Hierarchical equilibria of branching populations

Hao Yu ()
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Hao Yu: Department of Statistical and Actuarial Sciences, University of Western Ontario

No lrsp-TRS391, RePAd Working Paper Series from Département des sciences administratives, UQO

Abstract: In this paper we study high moment partial sum processes based on residuals of a stationary ARMA model with or without a unknown mean parameter. We show that they can be approximated in probability by the analogous processes which are obtained from the independent and identically distributed (iid) errors of the ARMA model. However, if a unknown mean parameter is used, there will be an additional term that depends on model parameters and a mean estimator. But, when properly normalized, this additional term will be cancelled out. Thus they converge weakly to the same Gaussian processes as if the residuals were iid. Applications to changepoint problems and goodness-of-fit are considered, in particular CUSUM statistics for testing ARMA model structure changes and the Jarque-Bera omnibus statistic for testing normality of the unobservable error distribution of an ARMA model.

Keywords: ARMA; residuals; high moment partial sum process; weak convergence; CUSUM; omnibus; skewness; kurtosis; (sqare root)n consistency. (search for similar items in EconPapers)
JEL-codes: C10 C40 (search for similar items in EconPapers)
Pages: 23 pages
Date: 2003-01-01
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