Adaptive Heterogeneous Autoregressive Models of Realized Volatility Based on a Genetic Algorithm

Ping Ji,Hui Qu

doi:10.1155/2014/943041

Abstract

The heterogeneous autoregressive (HAR) models of high-frequency realized volatility are inspired by the Heterogeneous Market Hypothesis and incorporate daily, weekly and monthly realized volatilities in the volatility dynamics with a (1,5,22) time horizon structure. We build on the HAR models and propose a new framework, adaptive heterogeneous autoregressive (AHAR) models, whose time horizon structures are optimized by a genetic algorithm. Our models can be applied to markets with different heterogeneous structures, and their time horizon structures can be adjusted adaptively as the market's heterogeneous structure varies. Moving window tests with five-minute returns of the CSI 300 index indicate that the (1,5,22) structure originally proposed for American stock markets is not the best choice for Chinese stock markets, and Chinese stock markets’ heterogeneous structure does vary over time. Using four common loss functions, we find that the AHAR models outperform the corresponding HAR models in most of the forecast windows and thus are reasonable choices for volatility forecasting practices.

Highlights

Improving the forecast accuracy of asset return volatility is a key goal for researchers and practitioners, owing to volatility’s critical role in asset pricing, portfolio construction, risk management, and trading strategy design
We build on the HAR models and propose the adaptive heterogeneous autoregressive (AHAR) models by using genetic algorithm optimized time horizon structures instead of the (1,5,22) structure used in the HAR models
Building on the heterogeneous autoregressive models inspired by the Heterogeneous Market Hypothesis, we propose adaptive heterogeneous autoregressive models by using genetic algorithm optimized time horizon structures instead of the (1,5,22) structure used in the HAR models

Summary

Introduction

Improving the forecast accuracy of asset return volatility is a key goal for researchers and practitioners, owing to volatility’s critical role in asset pricing, portfolio construction, risk management, and trading strategy design. Dunis and Huang [16] empirically showed that the recurrent neural network (RNN) models apparently outperform the GARCH(1,1) model in forecasting the GBP/USD and USD/JPY exchange rate volatilities in terms of both forecast accuracy and trading efficiency. Sermpinis et al [23] proposed the higher order neural networks (HONNs) for forecasting FTSE 100 futures’ 21-day-ahead realized volatility and demonstrated better performance in terms of both statistical accuracy and trading efficiency when compared with the multilayer perceptron (MLP), the RNN, the GJR (GARCH-family), and the RiskMetrics. The current applications of the HAR models all follow the (1,5,22) time horizon structure originally proposed for developed markets, using daily (1 day), weekly (5 days), and monthly (22 days) to represent the short-term, medium-term, and longterm investors’ trading frequencies, respectively. Taking the above into consideration, we propose adaptive heterogeneous autoregressive (AHAR) models in this paper, whose time horizon structures are optimized by a genetic algorithm.

Models and Methods

Empirical Evidence

Conclusions