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In this paper, we study a stationary AR(p)-ARCH(q) model with parameter vectors αandβ. We propose a method for computing the maximum likelihood estimator (MLE) of parameters under the nonnegative restriction. A similar method is also proposed for the case that the parameters are restricted by a simple order:rnα1 ≥ α2 ≥ … ≥ αg andβ1 ≥ β2 ≥ … ≥ βp. The strong consistency of the above two estimators is discussed. Furthermore, we consider the problem of testing homogeneity of parameters against the simple order restriction. We give the likelihood ratio (LR) test statistic for the testing problem and derive its asymptotic null distribution.