Volume 2, Issue 1, February 2014, Page: 1-13
Comparative Study of Portmanteau Tests for the Residuals Autocorrelation in ARMA Models
Samir K. Safi, Dept. of Economics and Statistics, Faculty of Commerce, the Islamic University of Gaza, Gaza, Palestine
Alaa A. Al-Reqep, Dept. of Statistics, Statistician Research, Gaza, Palestine
Received: Nov. 7, 2013;       Published: Dec. 10, 2013
DOI: 10.11648/j.sjams.20140201.11      View  2769      Downloads  196
Abstract
The portmanteau statistic for testing the adequacy of an autoregressive moving average (ARMA) model is based on the first m autocorrelations of the residuals from the fitted model. We consider some of portmanteau tests for univariate linear time series such as Box and Pierce [2], Ljung and Box [9], Monti [12], Peña and Rodríguez [13 and 14], Generalized Variance Test (Gvtest) by Mahdi and McLeod [11] and Fisher [4]. We conduct an extensive computer simulation time series data, to make comparison among these tests. We consider different model parameters for small, moderate and large samples to examine the effect of lag m on the power of the selected tests, and determine the most powerful test for ARMA models. The similar portmanteau tests models was evaluated for the real data set on electricity consumption in Khan Younis, Palestine (April 2009 - May 2013). We found that, portmanteau tests have the highest values of power for large sample data (N = 500) comparing to small and moderate samples (N = 50 and 200). We found that the portmanteau tests are sensitive to the chosen for m value. Indeed there are loss of the power values for lags m ranging from m = 5 to 20, where Box-Pierce, Ljung-Box and Monti tests have more power loss than the other selected tests. The power loss reaches its minimum values for large sample data comparing to small and moderate samples. In addition, the results of the simulation study and real data analysis showed that the most powerful tests varies between Gvtest and Fisher tests.
Keywords
ARMA Model, Portmanteau Test, Residual Analysis, Autocorrelation, Model Diagnostic, Simulation
To cite this article
Samir K. Safi, Alaa A. Al-Reqep, Comparative Study of Portmanteau Tests for the Residuals Autocorrelation in ARMA Models, Science Journal of Applied Mathematics and Statistics. Vol. 2, No. 1, 2014, pp. 1-13. doi: 10.11648/j.sjams.20140201.11
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