Seasonal and Non-Seasonal Exponential Smoothing - Automatic Search Tab

Select the Automatic search tab of the Seasonal and Non-Seasonal Exponential Smoothing dialog box to access options to perform an automatic search for the best set of parameters (given a user-defined lack-of-fit index; these are also described in exponential smoothing; see also, Time Series Analysis Index).

Element Name Description
Automatic search specifications As recommend by Gardner (1985), in order to obtain the best (most accurate) forecasts, you should determine the best smoothing parameters from the data. A quasi-Newton function minimization procedure (the same as in ARIMA) is used to minimize either the mean squared error, mean absolute error, or mean absolute percentage error. In most cases, this procedure is more efficient than the grid search, in particular when more than one parameter must be determined. Note that, by default, the parameter search is unconstrained, that is, parameter values outside the 0/1 boundaries may be estimated. When you click the Automatic estimation button, after the parameter search converges, invalid parameters will automatically be set to their respective minimum or maximum (e.g., α = -0.2 is set to α = 0; α = 1.2 is set to α = 1); and the α full set of results are displayed for the best parameters.
Max. number of iterations. Enter a value in the Max. number of iterations box to determine the maximum number of quasi-Newton iterations to be performed. Note that if the maximum number of iterations is exceeded during the automatic parameter search, additional iterations can be requested at that point. Thus, there is no need to specify an excessively large number in this field.
Convergence criterion This parameter determines the accuracy or precision with which the parameters will be estimated, or more specifically, the accuracy of the parameters with respect to the Lack of fit indicator (see below) that is selected. The estimation procedure terminates when the changes in the parameters over consecutive iterations are less than this value. Usually, the default value (.0001) is adequate to produce estimates for the best parameters with sufficient accuracy.
Unconstrained parameter estimation If the Unconstrained parameter estimation check box is selected (the default setting), the search algorithm is unconstrained, that is, parameter estimates outside the 0/1 boundaries may be produced (if they minimize the respective Lack of fit indicator). After the parameter search converges, invalid parameters are automatically set to the respective minimum or maximum (e.g., α = -0.2 is set to α = 0; α = 1.2 is set to α = 1). If this check box is not selected, then a large (penalty) value will be assigned to the Lack of fit value during the iterative parameter estimation whenever an invalid parameter estimate results. This usually "entices" the search algorithm to move away from the respective minima and maxima of the parameters. However, if, in fact, the best parameter values are near their minima or maxima (e.g., a constant slope, resulting in δ close to zero) then the parameter search may prematurely converge with less-than-optimal values for the other parameters. Therefore, the unconstrained minimization procedure is the recommended default.
Lack-of-fit indicator Use the options in the Lack-of-fit indicator group box to determine which lack-of-fit indicator will be minimized during the parameter estimation process. Various such indices have been proposed (see Makridakis, Wheelwright, and McGee, 1983), and they are described in exponential smoothing.
Mean squared error If the Mean squared error option button is selected, these values (MSE) are computed as the average of the squared error values. This is the most commonly used lack-of-fit indicator in most statistical fitting procedures
Mean absolute error If the Mean absolute error option button is selected, the mean absolute error (MAE) value is computed as the average absolute error value. If this value is 0 (zero), the fit (forecast) is perfect. As compared to the Mean squared error value (see above), this measure of fit will "de-emphasize" outliers, that is, unique or rare large error values affect the MAE less than the MSE value.
Mean abs. perc. error. Another measure of relative overall fit is the Mean absolute percentage error (MAPE). Both the above measures rely on the actual error value. It may seem reasonable to rather express the lack of fit in terms of the relative deviation of the one-step-ahead forecasts from the observed values, that is, relative to the magnitude of the observed values. For example, when trying to predict monthly sales that may fluctuate widely (e.g., seasonally) from month to month, we may be satisfied if our prediction "hits the target" with about ±10% accuracy. In other words, the absolute errors may be not so much of interest as are the relative errors in the forecasts. To assess the relative error the so-called percentage error (PE) can be computed as:

PEt = 100*(Xt-Ft)/Xt

where Xt is the observed value at time t, and Ft is the forecast (smoothed value). The mean percentage error is the average of the PE values for the entire series. This measure is often more meaningful than the mean squared error. For example, knowing that the average forecast is "off" by ±5% is a useful and easily interpretable result, whereas a mean squared error of 30.8 is not immediately interpretable.

Parameter start values These values will determine the initial value for the parameter search process. The meaning of the parameters is explained in the context of the Model on the Advanced tab and in exponential smoothing. In most cases, if the selected model is adequate for the data, the parameter values will converge at the same values, regardless of the parameter start values selected.
Automatic estimation After specifying the criteria for the automatic search, click the Automatic estimation button to perform the search. The parameter estimation procedure is iterative in nature, that is, parameter estimates are refined in successive iterations. A quasi-Newton algorithm is used to minimize the selected Lack of fit indicator. After the estimation procedure has been performed, the analysis results are displayed. If the parameter estimation procedure fails to converge, the Automatic Parameter Search dialog box is displayed and you have the option to request additional iterations.