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Slide 33:forecast error and performance measures: 6 equations

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Forecast Error and Performance Measures

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So we have a number of different forecast errors and performance measures: one is simply the forecast error at time t, written as the error at time t which is equal to the value, the actual data value, the x of t minus the forecast of t. So if the forecast were larger than the data, that's going to be a negative value; if the forecast were smaller than the data, that's going to be a positive value. So e of t is a signed quantity—can be either positive or negative. One very easily computed measure of deviation is the mean absolute deviation or MAD; that's equal to the sum of the absolute values of the forecast error at time t divided by the number of values that you have in your data stream. So if you made say 60 forecasts, 5 years of 12-month years, then you divide the errors, the absolute value of the errors by 60 and that gives you the mean absolute deviation. This is real quick for computers to do, obviously, so it's a fairly useful measure. You could also use the mean squared error, which is the sum of the errors, again, taking the mean of that, divide by n; the cumulative forecast error, which is just the sum of all the errors, so this can be some very large number; you can use the mean absolute percentage error, which is as it says the percentage error, the absolute value of the percentage error, or there's another value that we'll see printed out on the printouts, which is called the tracking signal, which is the cumulative forecast error divided by the mean absolute deviation, which will either be above or below 1. So those are some of the criteria that one could use.