Structural breaks and volatility forecasting in the copper futures market

• Author: Boqiang Lin,Xu Gong
• Published date: 01 March 2018
• DOI: http://doi.org/10.1002/fut.21867
• Date: 01 March 2018

Received: 14 January 2017

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Accepted: 4 August 2017

DOI: 10.1002/fut.21867

RESEARCH ARTICLE

Structural breaks and volatility forecasting in the copper

futures market

Xu Gong

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Boqiang Lin

School of Management, China Institute for

Studies in Energy Policy, Collaborative

Innovation Center for Energy Economics

and Energy Policy, Xiamen University,

Xiamen, Fujian, P. R. China

Correspondence

Boqiang Lin, School of Management, China

Institute for Studies in Energy Policy,

Collaborative Innovation Center for Energy

Economics and Energy Policy, Xiamen

University, Xiamen, Fujian, P. R. China.

Email: bqlin@xmu.edu.cn

Funding information

The Grant for Collaborative Innovation

Center for Energy Economics and Energy

Policy, Grant number: 1260-Z0210011;

National Natural Science Foundation of

China, Grant numbers: 71701176,

71633006; China Postdoctoral Science

Foundation, Grant number: 2017M612121;

Xiamen University Flourish Plan Special

Funding, Grant number: 1260-Y07200;

China National Social Science Fund,

Grant number: 15ZD058

This paper examines whether structural breaks contain incremental information for

forecasting the volatility of copper futures. Considering structural breaks in volatility,

we develop four heterogeneous autoregressive (HAR) models based on classical or

latest HAR-type models. Subsequently, we apply these models to forecast volatility in

the copper futures market. The empirical results reveal that our models exhibit better

in-sample and out-of-sample performances than classical or latest HAR-type models.

This suggests that structural breaks contain incremental prediction information for

the volatility of copper futures. More importantly, we argue that considering

structural breaks can improve the performances of most of existing HAR-type

models.

1

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INTRODUCTION

Base or industrial nonferrous metals (e.g., copper, aluminium, and zinc) play vital roles in industrial manufacturing and

economic activity worldwide (see Todorova, Worthington, & Souček, 2014). Their price fluctuations exert deep effects on the

global macro economy. In the meantime, the volatility of nonferrous metals prices has a important impact on the industrial

production of manufacturers, the relevant policy setting of policymakers, as well as the decision of financial traders for risk

management plan and portfolio allocation. This is particularly important in the current global economic uncertainty and volatile

commodity markets. Thus, the accurate prediction of volatility in the base nonferrous metals markets is an important issue for

businessman, governments, investors, and academics.

Most of the available studies mainly employ generalized autoregressive conditional heteroskedasticity-type (GARCH-type)

and stochastic volatility-type (SV-type) models based on low-frequency data to forecast volatility in the financial markets (e.g.,

Dai, Li, & Wen, 2016; Fiszeder & Perczak, 2016; Gong, He, Li, & Zhu, 2014; Opschoor, van Dijk, & Van der Wel, 2014).

Andersen and Bollerslev (1998) first propose a new proxy for volatility (i.e., realized volatility, RV) based on high-frequency

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data. Andersen, Bollerslev,Diebold, and Labys (2003) strongly

suggest that simple reducedform models with realized volatility

have better predictive effects than popular GARCH-type and

SV-type models in forecasting the volatility of financial assets.

Thus, increasing number of studies develop new models with

realized volatility for forecasting volatility in the financial

markets. However, in contrast to the significant volume of

work on the stock markets (e.g., Bannouh,Martens, & van Dijk,

2013; Kambouroudis, Mcmillan, & Tsakou, 2016; Wang, Ma,

Wei, & Wu, 2016), currency markets (e.g., Andersen et al.,

2003; Barunik, Krehlik, & Vacha, 2016), bond markets (e.g.,

Opschoor, Taylor, Van der Wel, & van Dijk, 2014), energy

markets (e.g.,Haugom, Langeland, Molnár, & Westgaard,2014;

Wen, Gong, & Cai, 2016), and precious metals markets (e.g.

Khalifa, Miao, & Ramchander, 2011; Luo & Ye, 2015),

computational studies on volatility prediction using high-frequency transaction data in base nonferrous metals markets remain

limited.Our study aims to contribute to this important but small literatureby forecasting volatility in nonferrousmetals assets based

on high-frequency transaction data for the most actively traded base non-ferrous contracts (i.e., copper futures contracts)on the

Shanghai Futures Exchange.

