Hurst Exponent Analysis on the Ghana Stock Exchange

Isaac Ampofi,Eric Neebo Wiah,Akyene Tetteh,Sampson Takyi Appiah

doi:10.11648/j.ajmcm.20200503.13

Abstract

This paper talks about the application of Hurst Index on the Ghana Stock Exchange (GSE). The aim of the paper was to find out, whether GSE daily returns have some autocorrelation (long-term dependency) and multifractality using the Hurst Index analysis. Hurst Index of daily returns of some selected stocks in the period of January 2018 to December 2018 constituting 247 trading days were computed using Rescale Range Method and the Periodogram Method. The findings show that, 91.7% of the stocks considered possess long-term dependency and only 8.3% shows multifractality. Besides, the average percentage error of the geometric fractional Brownian motion (GFBM) model was 16.68% with an efficiency accuracy of 83.32% whilst that of the geometric Brownian motion (GBM) model percentage error is 20.90% with an accuracy of 79.10%. This indicates that, the GFBM model yielded better predicting accuracy than GBM in the long-run and par predicting accuracy in the short-run.

Highlights

The Ghana Stock Exchange (GSE) which is one of the youngest and fastest growing Exchange in Africa has seen fewer contribution of literatures on stochastic modelling of its stock prices
Isaac Ampofi et al.: Hurst Exponent Analysis on the Ghana Stock Exchange persistency, more importantly the results suggest that, the Hurst Exponent is time varying even after adjusting shortrange dependency. [6, 7], show evidence of long memory on the European Options through a time-dependent volatility. [8] agued from Efficient Market Hypothesis (EMH) on Australian market that, if a stock time series has a high Hurst Exponent, the stock will be less risky and there will be less noise in the data set
The research was conducted purposely to develop a model that will take into account the Hurst exponent to model stock price in Ghana

Summary

Introduction

The Ghana Stock Exchange (GSE) which is one of the youngest and fastest growing Exchange in Africa has seen fewer contribution of literatures on stochastic modelling of its stock prices. The few literatures all focus on the Geometric Brownian Motion (GBM). This is evident from [1,2,3]. According to [4], the GBM could not account for the longrun prediction because of its memoryless property. Due to this deficiency, this paper studied the Geometric Fraction Brownian Motion which incorporates the Hurst Index as the catalyst for long-run prediction. If 0 ≤ H < 0.5 , the time series is said to have anti-persistent behavior, which means it is mean reverting. The series is said to have persistent behavior if 0.5 < H ≤1

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