On Consistency of Tests for Stationarity in Autoregressive and Moving Average Models of Different Orders
American Journal of Theoretical and Applied Statistics
Volume 5, Issue 3, May 2016, Pages: 146-153
Received: Apr. 26, 2016; Accepted: May 11, 2016; Published: May 25, 2016
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Authors
Akeyede Imam, Department of Mathematics, Federal University, Lafia, Nigeria
Danjuma Habiba, Department of Statistics, Federal Polytechnic Bali, Taraba State, Nigeria
Bature Tajudeen Atanda, Department of Mathematics, Statistics Kwara State Polytechnic Ilorin, Kwara State, Nigeria
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Abstract
The most important assumptions about econometrics and time series data is stationarity, This study therefore suggests that, in trying to decide by classical methods whether economic data are stationary or not, it would be useful to perform tests of the null hypothesis of stationarity as well as tests of the null hypothesis of a unit root. The study compared power and type I error of Augmented Dickey-Fuller (ADF), Kwiatkowski, Phillips, Schmidt and Shin (KPSS) and Phillips and Perron (PP) to test the null hypothesis of stationarity against the alternative of a unit root at different order of autoregressive and moving average and various sample sizes. Simulation studies were conducted using R statistical package to investigate the performance of the tests of stationarity and unit root at sample size 20, 40, ..., 200 at first, second and third orders of autoregressive (AR), moving average (MA) and mixed autoregressive and moving average (ARMA) models. The relative performance of the tests was examined by their percentage of their powers and type I errors. The study concluded that PP is the best over all the conditions considered for the models, sample sizes and orders. However, in terms of type 1 error rate PP still is the best.
Keywords
ADF, KPSS, Stationarity, Simulation
To cite this article
Akeyede Imam, Danjuma Habiba, Bature Tajudeen Atanda, On Consistency of Tests for Stationarity in Autoregressive and Moving Average Models of Different Orders, American Journal of Theoretical and Applied Statistics. Vol. 5, No. 3, 2016, pp. 146-153. doi: 10.11648/j.ajtas.20160503.20
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Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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