Forecasting Crude Oil Volatility Using the Deep Learning‐Based Hybrid Models With Common Factors

• Published date: 01 August 2024
• Author: Ke Yang,Nan Hu,Fengping Tian
• Date: 01 August 2024
• DOI: http://doi.org/10.1002/fut.22529

Journal of Futures Markets

RESEARCH ARTICLE

Forecasting Crude Oil Volatility Using the Deep

Learning‐Based Hybrid Models With Common Factors

Ke Yang

1,2

| Nan Hu

1

| Fengping Tian

3

1

School of Economics and Finance, South China University of Technology, Guangzhou, China |

2

Pazhou Lab, Guangzhou, China |

3

International School of

Business and Finance, Sun Yat‐sen University, Guangzhou, China

Correspondence: Ke Yang (yangkdc@scut.edu.cn) | Fengping Tian (tfengp@mail.sysu.edu.cn)

Received: 19 October 2023 | Accepted: 22 May 2024

Funding: The General Project of Ministry of Education Foundation on Humanities and Social Sciences, Grant/Award Number: 22YJA790077;

The Fundamental Research Funds for the Central Universities, Grant/Award Number: QNTD202305; The National Social Science Foundation of China,

Grant/Award Number: 19ZDA093; The National Natural Science Foundation of China, Grant/Award Numbers: 72201284, 71991474; The Guangdong Basic

and Applied Basic Research Foundation, Grant/Award Number: 2024A1515011002

Keywords: crude oil future | deep learning | factor structure | volatility forecasting

ABSTRACT

Based on empirical evidence of the Chinese commodity futures volatility dynamics, we propose a novel and flexible hybrid

model, denoted as SAE‐HAR‐DL, which combines a supervised autoencoder (AE) with the deep learning‐based HAR model

framework to capture essential common factor information and uses the reconstruction error of the AE component as a

regularizer to enhance the generalization ability of the testing subsample. The empirical findings strongly support the

effectiveness of this model in accurately forecasting crude oil futures volatility in the post‐COVID‐19 era, compared to the HAR,

HAR‐PCA, and HAR‐DL models. Moreover, a robustness check also demonstrates the positive contribution of common factors

to the volatility prediction of other commodity futures. Notably, we establish that these common factors act as effective

regularizers, mitigating prediction losses within the HAR model in extreme risk events such as the COVID‐19 pandemic and the

Russia–Ukraine conflict.

JEL Classification: G12, Q02, C53

1 | Introduction

Accurate forecasting of crude oil volatility holds significant

importance in various financial domains due to its substantial

impact on equity markets and economic activities. Numerous

scholarly investigations have focused on examining the predict-

ability of oil market volatility, utilizing discrete‐time generalized

autoregressive conditional heteroskedasticity (GARCH) and

stochastic volatility approaches to model the autoregressive

conditional heteroskedasticity (Engle 1982; Andersen and

Bollerslev 1998;Barndorff‐Nielsen and Shephard 2002;Andersen

et al. 2003). However, Corsi (2009) argues that traditional GARCH

and stochastic volatility frameworks inadequately capture the

intricate characteristics of financial markets. To address this

limitation, Corsi (2009) introduces the heterogeneous auto‐

regressive (HAR) model, which incorporates historical volatilities

at different frequencies to account for the diverse behavior of

market participants. Despite the satisfactory simplicity of the HAR

model, the complex structure of financial data can render it

insufficient for ignoring (signed) jump information or spillover

effect. Consequently, several augmentations to the fundamental

HAR model have been proposed, including HAR with jumps

(HAR‐J), HAR with signed jumps (HAR‐SJ), and factor‐

augmented HAR (FAHAR) model (Andersen, Bollerslev, and

Diebold 2007; Patton and Sheppard 2015; Kim and Baek 2020).

In the era of big data, the utilization of various features in

modeling and predicting volatility has gained significant

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https://doi.org/10.1002/fut.22529

attention. Nevertheless, conventional augmented models, such

as GARCH‐mixed data sampling (MIDAS) and HAR‐X, may

encounter limitations in scenarios where the explanatory

variables exhibit high correlation, low signal‐to‐noise ratio, or

possess nonlinear foundational structures. Consequently, re-

searchers have recently shifted their focus towards machine

learning and flexible deep learning methods (Mittnik,

Robinzonov, and Spindler 2015; Caporin and Poli 2017;

Audrino, Sigrist, and Ballinari 2020). In a recent study by

Christensen, Siggaard, and Veliyev (2022), a comprehensive set

of machine learning algorithms is employed to predict volatility,

revealing that even the original component of the HAR model

can accurate more precise predictions when coupled with

machine learning techniques like simple structured feed‐

forward networks.

