forecasting combined 10-31-05

# forecasting combined 10-31-05 - 1 Alpha value and...

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Single exponential smoothing is nothing more than a weighted average. The smoothing constant acts as the weight and depending on what value you give it (between 0 and 1), you weigh the time series values differently. Large alpha values weigh highly the most recent time series values in generating a forecast. In fact if alpha is chosen to be 1, then the forecast for next period is just the same as the actual value for the current period. A forecasting model with a high smoothing constant is called a RESPONSIVE model. That means it responds to the recent values in the time series and makes forecasts that try to emulate what has recently happened. F(t+1) = alpha (Yt )+ (1-alpha)Ft Assume Alpha=1, and assume that you are in period t. F(t+1) = 1(Yt) + 0(Ft) F(t+1) = Yt That would mean the forecast for next period (t+1) will be identical to the actual value for this period (period t). So, if Actual this month is 45, the forecast for next month will be 45! You can imagine that if a time series is highly volatile and values change drastically from one period to the next, to the next, you should not use a very responsive model (should not use a high alpha value) because the forecast will always be one period behind the actual. So, for example when the actual is high, the forecast for next period will be high (since the model is responsive). However, since the series is volatile, the actual value for the next period will be low. This means the high forecast that was made has made a big error. This continues from period to period, which basically means that the forecasts are going to off continually. On the other hand, small alpha values do the opposite. If alpha=0, the model will be highly "stable". It will generate forecasts that are averages of the actual values from many periods past! The weight is spread out so that more of the older values in the time series are used in making the forecast. Such forecasting model is called STABLE. A stable exponential model is a weighted average of several periods in the time series. If a time series is volatile, then you would need a somewhat stable model to forecast it. There is no magic formula for choosing the alpha value for an exponential smoothing model. Trial and error is the basis of all computer packages. Given a time series, you can specify the measure of accuracy (MSE or MAD or MAPE or some other measure of accuracy) that the software must use to find the best alpha for the series. Also remember that alpha could be any number between zero to one. So, it does not need to be expressed in 0.1 increments. For example, you could pick alpha to be 0.237 or 0.91 or 0.735, etc. QM/POM performs exponential smoothing and can be used to generate answers fast. It also

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forecasting combined 10-31-05 - 1 Alpha value and...

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