Journal of Official Statistics, Vol.7, No.2, 1991. pp. 181194

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The Autocorrelation of Residuals from the X11ARIMA Method

The problem of significant auto-correlation in the residuals of X11ARIMA and the U.S. Bureau of the Census X11 variant as well has generated much controversy.

This paper shows that the presence of significant autocorrelations at certain lags is not necessarily an indication of inadequacy of the methods. It is recognized that residuals from reasonable decompositions can contain some non-zero autocorrelations given the effect of the linear filters on white noise irregulars. In many cases, however, significant autocorrelation can generally be corrected by using different trend-cycle and seasonal filters, removing trading-day variations and Easter effects, and by using an additive decomposition model. The elimination of significant autocorrelation, however, is not recommended as a goal in itself. It should not be done without regard to the quality of the seasonally adjusted values and a priori information concerning the generating structure of the series under investigation.

Trend-cycle filters; seasonal filters; trading-day variations.

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