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code1

1-s2.0-S0140988318302238-mmc1

Data in Brief

data.xlsx 982KB

Out-of-sample forecasting

Rolling window prediction

Other benchmark models

sxdicss.m 1KB

icss.m 740B

icss_step2.m 348B

HARRVTYPE.m 27KB

rvdata.mat 462KB

xlbl.m 124B

confirm.m 248B

Logarithmic HAR models

Copy of HARRVTYPE.m 19KB

sxdicss.m 1KB

icss.m 740B

icss_step2.m 348B

HARRVTYPE.m 18KB

rvdata.mat 340KB

HARRVTYPE.asv 18KB

xlbl.m 124B

confirm.m 248B

Linear HAR models

Copy of HARRVTYPE.m 19KB

sxdicss.m 1KB

icss.m 740B

icss_step2.m 348B

HARRVTYPE.m 18KB

rvdata.mat 319KB

HARRVTYPE.asv 18KB

xlbl.m 124B

confirm.m 248B

MZ regression

mz regression -1w.wf1 205KB

mz regression -1m.wf1 203KB

mz regression -1d.wf1 411KB

DM test

DM test - 1M.dta 269KB

Codes.txt 5KB

DM test - 1W.dta 273KB

DM test -1D.dta 274KB

MCS test

R-HMAE.ox 2KB

R-MAE.ox 1KB

Parameter estimation

Codes.txt 3KB

Parameter estimation.dta 439KB

1-s2.0-S0140988318302238-mmc1.zip 3.47MB

The incremental information content of investor fear gauge for volatility forecasting in the crude oil futures market.pdf 622KB

The incremental information content of investor fear gauge for volatility

forecasting in the crude oil futures market

Xu Gong, Boqiang Lin

⁎

School of Management, China Institute for Studies in Energy Policy, Collaborative Innovation Center for Energy Economics and Energy Policy, Xiamen University, Xiamen 361005, China

abstractarticle info

Article history:

Received 15 March 2018

Received in revised form 8 May 2018

Accepted 11 June 2018

Available online 4 July 2018

JEL Classiﬁcation:

Q41

Q47

G13

G17

C53

C58

This paper aims to investigate whether investor fear gauge (IFG) contains incremental information content for

forecasting the volatility of crude oil futures. For this purpose, we use oil volatility index (OVX) to measure the

IFG. Adding the IFG to existing heter ogeneous autoregressive (HAR) models, we develop many HAR models

with IFG. Subsequently, we employ these HAR models to predict the volatility of crude oil futures. The results

from the parameter estimation and out-of-sample forecasting show that the in-sample and out-of-sample per-

formances of HAR models with IFG are signiﬁcantly better than their corresponding HAR models without IFG.

The results are robust in different ways. Thus, the HAR models with IFG are more bene ﬁcial to the decision

making of all participants (including ﬁnancial traders, manufacturers and policymakers) in the crude oil futures

market. More importantly, the results suggest that the investor fear gauge has a signiﬁcant positive effect on

volatility forecasting, and can help improve the performances of almost all the existing HAR models.

Keywords:

Volatility forecasting

Investor fear gauge

Crude oil futures

HAR models

Realized volatility

1. Introduction

The volatility of ﬁnancial assets is closely related to portfolio optimi-

zation, risk management, and option pricing (see, e.g., Andersen et al.

2017; Billio et al., 2017; Dai and Wen 2018; Moreira and Muir 2017).

In the crude oil futures market, volatility plays a vital role in the decision

of all part icipants in the crude oil futures mar ket, including traders,

manufacturers, as well as policymakers. Additionally, the volatility of

crude oil futures has an important impact on the global economy and

ﬁnancial stability (see, e.g., Charles and Darné 2017; Cheong 2009;

Gong and Lin, 2018a; Lin et al., 20 14; Wang et al. 2016a; Wen et al.

2018). Thus , understanding the volatility of crude oil futures is vital

for oil-related researchers and participants. Among the many issues re-

lated to the volatility of crude oil futures, forecasting volatility is one of

the major issues that have attracted the attentions of oil market-related

researchers and participants.

