Transformations of Variables - Autocorrelations Tab

Select the Autocorrs tab of the Transformations of Variables dialog box to access options to compute the autocorrelations, partial autocorrelations, and cross-correlations for the currently highlighted variable; these statistics will be displayed in a spreadsheet and drawn in a correlogram graph. Refer to the Overview for a brief description of how the pattern of (partial) autocorrelations aids in the determination of an appropriate ARIMA model.

Element Name Description
Autocorrelations & crosscorrelations Use the options in the Autocorrelations & crosscorrelations group box to compute the autocorrelations, partial autocorrelations, and crosscorrelations between two time series.
Autocorrelations Click the Autocorrelations button to display a spreadsheet and plot of the autocorrelations for a lag of 1 through the number specified in the Number of lags box (see below). The spreadsheet contains the autocorrelations, their standard errors, the so-called Box-Ljung statistic, and the significance level of that statistic. In general, the autocorrelation is the correlation of the series with itself, lagged by a particular number of observations. For details regarding the computations of those statistics, refer to autocorrelation.
p-value for highlighting Significant autocorrelations (significant Box-Ljung statistics) are highlighted in the spreadsheet. Enter a value in the p-value for highlighting box to specify the significance level that is used for highlighting.
White noise standard errors Under the assumption that the true moving average process in the series is of the order k-1, the approximate standard error of the autocorrelation rk is computed as:

StdErr(rk) = Ö{(1/N) * [1+2*Σ(ri2)]}

(for i = 1 to k-1)

Here, N is the number of observations in the series. Under the assumption that the series is a white noise process, that is, that all autocorrelations are equal to zero, the standard error of rk is computed as:

StdErr(rk) = Ö{(1/N) * [(N-k)/(N+2)]}

Select the White noise standard errors check box to compute the standard errors in this manner.

Partial autocorrelations Click the Partial autocorrelations button to display a spreadsheet and plot of the partial autocorrelations for a lag of 1 through the number specified in the Number of lags box (see below). The spreadsheet contains the partial autocorrelations and their standard errors. In general, the partial autocorrelation is the partial correlation of a series with itself, lagged by a particular number of observations, and controlling for all correlations for lags of lower order. For example, the partial autocorrelation for a lag of 2 represents the unique correlation of the series with itself at that lag, after controlling for the correlation at lag 1. For details regarding the computations of the partial autocorrelation and its standard error, refer to partial autocorrelation. Partial autocorrelations that are larger than two times their respective standard errors are highlighted in the spreadsheet.
Crosscorrelations Click the Crosscorrelations button to display a spreadsheet and plot of crosscorrelations for a lag of -k through +k, where k is the number specified in the Number of lags box (see below). The spreadsheet contains the crosscorrelations and their standard errors. In general, the crosscorrelation is the correlation of a series with another series, shifted by a particular number of observations. For details regarding the computations of the crosscorrelations and their standard errors refer to crosscorrelation. Correlations that are greater than 2 times their respective standard errors are highlighted in the spreadsheet.
Number of lags Enter a value in the Number of lags box to determine the maximum number of lags for which the autocorrelation and partial autocorrelations are computed.
Scatterplot with lagged series Use the options in the Scatterplot with lagged series group box to view 2D and 3D scatterplots.
2D scatterplot Click the 2D scatterplot button to display the Currently available variables and transformations dialog box, in which you select the second variable for the scatterplot. Click the OK button to display a 2D scatterplot of the highlighted variable in the active work area and the variable selected in the Currently available variables and transformations dialog. In this plot, the values of the highlighted variable will be lagged by k observations, as specified in the Plot highlighted variable with lag of box (see below). To review specific autocorrelations, choose the same variable for both axes of the plot.
3D scatterplot Click the 3D scatterplot button to display the Select variables (series) for the X and Y axes dialog box, in which you select two additional variables for the scatterplot. Click the OK button to display a 3D scatterplot of the highlighted variable in the active work area and the two other variables selected in the Select variables (series) for the X and Y axes dialog. In this plot, the values of the highlighted variable will be lagged by k observations, as specified in the Plot highlighted variable with lag of box (see below).
Plot highlighted variable with lag of Enter a value in the Plot highlighted variable with lag of box to specify the lag that should be used when plotting the highlighted variable.
Label points in scatterplot If the Label points in scatterplot check box is selected, the points in the scatterplot will be labeled with either case names, case numbers, dates, or consecutive integers, depending on the setting of the option buttons in the Label data points with group box on the Transformations of Variables dialog box - Review and Plot tab.