A note on the residual empirical process in autoregressive models

Sangyeol Lee

Statistics & Probability Letters, 1997, vol. 32, issue 4, 405-411

Abstract: Suppose that {Xt} is the stationary AR(p) process of the form: Xt - [mu] = [beta]1(Xt-1 - [mu]) + ... + [beta]p(Xt-p - [mu]) + [var epsilon]t, where {[var epsilon]t} is a sequence of i.i.d. random variables with mean zero and finite variance [sigma]2. In this paper, we study the asymptotic behavior of the empirical process computed from the least-squares residuals, for which some estimators of [mu] and [sigma]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.

Keywords: Stationary; AR(p); process; Goodness-of-fit; tests; Residual; empirical; process; Gaussian; process (search for similar items in EconPapers)
Date: 1997
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Citations: View citations in EconPapers (2)

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