Departure from normality of increasing-dimension martingales

Ignacio Arbus
Authors registered in the RePEc Author Service: Ignacio Arbués

Journal of Multivariate Analysis, 2009, vol. 100, issue 6, 1304-1315

Abstract: 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.

Keywords: 60F05; 60B12; 62M10; Central; limit; theorem; Banach; spaces; Residual; autocorrelation; Confidence; regions; Approximate; models (search for similar items in EconPapers)
Date: 2009
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