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.
| Published in | Science Journal of Applied Mathematics and Statistics (Volume 2, Issue 1) |
| DOI | 10.11648/j.sjams.20140201.11 |
| Page(s) | 1-13 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2013. Published by Science Publishing Group |
ARMA Model, Portmanteau Test, Residual Analysis, Autocorrelation, Model Diagnostic, Simulation
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| [6] | Kwan, A.C.C. and Wu, Y. (1997). "Further results on the finite sample distribution of Monti’s portmanteau test for the adequacy of an ARMA (p, q) model". Biometrika, Vol. 84(3), pp. 733-736. |
| [7] | Kwan, A.C.C., Sim, A. and Wu, Y. (2005). "A comparative study of finite-sample performance of some portmanteau tests for randomness of a time series", Computational Statistics and Data Analysis, Vol. 48, pp. 391-413. |
| [8] | Ljung, G.M. (1986). "Diagnostic testing of univariate time series models". Biometrika, Vol. 73(3), pp. 725-30. |
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APA Style
Samir K. Safi, Alaa A. Al-Reqep. (2013). Comparative Study of Portmanteau Tests for the Residuals Autocorrelation in ARMA Models. Science Journal of Applied Mathematics and Statistics, 2(1), 1-13. https://doi.org/10.11648/j.sjams.20140201.11
ACS Style
Samir K. Safi; Alaa A. Al-Reqep. Comparative Study of Portmanteau Tests for the Residuals Autocorrelation in ARMA Models. Sci. J. Appl. Math. Stat. 2013, 2(1), 1-13. doi: 10.11648/j.sjams.20140201.11
AMA Style
Samir K. Safi, Alaa A. Al-Reqep. Comparative Study of Portmanteau Tests for the Residuals Autocorrelation in ARMA Models. Sci J Appl Math Stat. 2013;2(1):1-13. doi: 10.11648/j.sjams.20140201.11
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Download@article{10.11648/j.sjams.20140201.11,
author = {Samir K. Safi and Alaa A. Al-Reqep},
title = {Comparative Study of Portmanteau Tests for the Residuals Autocorrelation in ARMA Models},
journal = {Science Journal of Applied Mathematics and Statistics},
volume = {2},
number = {1},
pages = {1-13},
doi = {10.11648/j.sjams.20140201.11},
url = {https://doi.org/10.11648/j.sjams.20140201.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20140201.11},
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.},
year = {2013}
}
TY - JOUR T1 - Comparative Study of Portmanteau Tests for the Residuals Autocorrelation in ARMA Models AU - Samir K. Safi AU - Alaa A. Al-Reqep Y1 - 2013/12/10 PY - 2013 N1 - https://doi.org/10.11648/j.sjams.20140201.11 DO - 10.11648/j.sjams.20140201.11 T2 - Science Journal of Applied Mathematics and Statistics JF - Science Journal of Applied Mathematics and Statistics JO - Science Journal of Applied Mathematics and Statistics SP - 1 EP - 13 PB - Science Publishing Group SN - 2376-9513 UR - https://doi.org/10.11648/j.sjams.20140201.11 AB - 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. VL - 2 IS - 1 ER -
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