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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 545413, 8 pages
Research Article

Mixed Portmanteau Test for Diagnostic Checking of Time Series Models

College of Statistical and Actuarial Sciences, University of the Punjab, Lahore, Pakistan

Received 1 April 2014; Revised 26 May 2014; Accepted 27 May 2014; Published 15 June 2014

Academic Editor: Li Weili

Copyright © 2014 Sohail Chand and Shahid Kamal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Model criticism is an important stage of model building and thus goodness of fit tests provides a set of tools for diagnostic checking of the fitted model. Several tests are suggested in literature for diagnostic checking. These tests use autocorrelation or partial autocorrelation in the residuals to criticize the adequacy of fitted model. The main idea underlying these portmanteau tests is to identify if there is any dependence structure which is yet unexplained by the fitted model. In this paper, we suggest mixed portmanteau tests based on autocorrelation and partial autocorrelation functions of the residuals. We derived the asymptotic distribution of the mixture test and studied its size and power using Monte Carlo simulations.