Multivariate realized volatility forecasts of agricultural commodity futures

• DOI: http://doi.org/10.1002/fut.22052
• Published date: 01 December 2019
• Date: 01 December 2019
• Author: Langnan Chen,Jiawen Luo

J Futures Markets. 2019;39:1565–1586. wileyonlinelibrary.com/journal/fut © 2019 Wiley Periodicals, Inc.

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1565

Received: 27 March 2019

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Accepted: 11 August 2019

DOI: 10.1002/fut.22052

RESEARCH ARTICLE

Multivariate realized volatility forecasts of agricultural

commodity futures

Jiawen Luo

1

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Langnan Chen

2

1

School of Business Administration, South

China University of Technology,

Guangzhou, China

2

Lingnan (University) College, Sun

Yat‐sen University, Guangzhou, China

Correspondence

Langnan Chen, Lingnan (University)

College, Sun Yat‐sen University, 135

Xingang West Road, Guangzhou, 510275

Guangdong, China.

Email: lnscln@mail.sysu.edu.cn

Funding information

National Natural Science Foundation of

China, Grant/Award Numbers: 71803049,

717774152; MOE (Ministry of Education

in China) Project of Humanities and

Social Sciences, Grant/Award Numbers:

17YJC630099, 17YJC790011; Natural

Science Foundation of Guangdong

Province, Grant/Award Numbers:

2018A030310400, 2017A030311038,

2017A030312001; Fundamental Research

Funds for the Central Universities,

Grant/Award Number: 2018BSXM10;

Philosophy and Social Science

Development Foundation of Guangzhou,

Grant/Award Number: 2019GZQN07

Abstract

We forecast the multivariate realized volatility of agricultural commodity

futures by constructing multivariate heterogeneous autoregressive (MHAR)

models with flexible heteroscedastic error structures that allow for non‐

Gaussian distribution, stochastic volatility, and heteroscedastic and serial

dependence. We evaluate the forecast performances of various models based on

both statistical and economic criteria. The in‐sample and out‐of‐sample results

suggest that the proposed MHAR models allowing for flexible heteroscedastic

covariance structures outperform the benchmark MHAR models. In addition,

the proposed Bayesian MHAR models allowing for tinnovations improve both

in‐sample and out‐of‐sample forecast performance of the corresponding MHAR

models with Gaussian innovations.

KEYWORDS

flexible covariance structure, MHAR models, multivariate volatility forecasts, performance

evaluations

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INTRODUCTION

Accurate forecasts of the multivariate volatility of agricultural commodities have important implications for derivative

pricing, portfolio selection, and risk management for both market participants and academic researchers. Existing studies

on multivariate forecasts rarely address the dynamic effects of disturbances in the multivariate volatility forecasts by

assuming the homoscedastic disturbance of residues. We propose a set of multivariate heterogeneous autoregressive

(MHAR) models with flexible error structures to accommodate the time‐varying, asymmetric, heteroscedastic, and serial

dependence features of innovations by relaxing the assumption of homoscedasticity of multivariate heterogeneous

autoregressive regression (HAR) disturbances. In this paper, we intend to answer the following questions. Are there any

dynamic effects from the disturbances that govern the evolution of covariance matrices of agriculture commodity futures?

Are the variances and covariances of agriculture futures described by the spillover effects? Do flexible settings of error

structures improve the forecast performances and portfolio selections of the multivariate volatility models?

Traditional multivariate volatility models in the literature include the multivariate generalized autoregressive

conditional heteroscedasticity (MGARCH) models and the multivariate stochastic volatility (MSV) models. Bauwens,

Laurent, and Rombouts (2006) and Asai, McAleer, and Yu (2006) provide a detailed review of these two models,

respectively. Although numerous extensions have been made to the flexible specifications of MGARCH‐type and

MSV‐type models, these models lose much intraday information due to the use of low‐frequency data and suffer from

the curse of dimensionality.