Compared to the existing studies on base nonferrous metals markets and volatility prediction, our study mainly includes the

following contributions. First, some studies find that there are structural breaks in the volatility of returns of financial assets (e.g.,

Aragó & Salvador, 2011; Wang, Bauwens, & Hsiao, 2013; Wen et al., 2016). However, existing research hardly focuses on

structural breaks in volatility of returns in the base nonferrous metals markets. In this paper, we apply the iterative cumulative

sum of squares (ICSS) algorithm proposed by Inclán and Tiao (1994) to test structural breaks in the volatility of returns of copper

futures. We find that there are many structural breaks in volatility of copper futures returns, especially over the periods slightly

before, during, and slightly after the financial crisis (i.e., the period from 2006 to 2010).

Second, the existing studies mainly employ models based on low-frequency data (e.g., GARCH-type and SV-type models)

to predict volatility of copper futures (e.g., Li & Li, 2015; Watkins & McAleer, 2008). Different from these studies, we use HAR-

type models based on high-frequency data to forecast volatility in the copper futures market. Furthermore, we develop 12 HAR-

type models with structural breaks (i.e., HAR-RV-SB, HAR-CJ-SB, HAR-S-RV-J-SB, HAR-RV-SJd-SB, LHAR-RV-SB,

LHAR-CJ-SB, LHAR-S-RV-J-SB, LHAR-RV-SJd-SB, HAR-RV-J-SB, HAR-RSV-SB, HAR-RSV-L-SB, and HAR-CSJd-SB

models) on the basis of existing HAR-type models without structural breaks. We find that each HAR-type model with structural

breaks outperforms the corresponding HAR-type models without structural breaks in forecasting the volatilities of copper

futures at the different time horizons. Moreover, the simplest HAR-type model with structural breaks (i.e., HAR-RV-SB model)

prerforms better than all HAR-type models without structural breaks (e.g., HAR-RV, HAR-CJ, HAR-S-RV-J, HAR-RV-SJd,

HAR-RV-J, HAR-RSV, HAR-RSV-L, and HAR-CSJd models). Our findings suggest that HAR-type models with structural

breaks are better volatility forecasting models and enhance the understanding of risk management plans of all participants in the

copper futures market.

Lastly and most importantly, comparing the in-sample and out-of-sample performances of HAR-type models with structural

breaks and their corresponding HAR-type models without structural breaks, we find that structural breaks contain significant

incremental information, which exceeds many volatility components. The incremental information is particularly obvious when

forecasting the volatilities of copper futures at the medium and long prediction horizons. This suggests that structural breaks

should not be jettisoned, especially in forecasting mid- and long-term volatilities in the copper futures market. More importantly,

we argue that considering structural breaks can improve the predictive ability of the majority of other existing HAR-type models

in addition to the models discussed in this paper.

The remainder of the paper is organized as follows. In the next section, we briefly review the literature on volatility prediction

in the base nonferrous metals markets and the development of the HAR-type models. Section 3 presents the data. Section 4 tests

the structural breaks in the variance of copper futures returns. In section 5, based on the results of section 4, we propose four

HAR-type models with structural breaks. Section 6 provides the in-sample evidence, including the parameter estimations

for four HAR-type models with structural breaks and the comparison of the different HAR-type models. Section 7 presents the

out-of-sample prediction. In this section, we compare the out-of-sample forecasting performances of different HAR-type

models. Section 8 is the robustness test for the results of the in-sample evidence and out-of-sample prediction. The final section

provides conclusions.

Highlights

1. There are many structural break points in return

volatility of the copper futures.

2. We propose 12 new heterogeneous autoregressive

models.

3. Our models outperform the existing heteroge-

neous autoregressive models.

4. Structural breaks contain additional ex ante

information for volatility forecasting.

5. The ex ante information is obvious in forecasting

mid- and long-term volatilities.

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LITERATURE REVIEW

In this section we review two parts of the literature, including volatility forecasting for base nonferrous metals assets and the

development of HAR-type models.

