On residuals and their autocorrelations in fitted time series models

David A. Pierce

Statistica Neerlandica, 1971, vol. 25, issue 3, 147-151

Abstract: Summary When discrete autoregressive‐moving average time series are fitted by least squares, both the residuals and their autocorrelations are for large n representable as singular linear transformations of the true errors (or white noise) and their autocomlations, respectively, and the matrices of these transformations arc both of the form I‐X(X'X)‐1X, where the rank of X is the number of parameters estimated. However, the large‐sample properties of these two sets of statistics are fundamentally different, a phenomenon which is of considerable importance for the use of the residual autocorrelations in performing tests of fit of these models.

Date: 1971
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