Abstract

This book chapter investigated the place of backtesting approach in financial time series analysis in choosing a reliable Generalized Auto-Regressive Conditional Heteroscedastic (GARCH) Model to analyze stock returns in Nigeria. To achieve this, The chapter used a secondary data that was collected from www.cashcraft.com under stock trend and analysis. Daily stock price was collected on Zenith bank stock price from October 21st 2004 to May 8th 2017. The chapter used nine different GARCH models (standard GARCH (sGARCH), Glosten-Jagannathan-Runkle GARCH (gjrGARCH), Exponential GARCH (Egarch), Integrated GARCH (iGARCH), Asymmetric Power Autoregressive Conditional Heteroskedasticity (ARCH) (apARCH), Threshold GARCH (TGARCH), Non-linear GARCH (NGARCH), Nonlinear (Asymmetric) GARCH (NAGARCH) and The Absolute Value GARCH (AVGARCH) with maximum lag of 2. Most the information criteria for the sGARCH model were not available due to lack of convergence. The lowest information criteria were associated with apARCH (2,2) with Student t-distribution followed by NGARCH(2,1) with skewed student t-distribution. The backtesting result of the apARCH (2,2) was not available while eGARCH(1,1) with Skewed student t-distribution, NGARCH(1,1), NGARCH(2,1), and TGARCH (2,1) failed the backtesting but eGARCH (1,1) with student t-distribution passed the backtesting approach. Therefore with the backtesting approach, eGARCH(1,1) with student distribution emerged the superior model for modeling Zenith Bank stock returns in Nigeria. This chapter recommended the backtesting approach to selecting reliable GARCH model.

Highlights

  • Time series is a series of observation collected with respect to time

  • This study focuses on the Generalized AutoRegressive Conditional Heteroscedastic (GARCH) models that are robust for forecasting the volatility of financial time series data; so GARCH model and some of its extensions are presented

  • The lowest information criteria were associated with apARCH (2,2) with Student t-distribution followed by Nonlinear Generalized Autoregressive Conditional Heteroskedasticity (NGARCH)(2,1) with skewed student t distribution

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Summary

Introduction

Time series is a series of observation collected with respect to time. The time could be in minutes, hours, daily, weekly, monthly, yearly etc. In the field of time series analysis, Autoregressive Moving Average (ARMA) and Autoregressive Integrated Moving Average (ARIMA) models are popular and excellent for modeling and forecasting univariate time series data as proposed by Box and Jenkins in 1970 but many times these models failed in analyzing and Linked Open Data - Applications, Trends and Future Developments forecasting financial time series [2], this is because the ARMA and ARIMA models are used to model conditional expectation of a process but in ARMA model, the conditional variance is constant This means that ARMA model cannot capture process with time-varying conditional variance (volatility) which is mostly common with economic and financial time series data [3]. The backtesting approach compliment the estimated GARCH model, in order to select a reliable GARCH model useful for real life application

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