2.1

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Volatility forecasting for base nonferrous metals assets

The accurate prediction of volatility in the base nonferrous metals markets plays a critical role in industrial production, policy

setting, risk management plan, and choices that affect portfolio allocation decisions. However, existing literature on forecasting

volatility of base nonferrous metals remains limited. In particular, very little research has been conducted using high-frequency

transaction data.

Based on low-frequency transaction data, Triantafyllopoulos (2008) develops a multivariate stochastic volatility with

Bayesian dynamic linear models to predict the volatility of aluminium, copper, lead, and zinc of the London metal exchange. The

empirical findings suggest that the proposed model can be effectively applied to predict the volatility of many metal assets.

Watkins and McAleer (2008) apply a rolling AR-GARCH model to predict the return volatility of aluminium and copper. Li and

Li (2015) combine the model averaging techniques and GARCH-type models to predict the volatility of copper futures and find

that the model averaging techniques can reduce the uncertainty of GARCH-type models for volatility in the copper futures

market.

Applying high-frequency transaction data, Khalifa et al. (2011) assess four measures of integrated volatility (i.e., daily

absolute returns, realized volatility, realized bipower volatility, and integrated volatility via Fourier transformation (IVFT)) for

gold, silver, and copper. Their findings show that the IVFT and realized volatility proxies produce the smallest forecasting errors

for the future volatility of these metals. Jiang, Liu, and Ye (2015) use the auto regression fractional integrated moving average

with realized volatility (ARFIMA-RV) and GARCH-type models to forecast the volatility of Chinese commodity futures

(including aluminium and copper futures). The out-of-sample forecast evaluations show that there are no significant differences

in their out-of-sample performances. Todorova (2015) predict the volatility of LME futures contracts of aluminum, copper, lead,

nickel, and zinc using the HAR, HAR-L, HAR-GARCH, and HAR-L-GARCH models. He finds that all HAR-type models

exhibit high prediction accuracy.

2.2

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HAR-type models

Accurately forecasting volatility in the financial markets is a challenging work, which has attracted considerable attention from

academics in the field of financial markets. Based on the heterogeneous market hypothesis of Müller et al. (1993), Corsi (2009)

proposes a heterogeneous autoregressive with realized volatility (HAR-RV) model. The HAR-RV model is proved to be

markedly better in forecasting volatility in the financial markets than the GARCH and ARFIMA-RV models. Corsi (2009)'s

work significantly promotes the use of the models, based on high-frequency transaction data, to predict the volatility of financial

assets. Many studies (e.g., Andersen, Bollerslev, & Huang, 2011; Celik & Ergin, 2014) prove that the predictive ability of

HAR-RV model is obviously superior to GARCH-type, SV-type, ARFIMA-RV, and VAR-RV models.

Furthermore, some studies develop new HAR-type models to further improve the prediction accuracy of volatility in the

financial markets. Andersen, Bollerslev, and Diebold (2007) decompose realized volatility into continuous sample path

variation and discontinuous jump variation and propose HAR-RV-J and HAR-CJ models, thereby improving the prediction

accuracy of models for forecasting volatility. Considering leverage effect, Asai, McAleer, and Medeiros (2012) develop a

LHAR-RV model based on the HAR-RV model, and Corsi and Renò (2012) propose a LHAR-CJ model based on the HAR-

CJ model. These two studies indicate that the leverage effect contain prediction information for future volatility in the

financial markets. Chen and Ghysels (2011) develop a new HAR-type model (i.e., the HAR-S-RV-J model) that includes

positive realized semivariance, negative realized semivariance, and discontinuous jump variation. They find that the HAR-S-

RV-J model performs well in out-of-sample forecasting, particularly at one-day ahead forecasts. Sévi (2014) develops HAR-

CSJ and HAR-CSJd models. The HAR-CSJ model includes the continuous sample path variation and signed jumps variation;

The HAR-CSJd model includes the continuous sample path variation, positive signed jumps variation, and negative signed

jumps variation. He finds that the in-sample performances of HAR-CSJ and HAR-CSJd models are better than the HAR-RV

model, but their out-of-sample performances are not significantly superior to the HAR-RV model. To explore the roles that

positive realized semivariance, negative realized semivariance, signed jump variation, positive signed jump variation, and

negative signed jump variation in volatility, Patton and Sheppard (2015) propose some new HAR-type models. For example, the

HAR-RSV and HAR-RSV-L models include the positive realized semivariances, negative realized semivariances, and

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