Dissect the error correction form

- [Instructor] Let's use the exponential smoothing formula in real situation. The worksheet shows the date of each observation in column A and the observations themselves in column B. Here we're recording and forecasting sales dollars. The forecasts appear in column C. You maybe wondering what are all those other forecasts in cell C3 through C20 doing here. We already know what the actual observations for those dates are, so what is there to be gained by forecasting them? The reason is that we want to assess the accuracy of the forecasts. I'll show you how that's done a little later on in this course. Notice the two highlighted cells C3 and C21. Cell C3 demonstrates that the first forecast is often taken to be the value of the first actual observation. There are other ways to set the first forecast, but the one shown here is certainly the simplest. The forecast of 941 in cell C3 is equal to the first observation, that of 941 in cell B2. Cell C21 shows that you can use simple exponential smoothing to obtain what's called a one step ahead forecast. The formula in cell C21 makes use of the prior forecast, the error in the prior forecast, and the smoothing constant. When it comes time on June 19, to make a forecast for June 20, each of the quantities in hand and you can make a forecast for the next day. Now notice the first actual forecast in cell C4. It picks up the prior forecast value in cell C3 and adds to that the product of the smoothing constant in cell H1 and the prior forecast error in cell D3. That's precisely what the error correction version of the smoothing formula is intended to do. Also notice that the formula employs dollar signs along with the cell address H1. The dollar signs anchor the reference to that cell. With the reference anchored, we can copy and paste the formula in cell C4 down through cell C21. Each of the pasted formulas will make reference to cell H1, but they will also make reference to the previous forecast and the previous forecast error. So for example the final forecast in cell C21 makes reference to the smoothing constant in cell H1, but also makes reference to the forecast in C20 and the forecast error in D20. This is a convenient place to have a look at what happens when alpha, the smoothing constant, takes on one of two extreme values. Suppose first that we set it to zero. When I do so, watch what happens to the forecasts in the chart. The series of forecasts becomes a constant straight line. The reason has everything to do with the formula. The formula adds the prior forecast to the product of the smoothing constant and the prior error. When the smoothing constant is zero the prior error has no effect on the next forecast and each forecast therefore is set equal to the one that proceeded it. The result is a straight line forecast, one that equals the first forecast and the baseline. Now set alpha to the other extreme value, 1.0, and again watch what happens to the forecasts in the chart. Each forecast is now equal to the prior actual observation. The error correction formula explains the reason. With the smoothing constant set to one, the formula works out to the sum of the prior forecast plus the prior error. But the prior error is calculated by subtracting the prior forecast from the prior actual. The effect of the error correction formula then is simply to add the error back into the forecast and the result is the prior actual observation. The point of exponential smoothing is to find the smoothing constant that minimizes the errors in the forecasts. Used on the proper kind of baseline for this sort of simple smoothing, the horizontal baseline, the optimum value for the smoothing constant is generally somewhere between zero and one. You'll see how to find the optimum value in chapter four of this course. In the mean time, let's take a look at the smoothing form of the equation.