Hao Yu () (Department of Statistical and Actuarial Sciences, University of Western Ontario)
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.
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Publisher Info
Paper provided by Département des sciences administratives, UQO in its series RePAd Working Paper Series with number
lrsp-TRS391.
Length: 23 pages Date of creation: 01 Jan 2003 Date of revision: Handle: RePEc:pqs:wpaper:0182005
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Find related papers by JEL classification: C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - General C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General