An Empirical Evaluation in GARCH Volatility Modeling: Evidence from the Stockholm Stock Exchange

Chaido Dritsaki

doi:10.4236/jmf.2017.72020

Abstract

In this paper, we use daily stock returns from the Stockholm Stock Exchange in order to examine their volatility. For this reason, we estimate not only GARCH (1,1) symmetric model but also asymmetric models EGARCH (1,1) and GJR-GARCH (1,1) with different residual distributions. The parameters of the volatility models are estimated with the Maximum Likelihood (ML) using the Marquardt algorithm (Marquardt [1]). The findings reveal that negative shocks have a large impact than positive shocks in this market. Also, indices for the return of forecasting have shown that the ARIMA (0,0,1)-EGARCH (1,1) model with t-student provide more precise forecasting on volatilities and expected returns of the Stockholm Stock Exchange.

Highlights

The development of econometrics led to the invention of adjusted methodologies for the modeling of mean value and variance
The results showed that the Generalized error distribution (GED)-Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model is better than the t-GARCH, and that the t-GARCH is better than N-GARCH
Since there are ARCH effects in the Stockholm stock return data, we can proceed with the estimation of the ARIMA(0,0,1)-GARCH models

Summary

Introduction

The development of econometrics led to the invention of adjusted methodologies for the modeling of mean value and variance. Models of generalized conditional autoregressive heteroscedasticity (GARCH) are based on the assumption that random components in models present changes on volatility. These models were developed by Engle [2], in a simple form, and they were generalized later by Bollerslev [3]. On GARCH models we assume that only the size of return of the conditional variance is defined and not the positivity or negativity of volatility’s return, which are unpredicted. Another crucial limitation of GARCH models is the non-negativity of parameters in order to ensure the positivity of the conditional variance. All these limitations cause difficulties in the estimation of GARCH models

Objectives

Methods

Results

Conclusion