Seasonal and Non-Seasonal Exponential Smoothing - Advanced Tab

Select the Advanced tab of the Seasonal and Non-Seasonal Exponential Smoothing dialog box to access the options described here. The general ideas of exponential smoothing and forecasting are explained in exponential smoothing.

Element Name Description
Model The exponential smoothing models available in the Model group box are arranged in a two-way classification, as proposed by Gardner (1985): The time series can either contain no seasonal component, an additive component, or a multiplicative seasonal component. In addition, you can select no upward or downward trend in the series, a linear trend, an exponential trend, or a damped trend. The combination of these characteristics results in 12 different exponential smoothing models (which include the classical models developed by Winters, Holt, and Brown). Refer to exponential smoothing models for more detailed descriptions and examples of these models.
Seasonal component: lag = Enter a value in the Seasonal component: lag = box to determine the length of one seasonal cycle. The default value is 12 (e.g., 12 months in each year). When changed, this parameter is retained (remembered) for other time series analyses involving a seasonal component [e.g., in ARIMA models or in Seasonal decomposition (Census I)]. Note that the Seasonal component: lag = box is only available when a seasonal model is selected (see below).
Alpha The value entered in the Alpha (α) box is the constant process smoothing parameter. The α (Alpha) parameter is necessary for all models. If α is 0 (zero), then all smoothed values will be equal to the initial value (S0, see also User-defined initial value below). If this parameter is 1, then each smoothed value (forecast) is equal to the respective previous observation. Values greater than 0 (zero) and less than 1 produce a forecast that is a weighted average of the previous observations, with the weights decreasing exponentially the "older" the previous observation. The closer the α parameter is to 0, the more slowly will the weights decrease (that is, the more slowly will the effect of prior observations disappear), the closer it is to 1, the faster will the weights decrease (and the greater will be the effect of immediately preceding or "younger" observations). In plots of the series, small values of α produce smooth fitted lines (forecasts) that only follow major trends or fluctuations spanning many observations; larger values of a (closer to 1) produce more jagged lines that are greatly influenced by even minor disturbances in the series.
Delta Parameter δ (Delta) is the seasonal smoothing parameter, and only needs to be specified for seasonal models. In general the one-step-ahead forecasts are computed as follows (for no trend models, for linear and exponential trend models a trend component is added to the model; see below):

Additive model:

Forecastt = St +It-p

Multiplicative model:

Forecastt = St *It-p

In this formula, St stands for the (simple) exponentially smoothed value of the series at time t, and It-p stands for the smoothed seasonal factor at time t minus p (the length of the season). Thus, compared to simple exponential smoothing, the forecast is "enhanced" by adding or multiplying the simple smoothed value by the predicted seasonal component. This seasonal component is derived analogous to the St value from simple exponential smoothing as:

Additive model:

It = It-p +δ*(1-α)*et

Multiplicative model:

It = It-p +δ*(1-α)*et/St

Put into words, the predicted seasonal component at time t is computed as the respective seasonal component in the last seasonal cycle plus a portion of the error (et; the observed minus the forecast value at time t). Parameter δ can assume values between 0 and 1. If it is zero, then the seasonal component for a particular point in time is predicted to be identical to the predicted seasonal component for the respective time during the previous seasonal cycle, which in turn is predicted to be identical to that from the previous cycle, and so on. Thus, if δ is zero, a constant unchanging seasonal component is used to generate the one-step-ahead forecasts. If the δ parameter is equal to 1, then the seasonal component is modified "maximally" at every step by the respective forecast error. In most cases, when seasonality is present in the time series, the optimum δ parameter will fall somewhere between 0 (zero) and 1(one).

Gamma and Phi Gamma (γ) and Phi (φ) are the trend smoothing parameters. Parameter γ needs to be specified for linear and exponential trend models, and for damped trend models without seasonality. Parameter φ must be specified for damped trend models. Analogous to the seasonal component, when a trend component is included in the exponential smoothing process, an independent trend component is computed for each time, and modified as a function of the forecast error and the respective parameter. If the γ parameter is 0 (zero), then the trend component is constant across all values of the time series (and for all forecasts). If the parameter is 1, then the trend component is modified "maximally" at every step by the respective forecast error. Parameter values that fall in-between represent mixtures of those two extremes. Parameter φ is a trend modification parameter, and affects how strongly changes in the trend will affect estimates of the trend for subsequent forecasts, that is, how quickly the trend will be "damped" or increased.
User-def. initial value If the User-def. initial value check box is selected, then the initial value of the smoothed series (S0, necessary in order to compute the forecast for the first observation) is taken from the value you enter in the adjacent box; otherwise S0 is computed from the data, depending on the model selected. Refer to exponential smoothing models for details of how S0 is computed in that case.
Initial trend If the Initial trend check box is selected, then the initial value for the trend (T0) is taken from the value you enter in the adjacent box; otherwise it is computed from the data, depending on the model chosen. An initial estimate of the trend (T0) is necessary, if a model with trend is selected, in order to compute the forecast for the first observation. Refer to exponential smoothing models for details of how T0 is computed in that case. Note that the Initial trend box is only available if a model with trend is selected.
Get seasonal factors from variable In order to compute the forecasts for the values in the first seasonal cycle of the series, an initial estimate of the seasonal component is necessary. If the Get seasonal factors from variable check box is not selected (default), then the initial seasonal factors are computed from the data (following the procedures described in seasonal decomposition (census I)). If the Get seasonal factors from variable check box is selected, then the Select variable with initial seasonal factors dialog is displayed, in which you select a variable that contains the initial seasonal factors in the first p values in the file (where p is the length of the seasonal cycle). Note that STATISTICA always takes the first p cases in the specified variable as the initial seasonal component, regardless of selection conditions that are in effect. For additive seasonality, the initial values for the seasonal component must add to 0 (zero); for multiplicative seasonality, the initial values for the seasonal component must add to the length of the seasonal cycle (p). Note that the Get seasonal factors from variable check box is only available if a model with a seasonal component is chosen.
Variable Click the Variable button to display the Select variable with initial seasonal factors dialog box, in which you select a variable that contains the initial seasonal factors in the first p values in the file (where p is the length of the seasonal cycle).
Make summary plot for each smooth If you select the Make summary plot for each smooth check box, after each analysis a summary plot is produced showing the values of the observed series, the smoothed series (forecasts), and the residuals (scaled against the right y-axis). This plot provides an immediate visual check of the adequacy of the forecasts and the distribution of the errors (residuals) across the series.
Add pred./errors to work area. If the Add pred./errors to work area check box is selected, then after each analysis the smoothed (forecast) values as well as residuals (observed minus smoothed values) will be appended to the active work area. If you choose to append those series, make sure that there is sufficient space in the active work area for the respective variable, that is, that there are at least two (not locked) backups available. Increase the Number of backups parameter if necessary. Also, be sure to Lock all important backups of the original variable (those that you want to retain); otherwise, those backups may be overwritten (refer to the section describing the memory management in the active work area). To lock a backup, double-click in the Lock column on the respective variable.
Other transformations and plots Click the Other transformations & plots button to display the Transformation of Variables dialog box, which contains options to perform a wide variety of transformations on the data. The transformed series will be appended to the active work area.