Time‐Varying Parameter Realized Volatility Models

• DOI: http://doi.org/10.1002/for.2454
• Author: Chongfeng Wu,Zhiyuan Pan,Yudong Wang
• Published date: 01 August 2017
• Date: 01 August 2017

Journal of Forecasting,J. Forecast. 36, 566–580 (2017)

Published online 28 November 2016 in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/for.2454

Time-Varying Parameter Realized Volatility Models

YUDONG WANG,1ZHIYUAN PAN2,3AND CHONGFENG WU4

1

School of Economics and Management, Nanjing University of Science and Technology, China

2

Institute of Chinese Financial Studies, Southwestern University of Finance and Economics,

Chengdu, Sichuan, China

3

Collaborative Innovation Center of Financial Security, Chengdu, Sichuan, China

4

Antai College of Economics and Management, Shanghai Jiao Tong University, China

ABSTRACT

In this paper, we introduce the functional coefficient to heterogeneous autoregressive realized volatility (HAR-RV)

models to make the parameters change over time. A nonparametric statistic is developed to perform a specification

test. The simulation results show that our test displays reliable size and good power.Using the proposed test, we find a

significant time variation property of coefficients to the HAR-RVmodels. Time-varying parameter (TVP) models can

significantly outperform their constant-coefficient counterparts for longer forecasting horizons. The predictive ability

of TVP models can be improved by accounting for VIX information. Copyright © 2016 John Wiley & Sons, Ltd.

KEY WORDS realized volatility; time-varying parameter; heterogeneous autoregressive realized volatility

model; specification test; forecasting

INTRODUCTION

The introduction of realized volatility (RV) or realized variance opens a new era of forecasting and modeling in

financial market volatility (Andersen and Bollerslev,1998; Andersen et al., 2000,2001a,b, 2003). This nonparametric

measure of volatility, defined as the sum of all available intraday squared returns, is considered a better proxy of

unobserved actual volatility than squared daily returns. Therefore, it is not surprising that wide-range volatility models

are developed to capture and forecast the dynamics of RV (see, for example, Andersen et al., 2005, 2007, 2011;

Barndorff-Nielsen, 2002; Bollerslev et al., 2016; Corsi, 2009; Corsi et al., 2010; Deo et al., 2006; Fleming et al.,

2003; Patton and Sheppard, 2015).

Among the models for RV, heterogeneous autoregressive realized volatility (HAR-RV) developed by Corsi (2009)

is one of the most popular. HAR-RV is a predictive regression which takes lagged daily, weekly and monthly RV as

the explanatory variable for future RV. The simulation and empirical results in Corsi (2009) suggest that the simple

HAR-RV can accommodate some ‘stylized facts’ in financial volatilitysuch as long memory, multiscaling and fat-tail

distribution. Given the good performance of HAR-RV in modeling and forecasting volatility, a series of meaningful

extensions have been proposed based on different decomposition methodologies of RV. For example, Andersen et al.

(2007) decomposes daily RV into a continuous sample path, and a significant jump component and their proposed

HAR-RV-CJ model uses these two components as the predictors of future RV. Corsi et al. (2010) improves the

decomposition method of Andersen et al. (2007) by introducing a new threshold of bipower variation for estimating

the jump component and develops a HAR-RV-TCJ model accordingly.

In this paper, we work with HAR-RV and its various extensions by contributing to the literature in three dimen-

sions. First, we introduce the functional coefficient into existing volatility models to make parameters change over

time. It is well known that volatility dynamics have always experienced structural breaks (see, for example, Baner-

jee and Urga, 2005; Granger and Hyung, 2004; Lamoureux and Lastrapes, 1990; Liu and Maheu, 2008; Rapach and

Strauss, 2008). Existing HAR-RV-type models are predictive regressions with a constant coefficient and therefore

cannot capture changes in predictive relationships (Wanget al., 2016). We improve upon existing HAR-RVmodels by

accounting for the time variation property in parameters. Recently, time-varying parameter (TVP) predictive regres-

sions have been used to forecast realized volatility (see, for example, Wang et al., 2016) and financial asset returns

(Dangl and Halling, 2012). Their TVP models are similar to state-space models by assuming that the parameter pro-

cess is a random walk without drift and only takes advantage of past information about parameter changes. Recently,

Chen et al. (2013) also put forward a TVP HAR-RV model by assuming the coefficientsare dominated by time t.Our

model is different from their specifications in the way that the parameter variation is the function of some explanatory

variables and can therefore include more additional information. We explicitly show the parameter estimators of the

Correspondence to: Institute of Chinese Financial Studies, Southwestern University of Finance and Economics, Chengdu, Sichuan, China.

E-mail: panzhiyuancd@126.com

Copyright © 2016 John Wiley & Sons, Ltd