The availability of high‐frequency intraday data motivates the studies on the high‐frequency‐data‐based realized

covariance (RCOV) estimators. Andersen, Bollerslev, Diebold, and Labys (2003), Barndorff Nielsen and Shephard

(2004), and Sheppard (2006) propose an RCOV estimator as an alternative approach to obtaining the continuous and

consistent nonparametric estimator of asset returns’covariance matrix, which is considered a precise estimator of the

asset covariance. McAleer and Medeiros (2008) and Andersen and Teräsvirta (2009) review in detail the literature on

RCOV modeling. Further extensions of the RCOV estimator include the multivariate realized kernel (RK) estimator

(Barndorff‐Nielsen, Hansen, Lunde, & Shephard, 2011), the regularization and blocking estimator (Hautsch, Kyj, &

Oomen, 2012), and the composite RKs (Lunde, Shephard, & Sheppard, 2016). In particular, Hautsch, Kyj, and Malec

(2015), Sharma and Vipul (2016), and Lunde et al. (2016) suggest that the high‐frequency‐data‐based multivariate

volatility models outperform those based on the daily data in portfolio selections.

The multivariate extensions of the HAR model proposed by Corsi (2009) are widely used in the literature for

multivariate volatility forecasts. The HAR model includes the daily, weekly, and monthly volatility components as

predictors based on the heterogeneous market hypothesis and the HARCH model of Müller et al. (1997). Audrino and

Corsi (2010) suggest that the HAR processes improve the in‐sample fit and out‐of‐sample forecast performances in

modeling the variance and covariance. Bauer and Vorkink (2011) propose a multivariate matrix logarithm HAR model

to forecast the covariance matrix of size‐sorted stock returns. Chiriac and Voev (2011) evaluate the forecast

performances of several multivariate volatility models based on high‐frequency data and use both Cholesky

decomposition and matrix log transformation methods to guarantee the positive definiteness of covariance matrices.

Moreover, Gribisch (2018) develops a latent dynamic factor model by combining the HAR process with the common

factor structure to forecast the RCOV matrices. Čech and Baruník (2017) construct a generalized HAR (GHAR) model

by incorporating the Cholesky factors of covariance matrix into a seemingly unrelated model structure and compare the

forecast performances of the proposed model with other multivariate models in the literature. Bollerslev, Patton, and

Quaedvlieg (2018) propose a scalar version of the MHAR model and incorporate the effect of time‐varying attenuation

biases into the multivariate HAR model to achieve greater economic gains for the covariance forecasts. The above

models make full use of high‐frequency data and yield a better forecast performance than do the GARCH‐type

multivariate volatility models with low‐frequency data.

The extended forms of a multivariate HAR model can be considered a restricted vector autoregression (VAR) model

that accommodates the long‐memory property of volatility. Carriero, Clark, and Marcellino (2016) construct a Bayesian

VAR model with heteroscedastic covariance that is driven by unobserved factors. Chan (2018) develops a class of

Bayesian VAR (BVAR) models that allow for non‐Gaussian, heteroscedastic, and serially dependent innovations. The

results suggest that the BVAR models with more flexible covariance structures outperform the BVAR models with

standard, independent, and homoscedastic innovations for both point and density forecasts. The relaxation of

homoscedastic disturbances also brings extra complexities to estimating the parameters, especially for the high‐

dimension models, as the incorporation of heteroscedastic covariance leads to a loss of symmetry in the model. Both

Chan (2018) and Carriero et al. (2016) employ a Kronecker structure of likelihood to accelerate the sampling of

parameters.

We forecast the RCOV of China’s agricultural commodity futures by constructing a group of MHAR models

with flexible heteroscedastic error covariance by incorporating various types of innovations including student‐tinnovations,

moving average (MA) innovations and innovations with a stochastic volatility structure and dynamic conditional correlation

(DCC)‐GARCH innovations. We then evaluate both in‐sample and out‐of‐sample forecast performances of various

multivariate volatility models. We compare the proposed models with some benchmark models in terms of forecast precision

criteria and economic criteria. We also investigate the performances from short‐to long‐term forecasts by using the iterated

forecast approach.

We contribute to the literature in the following aspects. First, the volatility of China’s agricultural commodity markets

has rarely been addressed in the literature. We forecast the multivariate realized volatility of agricultural commodity

futures by using high‐frequency data from China. Second, we proposea set of MHAR models with flexible error structures

that capture t he time‐varying, asymmetric, heteroscedastic, and serially dependent properties of innovations. The results

suggest that the proposed modelsimprove forecast performance. Third, we employ both matrixlog transformation and the

Cholesky decomposition approach to ensure the positive definiteness of forecast covariance matrices. Fourth, the

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