Time Series Analysis - Autocorrelations Tab

Select the Autocorrelations tab, which is located on several Time Series dialog boxes, to access options to compute the autocorrelations and partial autocorrelations 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.

The Autocorrelations tab is located in these dialog boxes: Single Series ARIMA, Interrupted Time Series ARIMA, Seasonal and Non-Seasonal Exponential Smoothing, Fourier (Spectral) Analysis, Ratios-to-Moving Averages Classical Seasonal Decomposition (Census Method I), the X-11 Monthly Seasonal Adjustment (Census Method II), X-11 Quarterly Seasonal Adjustment (Census Method II), and Distributed Lags Analysis.

Element Name Description
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 will report 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.
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 will report 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 will be highlighted in the spreadsheet.
p-value for highlighting Significant autocorrelations (significant Box-Ljung statistics) will be highlighted in the spreadsheet. Enter a value in the p-value for highlighting box (or adjust the value using the microscrolls) to specify the significance level to be used for highlighting.
Number of lags Enter a value in the Number of lags box (or adjust the value using the microscrolls) to determine the maximum number of lags for which the autocorrelations and partial autocorrelations will be computed.