کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1146653 | 957522 | 2009 | 12 صفحه PDF | دانلود رایگان |
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)k(n)-dimensional average of nn martingale differences to the corresponding Gaussian distribution satisfies certain inequalities. As a consequence, if the growth of k(n)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(∞∞) and the order of the model grows with the length of the series.
Journal: Journal of Multivariate Analysis - Volume 100, Issue 6, July 2009, Pages 1304–1315