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A note on the residual empirical process in autoregressive models

โœ Scribed by Sangyeol Lee

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
242 KB
Volume
32
Category
Article
ISSN
0167-7152

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โœฆ Synopsis

Suppose that {X,} is the stationary AR(p) process of the form: X, -/,t = fll(Xt.-i -la) + ... + [~t,(X,_p -I~) + ~:,, where {~:,} is a sequence of i.i.d, random variables with mean zero and finite variance a 2. In this paper, we study the asymptotic behavior of the empirical process computed from the least-squares residuals, for which some estimators of/~ and a 2 are substituted. Due to the estimation of the location and scale parameters, the limiting process of the residual empirical process is shown to be a Gaussian process which is not a standard Brownian bridge. The result is applicable to the goodness-of-fit test of the errors in autoregressive processes.

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