The Bias Estimation of Linear Regression Model with Autoregressive Scheme using Simulation Study
Keywords:OLS, GLS, BIAS, MONTE CARLO
In regression modeling, first-order auto correlated errors are often a problem, when the data also suffers from independent variables. Generalized Least Squares (GLS) estimation is no longer the best alternative to Ordinary Least Squares (OLS). The Monte Carlo simulation illustrates that regression estimation using data transformed according to the GLS method provides estimates of the regression coefficients which are superior to OLS estimates. In GLS, we observe that in sample size $200$ and $\sigma$=3 with correlation level $0.90$ the bias of GLS $\beta_0$ is $-0.1737$, which is less than all bias estimates, and in sample size $200$ and $\sigma=1$ with correlation level $0.90$ the bias of GLS $\beta_0$ is $8.6802$, which is maximum in all levels. Similarly minimum and maximum bias values of OLS and GLS of $\beta_1$ are $-0.0816$, $-7.6101$ and $0.1371$, $0.1383$ respectively. The average values of parameters of the OLS and GLS estimation with different size of sample and correlation levels are estimated. It is found that for large samples both methods give similar results but for small sample size GLS is best fitted as compared to OLS.
Aitken, A. C. (1935). On Least Squares and Linear Combinations of Observations. Proceedings of the Royal Statistical Society , 55, 42-48.
Ayinde, K., Adedayo, D. A., & Adepoju, A. A. (2012). Estimators of Linear Regression Model with Autocorrelated Error Terms and Prediction using Correlated Uniform Regressors. International Journal of Engineering Science and Technology , 4 (11), 4629-4638.
Cheung, Y. B. (2007). A Modified Least-Squares Regression Approach to the Estimation of Risk Differences. American Journal of Epidemiology , 166 (11), 1337-1344.
Dielman, T. E. (2009). A Note on Hypothesis Tests after Correction for Autocorrelation: Solace for the Cochrane-Orcutt Method? Journal of Modern Applied Statistical Methods , 8 (1), 100-109.
Guirk, A. M., & Spanos, A. (2002). The Linear Regression Model with Autocorrelated Errors: Just Say No to Error Autocorrelation. Annual Meeting of the American Agricultural Economics Association.
Hoo, K., Tvarlapati, K., Piovoso, M., & Hajare, R. (2002). A Method of Robust Multivariate Outlier Replacement. Computers and Chemical Engineering , 26 (1), 17-39.
Kiviet, J. F. (2011). Monte Carlo Simulation for Econometricians. Foundations and Trends in Econometrics , 5 (1-2), 1-81.
Rivest, L. (1994). Statistical Properties of Winsorized Means for Skewed Distributions. Biometrika , 81 (2), 373-383.
Safi, S., & White, A. (2006). The Efficiency of OLS in the Presence of Auto-Correlated Disturbances in Regression Models. Journal of Modern Applied Statistical Methods , 5 (1), 133-143.
Suvarna, M., & Ismail, B. (2016). Estimation of Linear Regression Model with Correlated Regressors in the Presence of Autocorrelation. International Journal of Statistics and Applications , 6 (2), 35-39.
Wenning, Z., & Valenci, E. (2019). A Monte Carlo Simulation Study on the Power of Autocorrelation Tests for ARMA Models. American Journal of Undergraduate Research , 16 (3), 59-67.
Yale, C., & Forsythe, A. B. (1976). Winsorized Regression. Technometrics , 18, 291-300.
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