Using the three-week moving average calculations in Table 17.9, the values for these three measures of forecast accuracy are Thus, the forecast for week 13 is 19 or 19,000 gallons of gasoline.įorecast Accuracy In Section 17.2 we discussed three measures of forecast accuracy: MAE, MSE, and MAPE.
To forecast sales in week 13, the next time period in the future, we simply compute the average of the time series values in weeks 10, 11, and 12.
Note how the graph of the moving average forecasts has tended to smooth out the random fluctuations in the time series. Figure 17.7 shows the original time series plot and the three-week moving average forecasts. A complete summary of the three-week moving average forecasts for the gasoline sales time series is provided in Table 17.9. Hence, the forecast of sales in week 5 is 21 and the error associated with this forecast is 18 – 21 = -3. Next, we compute the forecast of sales in week 5 by averaging the time series values in weeks 2-4.
Because the actual value observed in week 4 is 23, the forecast error in week 4 is 23 – 19 = 4. Thus, the moving average forecast of sales in week 4 is 19 or 19,000 gallons of gasoline. We begin by computing the forecast of sales in week 4 using the average of the time series values in weeks 1-3. To illustrate how moving averages can be used to forecast gasoline sales, we will use a three-week moving average (k = 3). So, managerial judgment based on an understanding of the behavior of a time series is helpful in choosing a good value for k. But larger values of k will be more effective in smoothing out the random fluctuations over time. Thus, a smaller value of k will track shifts in a time series more quickly. A moving average will adapt to the new level of the series and resume providing good forecasts in k periods. As mentioned earlier, a time series with a horizontal pattern can shift to a new level over time. If more past values are considered relevant, then a larger value of k is better. If only the most recent values of the time series are considered relevant, a small value of k is preferred. To use moving averages to forecast a time series, we must first select the order, or number of time series values, to be included in the moving average. Thus, the smoothing methods of this section are applicable. The time series plot in Figure 17.1 indicates that the gasoline sales time series has a horizontal pattern. To illustrate the moving averages method, let us return to the gasoline sales data in Table 17.1 and Figure 17.1.
As a result, the average will change, or move, as new observations become available. The term moving is used because every time a new observation becomes available for the time series, it replaces the oldest observation in the equation and a new average is computed. Mathematically, a moving average forecast of order k is as follows: The moving averages method uses the average of the most recent k data values in the time series as the forecast for the next period. These methods are easy to use and generally provide a high level of accuracy for short- range forecasts, such as a forecast for the next time period. Because the objective of each of these methods is to “smooth out” the random fluctuations in the time series, they are referred to as smoothing methods. However, without modification they are not appropriate when significant trend, cyclical, or seasonal effects are present. These methods also adapt well to changes in the level of a horizontal pattern such as we saw with the extended gasoline sales time series (Table 17.2 and Figure 17.2). In this section, we discuss three forecasting methods that are appropriate for a time series with a horizontal pattern: moving averages, weighted moving averages, and exponential smoothing.