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Using GLS to Generate Forecasts in Regression Models with Auto-correlated Disturbances with simulation and Palestinian Market Index Data

Received: 12 December 2013     Published: 30 December 2013
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Abstract

This paper involves an important statistical problem concerning forecasting in regression models in time series processes. It is well known that the most famous method of estimating and forecasting is the Ordinary Least Squares (OLS). OLS may be not the optimal in this context. So over the years many specialized estimation techniques have been developed, for example Generalized Least Squares (GLS). We are comparing the forecasting based on some estimators with the prediction using the GLS estimate. This comparison will be used by what is known as measures of forecast accuracy. We conduct an extensive computer simulation time series data, to make comparison among these methods. The similar forecasting criteria were developed and evaluated for the real data set on daily closing price in the Palestinian market index (Alquds Index). The data consists of 164 monthly observations and obtained from the website of the Palestine Stock Exchange. The main finding is that, for forecasting purposes there is not much gained in trying to identifying the exact order and form of the auto-correlated disturbances by using GLS estimation method. In addition, we noticed that the accuracy of forecasting using GLS method does not differ substantially than the other methods as Maximum Likelihood Estimation (MLE), Minimize Conditional Sum of Squares (CSS) and the combination of these two methods. Moreover, for parameter estimation, the GLS is nearly as efficient as the exact parameter estimation. On the other hand, the Ordinary Least Squares (OLS) method performs much less efficient than the other estimation methods and producing poor forecasting accuracy.

Published in American Journal of Theoretical and Applied Statistics (Volume 3, Issue 1)
DOI 10.11648/j.ajtas.20140301.12
Page(s) 6-17
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

Keywords

Generalized Least Squares, Ordinary Least Squares, Maximum Likelihood, Forecasting Accuracy, Simulation

References
[1] Abraham, B. and Ledolter, J. (2005). Statistical methods for forecasting. John Wiley & Sons, Inc.
[2] Cochrane, J. H. (2005). Time Series for Macroeconomics and Finance. University of Chicago.
[3] Cryer, J. and Chan, K. (2008). Time Series Analysis With Applications in R, 2nd Ed. Springer Science + Business Media, LLC.
[4] Everitt, B. S. and Hothorn, I. (2010). A Handbook of Statistical Analyses Using R, 2nd Ed. Taylor and Francis Group, LLC.
[5] Findley, D. (2003). Properties of Forecast Errors and Estimates of Misspecified RegARIMA and Intermediate Memory Models and the Optimality of GLS for One-Step-Ahead Forecasting. Methodology and Standards Directorate U.S. Bureau of the Census Washington D.C. 20233.
[6] Fox, J. (2002). Time-Series Regression and Generalized Least Squares. Appendix to An R and S-PLUS Companion to Applied Regression.
[7] Koreisha, G. and Fang, Y. (2004). Forecasting with serially correlated regression models. Journal of Statistical Computation and Simulation Vol. 74(9), 625–649.
[8] Lee, J. and Lund, R. (2004). Revisiting simple linear regression with autocorrelated errors, Biometrika, Vol. 91 (1): 240-245. doi: 10.1093/biomet/91.1.240
[9] Ojo, J. and Olatayo, T. (2009). On the Estimation and Performance of Subset Autoregressive Integrated Moving Average Models. European Journal of Scientific Research ISSN 1450-216X Vol.28 (2), 287-293.
[10] Safi, S. (2004). The efficiency of OLS in the presence of auto-correlated disturbances in regression models. PhD dissertation, American University Washington, D.C. 20016.
[11] Shittu, O.I. and Asemota, M.J. (2009). Comparison of Criteria for Estimating the Order of Autoregressive Process: A Monte Carlo Approach. European Journal of Scientific Research ISSN 1450-216X Vol. 30(3), 409-416.
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  • APA Style

    Samir K. Safi, Ehab A. Abu Saif. (2013). Using GLS to Generate Forecasts in Regression Models with Auto-correlated Disturbances with simulation and Palestinian Market Index Data. American Journal of Theoretical and Applied Statistics, 3(1), 6-17. https://doi.org/10.11648/j.ajtas.20140301.12

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    ACS Style

    Samir K. Safi; Ehab A. Abu Saif. Using GLS to Generate Forecasts in Regression Models with Auto-correlated Disturbances with simulation and Palestinian Market Index Data. Am. J. Theor. Appl. Stat. 2013, 3(1), 6-17. doi: 10.11648/j.ajtas.20140301.12