The existing literature shows that there are ample models based on

low-frequency data modeling used for predicting the volatility of crude

oil futures. These include historical volatility models (Xu and Ouenniche

2012), AR-type models (Xu and Ouenniche 2012), ARFIMA model (Choi

and Hammoudeh 2009), GARCH-type models (Arouri et al. 2012;

Manera et al. 2016), SV-type models (Baum and Zerilli 2016), power

autoregressive models (Sadorsky and McKenzie 2008), among others.

However, it is difﬁcult for the models based on low-frequency data to ac-

curately measure the whole-day volatility information of crude oil futures.

Andersen and Bollerslev (1998) propose a new proxy of volatility

using high-frequency data. The proxy variable is named the realized vol-

atility (RV). Corsi (2009) develop a heterogeneous autoregressive model

of realized volatility (HAR-RV model) on the basis of the heterogeneous

market hypothesis of Müller et al. (1993), and is later extended. On the

basis of the HAR-RV model, some researchers propose many new HAR

models, such as the HAR-RV-J, HAR-CJ (Andersen et al. 2007), LHAR-RV

(Asai et al. 2012), LHAR-RV (Corsi and Renò, 2012), HAR-S-RV-J (Chen

and Ghysels 2011) models. The HAR models are some of the most popular

models for forecasting volatility in the ﬁnancial markets. Thus, this paper

employs the HAR models to predict the volatility of crude oil futures.

Notably, Chicago Board of Trade (CBOT) proposed the oil volatility

index (OVX) in 2007. The OVX can be used to mea sure the investor

fear gauge (IFG) in the crude oil market (see Ji and Fan 2016; Liu et al.

2017). The IFG (or OVX) is closely related to the crude oil futures mar-

ket. Some studies ﬁnd that the IFG (or OVX) has an important effect

Energy Economics 74 (2018) 370–386

⁎ Corresponding author.

E-mail address: bqlin@xmu.edu.cn (B. Lin).

https://doi.org/10.1016/j.eneco.2018.06.005

Contents lists available at ScienceDirect

Energy Economics

journal homepage: www.elsevier.com/locate/eneeco

on the returns and volatility of crude oil futures (e.g., Aboura and

Chevallier 2013; Haugom et al. 2014; Ji and Fan 2016). This paper de-

velops HAR models with IFG to examine whether investor fear gauge

contains incremental information content for forecasting the volatility

of crude oil futures. The paper mai nly has three contributions. First,

the paper forecasts the volatility of crude oil futures b ased on high-

frequency data. Using high-frequency data can obtain more accurate

estimator for volatility, so our results are more reliable than those ob-

tained using low-frequency data. However, existing literature that pre-

dicts the volatility of crude oil futures based on high-frequency data is

limited. Thus, our study is an important complement to the literature

on volatility forecasting based on high-frequency data.

Second, most of the existing studies investigate the relationship be-

tween returns and volatility of crude oil futures and investor fear gauge

(e.g., Ji and Fan 2016; Liu et al. 2017). Different from these studies, our

study investigates whe ther investor fear gauge play an irreplaceabl e

role in the prediction of the volati lity of crude oi l futures. From the

parameter estimation and out-of-sample evaluation of the HAR models,

we ﬁnd that investor fear gauge (IFG) contains additional ex ante infor-

mation for the future volatility of crude oil futures, relative to volatility

components, leverage effects and structural breaks. The result means

that the IFG s hould be considered while forecasting the volatility of

crude oil futures.

