Scholarly works

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Bootstrap approach for estimating seemingly unrelated regressions with varying degrees of autocorrelated disturbances
(2013) Ebukuyo, O. B.; Adepoju, A. A.; Olamide, E. I.
The Seemingly Unrelated Regressions (SUR) model proposed in 1962 by Arnold Zellner has gained a wide acceptability and its practical use is enormous. In this research, two methods of estimation techniques were examined in the presence of varying degrees of _rst order Autoregressive [AR(1)] coefficients in the error terms of the model. Data was simulated using bootstrapping approach for sample sizes of 20, 50, 100, 500 and 1000. Performances of Ordinary Least Squares (OLS) and Generalized Least Squares (GLS) estimators were examined under a definite form of the variance-covariance matrix used for estimation in all the sample sizes considered. The results revealed that the GLS estimator was efficient both in small and large sample sizes. Comparative performances of the estimators were studied with 0.3 and 0.5 as assumed coefficients of AR(1) in the first and second regressions and these coefficients were further interchanged for each regression equation, it was deduced that standard errors of the parameters decreased with increase in the coefficients of AR(1) for both estimators with the SUR estimator performing better as sample size increased. Examining the performances of the SUR estimator with varying degrees of AR(1) using Mean Square Error (MSE), the SUR estimator performed better with autocorrelation coefficient of 0.3 than that of 0.5 in both regression equations with best MSE obtained to be 0.8185 using _ = 0:3 in the second regression equation for sample size of 50. Key words: Autocorrelation||Bootstrapping||Generalized least squares||Ordinary least squares||Seemingly unrelated regressions
Efficiency in linear model with AR (1) and correlated error-regressor
(African Research Review, 2009-04) Olutunji., O.J.; Adepoju., A.A
In this study, we conduct several Monte-Carlo experiments to examine the sensitivity of the estimators relative to OLS using the Variance and RMSE criteria, in the presence of first order autocorrelated error terms which are also correlated with geometric regressor. We examine the of efficiency to ı, _, as well as, its asymptotic behaviour, N, when the above two assumptions are violated. We observe that CORC and HILU give similar result, same for ML and MLGRID. OLS is more efficient than CORC and HILU while ML and MLGRID dominate OLS. In the scenarios, efficiency does increase with increase in autocorrelation level, only ML and MLGRID at _ = 0.05 show that efficiency increases with increase in autocorrelation level. All estimators show that efficiency reducesas significant level increases only when the autocorrelation value and samplesize are small (_ = 0.4, N = 20). There is more efficiency gain when N and _are large at all significant correlation levels. Asymptotically, the efficiency of FGLS estimators increase with increasing autocorrelation but it is in different to the correlation levels. The asymptotic ranking is CORC and HILU followed by MLGRID and ML.
Estimating seemingly unrelated regressions with first order autoregressive disturbances
(CSCanada, 2013-05) Olamide, E. I.; Adepoju, A. A.
In Seemingly Unrelated Regressions (SUR) model, disturbances are assumed to be correlated across equations and it will be erroneous to assume that disturbances behave independently, hence, the need for an efficient estimator. Literature has revealed gain in efficiencyof the SUR estimator over the Ordinary Least Squares (OLS) estimator when the errors are correlated across equations. This work, however, considers methods of estimating a set of regression equations when disturbances are both contemporaneously and serially correlated. The Feasible Generalized Least Squares (FGLS), OLS and Iterative Ordinary Least Squares (IOLS) estimation techniques were considered and the form of autocorrelation examined. Prais-Winstein transformation was conducted on simulated data for the different sample sizes used to remove autocorrelations. Results from simulation studies showed that the FGLS was efficient both in small samples and large samples. Comparative performances of the estimators were investigated on the basis of the standard errors of the parameter estimates when estimating the model with and without AR(1) and the results showed that the estimators performed better with AR(1) as the sample size increased especially from 20. On the criterion of the Root Mean Square, the FGLS was found to have performed better with AR(1) and it was revealed that bias reduces as sample size increases. In all cases considered, the SUR estimator performed best. It was consistently most efficient than the OLS and IOLS estimators
Simultaneous equation estimation with first order auto correlated disturbances
(2013-08) Ojo, Y. O.; Adepoju, A. A.
The estimation of the parameters of simultaneous equation problem is usually affected by the existence of mutual correlation between pairs of random deviates, which is a violation of the assumption of no autocorrelation between the error terms. In practice the form of correlation between the pairs of random deviates is not known. This study therefore examined a two-equation model in which the correlation between the random deviates is assumed to follow a first-order Autoregressive [AR (1)] process. Data was simulated using Monte Carlo approach with varying sample sizes each replicated 1000 times. The behaviour of OLS, 2SLS, LIML and 3SLS were evaluated using Variance, Root Mean Square Error (RMSE) and Absolute Bias (AB). The absolute bias estimates decrease in most cases as the sample size increases. The variances obtained by all the estimators reduced consistently as the sample size increases. There was no clear pattern in the behaviour of the RMSE across sample sizes. The results for = 0.3 were better than when = 0.0 with respect to each criterion but retained the same pattern. This work established that when was different from zero, the estimators performed better, hence the choice of should be carefully made as this may significantly affect the performances of the estimators