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    AMA Style

    Samir K. Safi, Ehab A. Abu Saif. Using GLS to Generate Forecasts in Regression Models with Auto-correlated Disturbances with simulation and Palestinian Market Index Data. Am J Theor Appl Stat. 2013;3(1):6-17. doi: 10.11648/j.ajtas.20140301.12

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  • @article{10.11648/j.ajtas.20140301.12,
      author = {Samir K. Safi and Ehab A. Abu Saif},
      title = {Using GLS to Generate Forecasts in Regression Models with Auto-correlated Disturbances with simulation and Palestinian Market Index Data},
      journal = {American Journal of Theoretical and Applied Statistics},
      volume = {3},
      number = {1},
      pages = {6-17},
      doi = {10.11648/j.ajtas.20140301.12},
      url = {https://doi.org/10.11648/j.ajtas.20140301.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20140301.12},
      abstract = {This paper involves an important statistical problem concerning forecasting in regression models in time series processes. It is well known that the most famous method of estimating and forecasting is the Ordinary Least Squares (OLS). OLS may be not the optimal in this context. So over the years many specialized estimation techniques have been developed, for example Generalized Least Squares (GLS). We are comparing the forecasting based on some estimators with the prediction using the GLS estimate. This comparison will be used by what is known as measures of forecast accuracy. We conduct an extensive computer simulation time series data, to make comparison among these methods. The similar forecasting criteria were developed and evaluated for the real data set on daily closing price in the Palestinian market index (Alquds Index). The data consists of 164 monthly observations and obtained from the website of the Palestine Stock Exchange. The main finding is that, for forecasting purposes there is not much gained in trying to identifying the exact order and form of the auto-correlated disturbances by using GLS estimation method. In addition, we noticed that the accuracy of forecasting using GLS method does not differ substantially than the other methods as Maximum Likelihood Estimation (MLE), Minimize Conditional Sum of Squares (CSS) and the combination of these two methods. Moreover, for parameter estimation, the GLS is nearly as efficient as the exact parameter estimation. On the other hand, the Ordinary Least Squares (OLS) method performs much less efficient than the other estimation methods and producing poor forecasting accuracy.},
     year = {2013}
    }
    

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  • TY  - JOUR
    T1  - Using GLS to Generate Forecasts in Regression Models with Auto-correlated Disturbances with simulation and Palestinian Market Index Data
    AU  - Samir K. Safi
    AU  - Ehab A. Abu Saif
    Y1  - 2013/12/30
    PY  - 2013
    N1  - https://doi.org/10.11648/j.ajtas.20140301.12
    DO  - 10.11648/j.ajtas.20140301.12
    T2  - American Journal of Theoretical and Applied Statistics
    JF  - American Journal of Theoretical and Applied Statistics
    JO  - American Journal of Theoretical and Applied Statistics
    SP  - 6
    EP  - 17
    PB  - Science Publishing Group
    SN  - 2326-9006
    UR  - https://doi.org/10.11648/j.ajtas.20140301.12
    AB  - This paper involves an important statistical problem concerning forecasting in regression models in time series processes. It is well known that the most famous method of estimating and forecasting is the Ordinary Least Squares (OLS). OLS may be not the optimal in this context. So over the years many specialized estimation techniques have been developed, for example Generalized Least Squares (GLS). We are comparing the forecasting based on some estimators with the prediction using the GLS estimate. This comparison will be used by what is known as measures of forecast accuracy. We conduct an extensive computer simulation time series data, to make comparison among these methods. The similar forecasting criteria were developed and evaluated for the real data set on daily closing price in the Palestinian market index (Alquds Index). The data consists of 164 monthly observations and obtained from the website of the Palestine Stock Exchange. The main finding is that, for forecasting purposes there is not much gained in trying to identifying the exact order and form of the auto-correlated disturbances by using GLS estimation method. In addition, we noticed that the accuracy of forecasting using GLS method does not differ substantially than the other methods as Maximum Likelihood Estimation (MLE), Minimize Conditional Sum of Squares (CSS) and the combination of these two methods. Moreover, for parameter estimation, the GLS is nearly as efficient as the exact parameter estimation. On the other hand, the Ordinary Least Squares (OLS) method performs much less efficient than the other estimation methods and producing poor forecasting accuracy.
    VL  - 3
    IS  - 1
    ER  - 

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Author Information
  • Dept. of Economics and Statistics, Faculty of Commerce, the Islamic University of Gaza, Gaza, Palestine

  • Statistician Researcher, Gaza, Palestine

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