Departure from normality of increasing-dimension martingales

JOURNAL OF MULTIVARIATE ANALYSIS

卷:100

Article

Arbues, Ignacio

关键词: Central limit theorem;    Banach spaces;    Residual autocorrelation;    Confidence regions;    Approximate models;   

DOI  :  10.1016/j.jmva.2008.11.004

来源: Elsevier

【 摘 要 】

In this paper, we consider sequences of vector martingale differences of increasing dimension. We show that the Kantorovich distance from the distribution of the k(n)-dimensional average of n martingale differences to the corresponding Gaussian distribution satisfies certain inequalities. As a consequence, if the growth of k(n) is not too fast, then the Kantorovich distance converges to zero. Two applications of this result are presented. The first is a precise proof of the asymptotic distribution of the multivariate portmanteau statistic applied to the residuals of an autoregressive model and the second is a proof of the asymptotic normality of the estimates of a finite autoregressive model when the process is an AR(infinity) and the order of the model grows with the length of the series. (C) 2008 Elsevier Inc. All rights reserved.

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