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), 2024. Published by Science Publishing Group |
Generalized Least Squares, Ordinary Least Squares, Maximum Likelihood, Forecasting Accuracy, Simulation
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| [7] | Koreisha, G. and Fang, Y. (2004). Forecasting with serially correlated regression models. Journal of Statistical Computation and Simulation Vol. 74(9), 625–649. |
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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
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
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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Download@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}
}
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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