Departure from normality of increasing-dimension martingales
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.
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Volume (Year): 100 (2009)
Issue (Month): 6 (July)
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- Lewis, Richard & Reinsel, Gregory C., 1985. "Prediction of multivariate time series by autoregressive model fitting," Journal of Multivariate Analysis, Elsevier, vol. 16(3), pages 393-411, June.
- Bruggemann, Ralf & Lutkepohl, Helmut & Saikkonen, Pentti, 2006.
"Residual autocorrelation testing for vector error correction models,"
Journal of Econometrics,
Elsevier, vol. 134(2), pages 579-604, October.
- Ralf BRUEGGEMANN & Helmut LUETKEPOHL & Pentti SAIKKONEN, 2004. "Residual Autocorrelation Testing for Vector Error Correction Models," Economics Working Papers ECO2004/08, European University Institute.
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