every 52 periods. The number of time periods in a seasonal pattern depends on how often the observations are collected.

In another example, we may be looking at daily data on the number of guests staying over night at a downtown hotel. Our intuition might tell us that we expect high numbers on Monday, Tuesday, and Wednesday nights, low numbers on Friday and Saturday, and medium numbers on Thursday and Sunday. So our pattern would be as follows, starting with Sunday: medium, high, high, high, medium, low, low. The pattern would repeat itself every seven days.

The approach in this note for treating such seasonal patterns is illustrated in Figures 1 through 4. Figure 1 shows the original data, which exhibits a seasonal pattern. From examining the data and from our own judgment, we can hypothesize an m-period seasonal pattern. Next, using the numerical approach of the next section we deseasonalize the data, obtaining Figure 2. Then, using the best forecasting method available, we make a forecast in deseasonalized terms. Figure 3 shows deseasonalized forecasts for the next two periods. Finally, we reseasonalize the forecast to account for the seasonal pattern, as depicted in Figure 4.

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Keywords: forecasting, statistics, time series

Suggested Citation

Bodily, Samuel E. and Weatherford, Larry, Seasonality in Time Series Forecasting. Darden Case No. UVA-QA-0407, Available at SSRN:

Samuel E. Bodily (Contact Author)

University of Virginia - Darden School of Business ( email )

P.O. Box 6550
Charlottesville, VA 22906-6550
United States
434-924-4813 (Phone)
434-293-7677 (Fax)


Larry Weatherford

University of Wyoming - College of Business

1000 E. University Avenue
Laramie, WY 82071
United States

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