Exploring the Behaviour and Modelling the Timeseries of Six (6) Securities

Abstract

This study explores the behaviour and models the time series of six selected securities in Nigeria, comprising five sectoral indices and the Nigerian exchange rate (USDNGN), using daily data from the Nigerian Exchange Limited (NGX). The objective is to evaluate the empirical characteristics of these financial time series and identify appropriate models for capturing their volatility dynamics. To achieve this, a suite of volatility models, including ARCH, GARCH, EGARCH, TGARCH, GARCH-M, and PARCH, were applied to the dataset. Model performance was assessed using widely recognized statistical criteria, including Akaike’s Information Criterion (AIC), Schwarz’s Bayesian Information Criterion (SBIC), Hannan-Quinn Information Criterion (HQIC), and Log-Likelihood values. The models were evaluated for their ability to capture key features such as volatility clustering, asymmetry, and persistence in returns. The results reveal that the logistic distribution provides a better fit for the return distributions of the examined securities compared to traditional normal or lognormal assumptions, due to its ability to account for heavy tails and skewness. Furthermore, among the volatility models, those incorporating asymmetry and power effects, particularly PARCH, demonstrated superior performance, highlighting the importance of model selection in financial time series analysis. This research contributes to the growing literature advocating for more flexible distributional assumptions and advanced volatility models in financial modelling. The findings offer valuable insights for investors, financial analysts, and policymakers seeking to enhance risk assessment and forecasting accuracy in emerging markets like Nigeria.