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Open AccessArticle

Do We Need Stochastic Volatility and Generalised Autoregressive Conditional Heteroscedasticity? Comparing Squared End-Of-Day Returns on FTSE

by David E. Allen 1,2,3,* and Michael McAleer 2,4,5,6,7,8
1
School of Mathematics and Statistics, University of Sydney, Sydney 2006, Australia
2
Department of Finance, Asia University, Taichung 41354, Taiwan
3
School of Business and Law, Edith Cowan University, Joondalup 6027, Australia
4
Discipline of Business Analytics, University of Sydney Business School, Sydney, NSW 2006, Australia
5
Econometric Institute, Erasmus School of Economics, Erasmus University Rotterdam, 3062 Rotterdam, The Netherlands
6
Department of Economic Analysis and ICAE, Complutense University of Madrid, 28040 Madrid, Spain
7
Department of Mathematics and Statistics, University of Canterbury, Christchurch 8041, New Zealand
8
Institute of Advanced Sciences, Yokohama National University, Kanagawa 240-8501, Japan
*
Author to whom correspondence should be addressed.
Risks 2020, 8(1), 12; https://doi.org/10.3390/risks8010012
Received: 29 June 2019 / Revised: 12 December 2019 / Accepted: 13 January 2020 / Published: 1 February 2020
(This article belongs to the Special Issue Measuring and Modelling Financial Risk and Derivatives)
The paper examines the relative performance of Stochastic Volatility (SV) and Generalised Autoregressive Conditional Heteroscedasticity (GARCH) (1,1) models fitted to ten years of daily data for FTSE. As a benchmark, we used the realized volatility (RV) of FTSE sampled at 5 min intervals taken from the Oxford Man Realised Library. Both models demonstrated comparable performance and were correlated to a similar extent with RV estimates when measured by ordinary least squares (OLS). However, a crude variant of Corsi’s (2009) Heterogeneous Autoregressive (HAR) model, applied to squared demeaned daily returns on FTSE, appeared to predict the daily RV of FTSE better than either of the two models. Quantile regressions suggest that all three methods capture tail behaviour similarly and adequately. This leads to the question of whether we need either of the two standard volatility models if the simple expedient of using lagged squared demeaned daily returns provides a better RV predictor, at least in the context of the sample. View Full-Text
Keywords: stochastic volatility; GARCH (1,1); FTSE; RV 5 min; HAR model; demeaned daily squared returns stochastic volatility; GARCH (1,1); FTSE; RV 5 min; HAR model; demeaned daily squared returns
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Allen, D.E.; McAleer, M. Do We Need Stochastic Volatility and Generalised Autoregressive Conditional Heteroscedasticity? Comparing Squared End-Of-Day Returns on FTSE. Risks 2020, 8, 12.

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