Estimators of Linear Regression Model with Non-Spherical Disturbance: Evidence from Nigerian Inflation-Trend and Economic Time Series Data
DOI:
https://doi.org/10.62054/ijdm/0204.19Abstract
Ordinary Least Squares (OLS) estimation loses efficiency when some of the linear regression assumptions about error terms are violated. These conditions are common in applied econometrics. The research proposes four new estimators, each with two weight structures (W1 and W2), to address violations of no autocorrelation and homoscedasticity in the error terms, commonly referred to as non-spherical disturbances. The proposed estimators are: the Maximum Likelihood Weighted Estimator (MLWE), the Weighted Maximum Likelihood Estimator (WMLE), the Cochrane–Orcutt Weighted Estimator (COWE), and the Weighted Cochrane–Orcutt Estimator (WCOE). Monte Carlo simulations across different sample sizes demonstrate that OLS exhibits substantial error in small samples, whereas the proposed estimators consistently maintain low error and significant efficiency gains. Among the estimators, MLWE W2 and COWE W2 demonstrated the strongest performance across scenarios. Application to Nigerian macroeconomic data confirms the simulation results: diagnostic tests reveal violations of OLS assumptions, and the alternative estimators delivered more precise coefficients, smaller standard errors, and higher explanatory power. These findings underscore the value of the proposed methods as practical and robust alternatives to OLS, particularly in settings where heteroscedasticity and autocorrelation co-occur.
References
Ayinde, K. (2006). A comparative study of the performances of the OLS and some GLS estimators when regressors are both stochastic and collinear. West African Journal of Biophysics and Biomathematics, 2, 54–67.
Ayinde, K., & Ipinyomi, R. A. (2007). A comparative study of the OLS and some GLS estimators when normally distributed regressors are stochastic. Trends in Applied Sciences Research, 2(4), 354–359.
Ayinde, K., & Lukman, F. L. (2013). Combined estimators as alternative to multicollinearity estimation methods. International Journal of Current Research, 6(1), 4505–4510.
Ayinde, K., Bello, A. A., Ayinde, O. E., & Adekanmbi, D. B. (2014). Modeling Nigerian government revenue and total expenditure: Combined estimators’ analysis and error correction model approach. Central European Journal of Economic Modeling and Econometrics, 7, 1–14.
Ayinde, K., Kuranga, J., & Lukman, A. F. (2015). Modeling Nigerian government expenditure, revenue and economic growth: Cointegration, error correction mechanism and combined estimators’ analysis approach. Asian Economic and Financial Review, 5(6), 858–869.
Bai, J., Choi, S. H., & Liao, Y. (2021). Feasible generalized least squares for panel data with cross-sectional and serial correlations. Empirical Economics, 60(1), 309–326. https://doi.org/10.1007/s00181-020-01977-2
Baltagi, B. H. (2021). Econometrics (6th ed.). Springer. https://doi.org/10.1007/978-3-030-80149-6
Cochrane, D., & Orcutt, G. H. (1949). Application of least squares regression to relationships containing autocorrelated error terms. Journal of the American Statistical Association, 44(245), 32–61. https://doi.org/10.1080/01621459.1949.10483290
Davidson, R., & MacKinnon, J. G. (2004). Econometric theory and methods. Oxford University Press.
Fomby, T. B., Hill, R. C., & Johnson, L. (1988). Applied Econometric Time Series. Academic Press.
Gafarov, B. (2023). Generalized Automatic Least Squares: Efficiency gains from misspecified heteroscedasticity models (arXiv:2304.07331). arXiv. https://doi.org/10.48550/arXiv.2304.07331
Greene, W. H. (2018). Econometric Analysis (8th ed.). Pearson Education.
Gujarati, D. N., & Porter, D. C. (2009). Basic Econometrics (5th ed.). McGraw-Hill/Irwin.
Hansen, B. E. (2022). Econometrics. Princeton University Press.
Hildreth, C., & Lu, J. Y. (1960). Demand relationships with autocorrelated disturbances (Statistical Bulletin No. 276). Michigan State University Agricultural Experiment Station.
Kleiber, C. (2001). Finite sample efficiency of OLS in linear regression models with long-memory disturbances. Economics Letters, 72(2), 131–136. https://doi.org/10.1016/S0165-1765(01)00435-8
Kramer, N. (1980). Introduction to Econometrics. Harper & Row.
Lukman, A. F., Arowolo, O., & Ayinde, K. (2014). Some robust ridge regression methods for handling multicollinearity and outliers. International Journal of Sciences: Basic and Applied Research, 16(2), 192–202.
Maddala, G. S. (2002). Introduction to Econometrics (3rd ed.). Wiley.
Moriya, K., & Noda, A. (2025). A note on the asymptotic properties of the GLS estimator in multivariate regression with heteroskedastic and autocorrelated errors (arXiv:2503.13950). arXiv. https://doi.org/10.48550/arXiv.2503.13950
Newey, W. K., & West, K. D. (1987). A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix, Econometrica, 55(3), 703–708. https://doi.org/10.2307/1913610
Prais, S. J., & Winsten, C. B. (1954). Trend Estimators and Serial Correlation. Econometrica, 22(2), 195–218. https://doi.org/10.2307/1907187
Stock, J. H., & Watson, M. W. (2020). Introduction to econometrics (4th ed.). Pearson.
White, H. (1980). A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity, Econometrica, 48(4), 817–838. https://doi.org/10.2307/1912934
Wooldridge, J. M. (2010). Econometric Analysis of Cross-Section and Panel Data (2nd ed.). MIT Press.
Wooldridge, J. M. (2016). Introductory Econometrics: A Modern Approach (6th ed.). Cengage Learning
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Olusegun O. Alabi, Saidi O. Lawal, Toba T. Bamidele, Abimbola H. Bello (Author)
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors are solely responsible for obtaining permission to reproduce any copyrighted material contained in the manuscript as submitted. Any instance of possible prior publication in any form must be disclosed at the time the manuscript is submitted and a
copy or link to the publication must be provided.
The Journal articles are open access and are distributed under the terms of the Creative
Commons Attribution-NonCommercial-NoDerivs 4.0 IGO License, which permits use,
distribution, and reproduction in any medium, provided the original work is properly cited.
No modifications or commercial use of the articles are permitted.
