| Diagnostic Checking in Linear Processes With Infinite Variance (2007) | |||||||||||||
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| We consider empirical autocorrelations of residuals from infinite variance autoregressive processes. Unlike the finite-variance case, it emerges that the limiting distribution, after suitable normalization, is not always more concentrated around zero when residuals rather than true innovations are employed. 1 Introduction and summary In the context of standard ARMA-models y t \Gamma OE 1 y t\Gamma1 \Gamma \Delta \Delta \Delta \Gamma OE p y t\Gammap = ffl t + ` 1 ffl t\Gamma1 + \Delta \Delta \Delta + ` q ffl t\Gammaq (t = 1; . . . ; n) (1) it is common practice to check the residuals ffl t from the fitted process for possible remaining autocorrelation. If the ffl t 's are iid(0; oe 2 ) (which in particular implies a finite variance) it is well known from Box and Pierce (1970) that the standardized empirical autocorrelations have a limiting normal distribution with mean zero, i.e. p n ae i := p n n t=i+1 ffl t ffl t\Gammai n t=1 ffl 2 t d ! N (0; c i ) ; (2) 1 Research suppo... | |||||||||||||
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