FORECASTING:INCORPORATING SEASONAL EFFECTS INTO FORECASTING METHODS

INCORPORATING SEASONAL EFFECTS INTO FORECASTING METHODS

It is fairly common for a time series to have a seasonal pattern with higher values at certain times of the year than others. For example, this occurs for the sales of a product that is a popular choice for Christmas gifts. Such a time series violates the basic assumption of a constant-level model, so the forecasting methods presented in the preceding section should not be applied directly.

Fortunately, it is relatively straightforward to make seasonal adjustments in such a time series so that these forecasting methods based on a constant-level model can still be applied. We will illustrate the procedure with the following example.

Example. The COMPUTER CLUB WAREHOUSE (commonly referred to as CCW) sells various computer products at bargain prices by taking telephone orders directly from customers at its call center. Figure 27.3 shows the average number of calls received per day in each of the four quarters of the past three years. Note how the call volume jumps up sharply in each Quarter 4 because of Christmas sales. There also is a tendency for the call volume to be a little higher in Quarter 3 than in Quarter 1 or 2 because of back-to-school sales.

To quantify these seasonal effects, the second column of Table 27.1 shows the average daily call volume for each quarter over the past three years. Underneath this column, the overall average over all four quarters is calculated to be 7,529. Dividing the average for each quarter by this overall average gives the seasonal factor shown in the third column.

In general, the seasonal factor for any period of a year (a quarter, a month, etc.) measures how that period compares to the overall average for an entire year. Specifically, using historical data, the seasonal factor is calculated to be

Your OR Courseware includes an Excel template for calculating these seasonal factors.

The Seasonally Adjusted Time Series

It is much easier to analyze a time series and detect new trends if the data are first adjusted to remove the effect of seasonal patterns. To remove the seasonal effects from the time series shown in Fig. 27.3, each of these average daily call volumes needs to be divided by the corresponding seasonal factor given in Table 27.1. Thus, the formula is

Applying this formula to all 12 call volumes in Fig. 27.3 gives the seasonally adjusted call volumes shown in column F of the spreadsheet in Fig. 27.4.

In effect, these seasonally adjusted call volumes show what the call volumes would have been if the calls that occur because of the time of the year (Christmas shopping, back- to-school shopping, etc.) had been spread evenly throughout the year instead. Compare the plots in Figs. 27.4 and 27.3. After considering the smaller vertical scale in Fig. 27.4, note how much less fluctuation this figure has than Fig. 27.3 because of removing seasonal ef- fects. However, this figure still is far from completely flat because fluctuations in call volume occur for other reasons beside just seasonal effects. For example, hot new products attract a flurry of calls. A jump also occurs just after the mailing of a catalog. Some random fluctuations occur without any apparent explanation. Figure 27.4 enables seeing and analyzing these fluctuations in sales volumes that are not caused by seasonal effects.

The General Procedure

After seasonally adjusting a time series, any of the forecasting methods presented in the preceding section (or the next section) can then be applied. Here is an outline of the gen- eral procedure.

1. Use the following formula to seasonally adjust each value in the time series: actual value

Seasonally adjusted value = --.

seasonal factor

2. Select a time series forecasting method.

3. Apply this method to the seasonally adjusted time series to obtain a forecast of the next seasonally adjusted value (or values).

4. Multiply this forecast by the corresponding seasonal factor to obtain a forecast of the next actual value (without seasonal adjustment).

As mentioned at the end of the preceding section, an Excel template that incorporates seasonal effects is available in your OR Courseware for each of the forecasting methods to assist you with combining the method with this procedure.