However, the application of deep learning algorithms in

modeling and predicting volatility has encountered overfitting,

primarily due to issues such as limited sample sizes and low

signal‐to‐noise ratios. These challenges are particularly evident

when forecasting crude oil futures volatility in the Chinese

futures market, which began trading in March 2018 and has

since faced numerous external shocks, most notably the

COVID‐19 pandemic. These shocks, akin to financialization,

have amplified the existence of common factors and the

comovement of volatility across the entire futures market

(Degiannakis and Filis 2017; Christoffersen, Lunde, and

Olesen 2019). Solely relying on historical volatility raises

concerns regarding the adequacy of such information for

realized volatility modeling. Derivative models of HAR like

heterogeneous auto‐regressive‐principal component analysis

(HAR‐PCA) are unsupervised algorithms that cannot account

for the nonlinear relationship between predictors and the target

variable. Recent research by Zhang et al. (2023) attempts to

address this issue through a stepwise supervised estimation

algorithm. However, this approach faces challenges in achiev-

ing a balance between factor extraction and volatility prediction

tasks. Consequently, dynamically selecting appropriate weights

for common factors and engaging in multiobjective optimiza-

tion has emerged as a crucial research direction in response to

the frequent occurrence of extreme risk events.

This paper sheds light on Chinese commodity futures volatility

dynamics in the post‐COVID‐19 era and proposes data‐driven

hybrid forecasting models. Our primary objective is to augment

the predictive accuracy of the deep learning‐based HAR hybrid

model by employing a common factor component as a

regularizer. We first reveal several characteristics regarding

the realized volatility series in the Chinese commodity futures

markets. The daily realized kernel commodity futures volatility

has high persistence, and its logarithm is close to normally

distributed. The expected logarithm of realized kernel volatility

in the Chinese commodity futures markets has increased

sharply during the COVID‐19 pandemic. We also present novel

empirical evidence concerning the dynamics of the common

factor structure. Our findings reveal a significant increase in the

strength of the common factor structure in realized commodity

futures volatility during the COVID‐19 pandemic. Moreover,

this heightened common factor structure persists in the post‐

COVID‐19 era, imparting crucial insights for the prediction of

crude oil futures volatility. From an economic perspective, we

observe a negative relationship between the common factor and

the return of Brent and Shanghai crude oil futures. The

common factor displays a robust association with volatility in

other markets, indicating substantial comovement across assets.

We then propose a novel and flexible hybrid model that

combines a supervised autoencoder (SAE) with deep learning‐

based forecasting frameworks (i.e., feedforward network [FFN],

convolutional neural network [CNN], and bidirectional long

short‐term memory [BiLSTM]) to capture the dynamics of the

common factor structure. The proposed model employs the

reconstruction error of the autoencoder (AE) component as a

regularizer thus improving the generalization ability of the

testing subsample. Our empirical analysis reveals that the SAE‐

HAR‐FFN and SAE‐HAR‐CNN models exhibit superior predic-

tive performance compared to the HAR benchmark. Specifi-

cally, the out‐of‐sample R

2

metric of the proposed models

surpasses the HAR benchmark by a significant margin of

12.16% (16.15%), 42.36% (49.29%), and 47.11% (46.61%) at the

daily, weekly, and monthly horizons, respectively. A series of

rigorous robustness checks further validate our main findings.

Our study offers compelling evidence of the essential role of the

regularization technique utilized in the reconstruction compo-

nent, especially during the COVID‐19 pandemic and its

aftermath. Notably, our proposed SAE‐HAR‐FFN and SAE‐

HAR‐CNN models, which incorporate a multiobjective optimi-

zation algorithm and dynamic parameter selection, effectively

mitigate the surge in loss values during both the COVID‐19

pandemic and its aftermath (including the Russia–Ukraine

conflict period).

The paper builds upon recent works by Christoffersen, Lunde,

and Olesen (2019) and Christensen, Siggaard, and Veliyev

(2022). The former investigates the dynamics of the common

factor structure in the US futures market during the period of

financialization, revealing a strengthened common factor

among realized commodity futures volatility. Moreover, a

strong correlation has been observed between the common

factor and macroeconomic variables. Furthermore, a significant

body of literature provides substantial evidence for the vital

importance of macroeconomic factors in modeling and fore-

casting volatility (Chiang, Hughen, and Sagi 2015; Prokopczuk,

Stancu, and Symeonidis 2019; Kang, Nikitopoulos, and

Prokopczuk 2020; Nikitopoulos, Thomas, and Wang 2023).

These findings prompt us to investigate the common factor

structure in the Chinese futures markets under the impact of

COVID‐19. Our DL‐based hybrid model design is also related to

Christensen, Siggaard, and Veliyev (2022), who study volatility

predictability using multiple machine learning methods,

including regularization, tree‐based algorithms, and feed‐

forward networks. They find the simple feed‐forward structure

can achieve more accurate predictions for realized volatility

compared to the pure HAR model, even when input with the

same HAR components. The study prompts us to apply state‐of‐

the‐art DL‐based techniques to construct hybrid forecasting

frameworks that can adapt to the common factor dynamics in

the Chinese futures market.

Our research diverges from existing literature in three key

aspects. First, we focus on the common factor structure of

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