Departure from normality of increasing-dimension martingales
AbstractIn 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Journal of Multivariate Analysis.
Volume (Year): 100 (2009)
Issue (Month): 6 (July)
Contact details of provider:
Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
Find related papers by JEL classification:
- 60F - - - - - -
- 60B - - - - - -
- 62M - - - - - -
- Cen - Mathematical and Quantitative Methods - - - - -
- lim - - - - - -
- the - - - - - -
- Ban - Schools of Economic Thought and Methodology - - - - -
- spa - - - - - -
- Res - Urban, Rural, Regional, Real Estate, and Transportation Economics - - - - -
- aut - - - - - -
- Con - Mathematical and Quantitative Methods - - - - -
- reg - - - - - -
- App - General Economics and Teaching - - - - -
- mod - - - - - -
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Ralf BRUEGGEMANN & Helmut LUETKEPOHL & Pentti SAIKKONEN, 2004.
"Residual Autocorrelation Testing for Vector Error Correction Models,"
Economics Working Papers
ECO2004/08, European University Institute.
- 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.
- 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.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If references are entirely missing, you can add them using this form.