Title: On the Durbin-Watson statistic based on a Z-test in large samples

Authors: Mei-Yu Lee

Addresses: Department of Applied Finance, Yuanpei University, 306, Yuanpei Str., Hsinchu 30015, Taiwan

Abstract: This paper formulates the Z-test of the Durbin-Watson (DW) statistic by the true sampling distribution of the DW statistic under the null hypothesis of no serial correlation. Two important results are determined. First, the variance of the DW statistic is convexly related to the degree of freedom, T − k − 1. Thus, the degree of freedom determines the Z-test formula of the DW test. Secondly, the law of large numbers induces the sampling distribution of the DW statistic to converge to a normal distribution.

Keywords: law of large numbers; CLT; central limit theorem; Z-test; Durbin-Watson test; Durbin-Watson statistic; large samples; variance; degree of freedom; sampling distribution.

DOI: 10.1504/IJCEE.2016.073370

International Journal of Computational Economics and Econometrics, 2016 Vol.6 No.1, pp.114 - 121

Received: 08 Oct 2014
Accepted: 17 Jun 2015

Published online: 15 Nov 2015 *

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