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time_series_methods.docxTime Series Methods
Time series methods are statistical techniques that make use of historical data accumulated over a period of time. Time series methods assume that what has occurred in the past will continue to occur in the future. As the name time series suggests, these methods relate the forecast to only one factor—time. These methods assume that identifiable historical patterns or trends for demand over time will repeat themselves. They include the moving average, exponential smoothing, and linear trend line; and they are among the most popular methods for short-range forecasting among service and manufacturing companies. In a 2007 survey of firms across different industries conducted by the Institute of Business Forecasting, over 60% of the firms used time series models, making it the most popular forecasting method by far. One of the reasons time series models are so popular is that they are relatively easy to understand and use. The survey also showed that the most popular time series models are moving averages and exponential smoothing.1
1C. L. Jain, “Benchmarking Forecasting Models,” Journal of Business Forecasting 24 (4; Winter 2005–06), pp. 9–12.
In a naive forecast demand in the current period is used as the next period’s forecast.
A time series forecast can be as simple as using demand in the current period to predict demand in the next period. This is sometimes called a naive or intuitive forecast. For example, if demand is 100 units this week, the forecast for next week’s demand is 100 units; if demand turns out to be 90 units instead, then the following week’s demand is 90 units, and so on. This type of forecasting method does not take into account historical demand behavior; it relies only on demand in the current period. It reacts directly to the normal, random movements in demand.
The simple moving average method uses several demand values during the recent past to develop a forecast. This tends todampen, or smooth out, the random increases and decreases of a forecast that uses only one period. The simple moving average is useful for forecasting demand that is stable and does not display any pronounced demand behavior, such as a trend or seasonal pattern.
Moving average is good for stable demand with no pronounced behavioral patterns.
Moving averages are computed for specific periods, such as three months or five months, depending on how much the forecaster desires to “smooth” the demand data. The longer the moving average period, the smoother it will be. (Alternatively, a shorter moving average is more susceptible to simple random variation.) The formula for computing the simple moving average is
where
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n |
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number of periods in the moving average |
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Di |
= |
demand in period i |
Example 12.1 Computing a Simple Moving Average
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Q: |
The Heartland Produce Company sells and delivers food produce to restaurants and catering services within a 100-mile radius of its warehouse. The food supply business is competitive, and the ability to deliver orders promptly is a factor in getting new customers and keeping old ones. The manager of the company wants to be certain enough drivers and vehicles are available to deliver orders promptly and they have adequate inventory in stock. Therefore, the manager wants to be able to forecast the number of orders that will occur during the next month (i.e., to forecast the demand for deliveries). From records of delivery orders, management has accumulated the following data for the past 10 months, from which it wants to compute three- and five-month moving averages.
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Solution |
Let us assume that it is the end of October. The forecast resulting from either the three- or five-month moving average is typically for the next month in the sequence, which in this case is November. The moving average is computed from the demand for orders for the prior three months in the sequence according to the following formula:
The five-month moving average is computed from the prior five months of demand data as follows:
The three- and five-month moving average forecasts for all the months of demand data are shown in the following table. Actually, the manager would use only the forecast for November based on the most recent monthly demand. However, the earlier forecasts for prior months allow us to compare the forecast with actual demand to see how accurate the forecasting method is—that is, how well it does. Three- and Five-Month Averages
Both moving average forecasts in the preceding table tend to smooth out the variability occurring in the actual data. This smoothing effect can be observed in the following figure in which the three-month and five-month averages have been superimposed on a graph of the original data:
The five-month moving average in the previous figure smooths out fluctuations to a greater extent than the three-month moving average. However, the three-month average more closely reflects the most recent data available to the produce company manager. In general, forecasts using the longer-period moving average are slower to react to recent changes in demand than would those made using shorter-period moving averages. The extra periods of data dampen the speed with which the forecast responds. Establishing the appropriate number of periods to use in a moving average forecast often requires some amount of trial-and-error experimentation. |
The disadvantage of the moving average method is that it does not react to variations that occur for a reason, such as cycles and seasonal effects. Factors that cause changes are generally ignored. It is basically a “mechanical” method, which reflects historical data in a consistent way. However, the moving average method does have the advantage of being easy to use, quick, and relatively inexpensive. In general, this method can provide a good forecast for the short run, but it should not be pushed too far into the future.
Longer-period moving averages react more slowly to recent demand changes than shorter-period moving averages; shorter-period moving averages are more susceptible to simple random variation.
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