Robust estimation technique and robust autocorrelation diagnostic for multiple Linear Regression Model with autocorrelated errors

Autocorrelated errors cause the Ordinary Least Squares (OLS) estimators to become inefficient. Hence, it is very essential to detect the autocorrelated errors. The Breusch-Godfrey (BG) test is the most commonly used test for detection of autocorrelated errors. Since this test is easily affected by high leverage points, the robust Modified Breusch-Godfrey (MBG) test is proposed. The results of the study indicate that the MBG test is a robust test to detect the autocorrelated errors. Thus far, there is no specific method proposed to identify high leverage points in linear model with autocorrelated errors. Hence, the Diagnostic Robust Generalized Potentials Based on Index Set Equality (DRGP(ISE)) is proposed to close the gap in the literature. The findings indicate that DRGP(ISE) is an excellent and fast identification method to detect the high leverage in linear model with autocorrelated errors. High leverage points have tremendous effect in regression analysis. In this study we verified that high leverage points is another cause of autocorrelation. Not much research has been done to investigate autocorrelation-influential observations. Hence, the Robust Autocorrelation-Influential Measure based on DRGP (RAIM(DRGP)) is formulated to identify the autocorrelation-influential observations in autocorrelated data. The RAIM(DRGP) is found to do a credible job to identify the high leverage autocorrelation-enhancing and autocorrelation -reducing observations and autocorrelation-influential observations. Cochrane-Orcutt Prais-Winsten (COPW) iterative method is the most commonly used remedial measure to rectify the autocorrelation problems. However, this procedure is extremely vulnerable in the presence of high leverage points. On the other hand, the autocorrelation may be caused by the presence of high leverage points. The Robust Cochrane-Orcutt Prais-Winsten (RCOPW) iterative method is therefore developed. The results of the study show that RCOPW estimation is a robust remedial measure in the case when the autocorrelated data come together with the presence of high leverage points and also in the autocorrelation caused by the high leverage points. The existing diagnostic plot does not take into the consideration of autocorrelated errors. Thus, the robust remedial of autocorrelated errors - Robust Cochrane-Orcutt Prais-Winsten (RCOPW) is incorporated in the diagnostic plot to form the Diagnostic Plot for Autocorrelation Based on Standardized Cochrane-Orcutt Prais-Winsten Residuals (DPA-RCOPW). The results based on simulated autocorrelated data and well known outlying datasets show that DPA-RCOPW successfully identifies and classifies the outlying observations according to its types precisely. In this study, an alternative method of finding confidence intervals of regression parameters for autocorrelated data in the presence of high leverage points and for autocorrelation caused by high leverage points is proposed. The findings provide strong evidences that the Diagnostic Before Bootstrap based on Robust Cochrane-Orcutt Prais-Winsten estimate (DBB RCOPW) estimate is a robust procedure and consistently provides close answers to the actual confidence intervals of the regression parameters for data with autocorrelated errors in the presence of high leverage points and for autocorrelation caused by high leverage points.

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