A Robust Principal Component Analysis for Estimating Economic Growth in Nigeria in the Presence of Multicollinearity and Outlier

Authors

A. Ebiwonjumi, School of Mathematics, Statistics and Computer Science, University of KwaZulu, Natal, Durban, South AfricaFollow
R. Chifurira, School of Mathematics, Statistics and Computer Science, University of KwaZulu, Natal, Durban, South AfricaFollow
K. Chinhamu, School of Mathematics, Statistics and Computer Science, University of KwaZulu, Natal, Durban, South AfricaFollow

Author Country (or Countries)

South Africa

Abstract

This study examined economic growth (RGDP) in relation to internal debt (INDT), external debt (EXDT), interest rate (RINR), exchange rate (REXR) and trade openness (OPEN) in the presence of multicollinearity and outlier. A quarterly data gathered from Central Bank of Nigeria from 1986 to 2021 were used. Exploratory data analysis and diagnostic carried out using variance inflation factor and Grubb’s test revealed linear relation among the variables under investigation and ascertained the presence of multicollinearity and outlier in the data set. The principal component analysis revealed that INDT and EXDT accounts for 38.4% and 29.2% of the variance and as such their component PINDT and PEXDT were chosen to reduce the collinearity. Also, a robust M-estimation method results revealed that the impact of PINDT, PEXDT, RINR, REXR and OPEN on the RGDP were positive and significant for PEXDT and OPEN on the RGDP. Specifically, PINDT, PEXDT, RINR, REXR and OPEN increased the Nigeria’s economic growth to the turn of 0.10%, 0.02%, 0.04%, 0.06% and 3.01% respectively during the period under consideration. Consequently, combining principal component with M-estimator of weighted bisquare with 4.685 turning and median centered as scale was revealed as the most efficient estimation technique that jointly addressed the two identified assumptions violation. This was based on predictive power of the fitted model that revealed M-estimator had minimum root mean square error (RMSE) and mean absolute error (MAE) when compared with the S-estimator and MM-estimator respectively. Therefore, it be concluded that economic challenges witnessed during the period under study greatly affected the identified determinants which in turn translated to the economic growth. Hence, a robust principal component regression technique remains the best and unbiased technique for modeling and estimating the parameters of a linear model when multicollinerity and outliers were jointly present in the data set. Keywords:

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/jsap/120224

Recommended Citation

Ebiwonjumi, A.; Chifurira, R.; and Chinhamu, K. (2023) "A Robust Principal Component Analysis for Estimating Economic Growth in Nigeria in the Presence of Multicollinearity and Outlier," Journal of Statistics Applications & Probability: Vol. 12: Iss. 2, Article 25.
DOI: http://dx.doi.org/10.18576/jsap/120224
Available at: https://digitalcommons.aaru.edu.jo/jsap/vol12/iss2/25