A HYBRID APPROACH TO FORECASTING STOCK INDICES USING THE ARMA–GARCH AND ARMA–EGARCH MODELS: EVIDENCE FROM THE NIGERIAN STOCK EXCHANGE
Abstract
The modeling of stock indices on the Nigerian Stock Exchange (NSE) has been carried out using Gaussian-related distributions even when the observed data are not normal. It is necessary to incorporate distributions that are non-normal. Therefore, this study examined the application of clas-sical and hybrid econometric models to forecast the daily movements of the Nigerian Stock Exchange Index (NSE 30). Five competing models were evalu-ated: the Autoregressive Integrated Moving Average (ARIMA), the Generalized Autoregressive Conditional Heteroskedasticity (GARCH), the Exponential GARCH (EGARCH), and two hybrid extensions that combine mean and variance equations, namely ARIMA–GARCH and ARIMA–EGARCH. Preliminary time–series diagnostics, including stationarity, normality, autocorrelation, and heteroskedasticity tests, revealed that the log–return series is stationary, non–normally distributed, and characterised by conditional volatility clustering. The ARIMA(1,1,2) model, identified through the Akaike Information Criterion, served as the baseline specification for subsequent volatility modelling. Empirical analysis indicates that incorporating volatility dynamics substan-tially enhances forecasting performance. The EGARCH(1,1) model captures leverage effects in the NSE 30 series by giving greater weight to negative shocks, while the symmetric GARCH(1,1) model explains volatility persistence. When combined with ARIMA, both hybrid models deliver the most accurate forecasts, with identical lowest error values, and the DieboldMariano test confirms their clear superiority over the standalone ARIMA model.
References
[2] A. A. Adebiyi, A. O. Adewumi, C. K. Ayo. Stock Price Prediction Using the ARIMA Model. UKSim-AMSS 16th Int. Conf. on Computer Modelling and Simulation (2014), 106–112.
[3] P. Zikova, J. Vesela. Forecasting Stock Market Indices Using ARIMA and ARIMA–GARCH Models. Journal of Risk and Financial Management. 16(1) (2023), 1–22.
[4] S. Li. Stock Closing Price Prediction Based on the ARIMA-GARCH Model. Financial & Business Economics Management (FBEM) (2023).
[5] R. Pandey. Stock Price Prediction: An Integrated Review of Traditional and Modern Com-putational Models. SSRN Working Paper (2025).
[6] M. Adhikari. Forecasting Stock Index Closing Points Using ARIMA-GARCH with a Rolling Data Window. Int. J. Science and Research Archive. 13(1) (2024), 3115–3125.
[7] R. F. Engle. Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica. 50(4) (1982), 987–1007.
[8] T. Bollerslev. Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econo-metrics. 31 (1986), 307–327.
[9] S. Schmidt. Forecasting Nordic Stock Market Volatility During COVID-19 Using GARCH Family Models. Ume School of Business, Economics and Statistics, Ume University (2021).
[10] P. D. Yoo. Forecasting the KOSPI Stock Index Using an Autoregressive Integrated Moving Average Model. Asia–Pacific Financial Markets. 14(1) (2007), 1–16.
[11] S. Toma. Empirical Comparison of ARIMA and GARCH Models for Stock Price Forecast-ing. Informatica Economica. 27(3) (2023), 61–72.
[12] M. Gao. Research on the Application of ARIMA–GARCH Model in Stock Price Forecasting. E3S Web of Conferences. 276 (2021), 02030.
[13] F. X. Diebold, R. S. Mariano. Comparing Predictive Accuracy. Journal of Business & Economic Statistics. 13(3) (1995), 253–263.
[14] U. Triacca. The Diebold–Mariano Test: Comparing Predictive Accuracy of Two Forecasts. Lecture Notes, University of LAquila (2016).
[15] C. M. Jarque, A. K. Bera. Efficient Tests for Normality, Homoscedasticity and Serial Independence of Regression Residuals. Economics Letters. 6 (1980), 255–259.
[16] G. M. Ljung, G. E. P. Box. On a Measure of Lack of Fit in Time Series Models. Biometrika. 65(2) (1978), 297–303.
[17] M. I. Ekum, T. O. Owolabi, T. Alakija. Modeling Volatility in Selected Nigerian Stock Market. Int. J. Economics and Financial Management. 3(1) (2018), 30–43.
[18] G. E. P. Box, G. M. Jenkins, G. C. Reinsel, G. M. Ljung. Time Series Analysis: Forecasting and Control. John Wiley & Sons. New Jersey (2008).
[19] X. Huang, P. You, X. Gao, D. Cheng. Stock Price Prediction Based on ARIMA-GARCH and LSTM. Proceedings of ICBIS (2023), 438–448.
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