Third, we develop many HAR models with IFG, based on the existing

HAR models. The empirical results show that the HAR models with IFG

outperform their corresponding HAR models without IFG while fore-

casting the volatility of crude oil futures. We ﬁnd that the above results

are robust for logarithmic HAR models, after controlling for structural

breaks, and other benchmark HAR models. More importantly, we

argue that taking account of investor fear gauge (IFG) can help improve

the out-of-sample predictive abilities of most of the other existing HAR

models (such a s the HAR-CSJ model (Sévi 2014), the HAR-RV-type

models with regime switching (Ma et al. 2017), the TVP-HAR-RV and

TVP-HAR-RV-TCJ models (Wang et al. 2017), besides the HAR models

used in this paper. The ﬁndings suggest th at using the HAR models

with IFG can obtain more accurate predicted values of volatility in

crude oil future s market, which is more beneﬁcial to the decision of

oil market investors, manufacturers and policymakers.

The rest of this paper is structured as follows. Section 2 is the

literature review. Section 3 reports the estimations of some volatility

components. Section 4 develops six HAR models with IFG, including

HAR-RV-IFG, LHAR-RV-IFG, HAR-CJ-IFG, HAR-S-RV-J-IFG, HAR-RV-SJd-

IFG, and HAR-RV-ARJ-IFG models. Section 5 presents the data and

summary statistics. Section 6 estimates the parameter of the HAR

models. Section 7 provides the out-of-sample results for c omparing

the HAR models without IFG and HAR models with IFG, and investigates

the role of investor fear gauge (IFG) in volatility forecasting in the crude

oil futures market. Section 8 provides the robustness test for the out-of-

sample results. The conclusion is presented in Section 9.

2. Literature review

In th is section we mainly review two parts of the literature,

including volatility forecasting in the crude oil futures market and the

development of HAR models.

2.1. Volatility forecasting in the crude oil futures market

The accurate prediction of volatility has a positive effect on the deci-

sion of investors, manufacturers, as well as policymakers in the crude oil

futures market. Thus, many researchers pay close attention to volatility

forecasting, and attempt to propose new methods to improve the pre-

diction ac curacy of existing methods for forecastin g volatility in the

crude oil futures market.

Most of the existing literatures on forecasting the volatility of crude

oil futures are based on low-frequency data. The GARCH-type models

are some of the most popular methods for forecasting the volatility of

crude oil futures. Sadorsky (2006) ﬁnd that GARCH model reveals

good perform ance for forecasting volatility in the crude oil f utures

market. Narayan and Narayan (2007) use GARCH-type models to test

the role of regimes and market conditions in forecasting volatilities in

four petroleum futures markets. Cheong (2009) show that the simplest

GARCH model provides a good forecasting ability for the volatility of

Brent crude oil futures. Arouri et al. (2012) indicate that GARCH models

with instability and long memory features have good predictive ability

for the volatilities of oil spot and futures prices. Hou and Suardi

(2012) employ the nonp arametric GARCH model to predict the

volatilities of Brent and WTI crude oil futu res. The results show that

nonparametric GARCH model provides better volatility forecasts than

parametric GARCH model. Klein and Walther (2016) employ the mix-

ture memory GARCH model to forecast the volatility of Brent and WTI

crude oil futures. Lux et al. (2016) c ombine the Markov-switching

multifractal (MSM) method and a battery of GARCH-type models to

model and predict volatility in WTI crude oil futures market. Manera

et al. (2016) introduce alternati ve measures of speculation into the

variance equation of GARCH model and test the effect of speculation

on the volatility of crude oil futures.

In addition to GARCH-type models, some models based on low-

frequency data are used to predict the volatility of crude oil futures. For

example, Sadorsky and McKenzie (2008) employ power autoregressive

models to forecast the volatility of WTI crude oil futures. Choi and

Hammoudeh (2009) employ the parsimonious ARMA with short-term

processes and ARFIMA models to forecast the volatility of crude oil prices.

Xu and Ouenniche (2012) use fourteen forecasting models (including his-

torical volatility models and AR-type models) to forecast the volatility of

crude oil prices. Baum and Zerilli (2016) use the stochastic volatility

model (SV model) and SV model with jumps (SVJ model) to forecast

the volatility of crude oil futures.

In recent years, volatility forecasting mod els based on high-

frequency data have become very important methods for predicting

volatility in the ﬁnancial markets. However, the literature on the fore-

cast of volatility of crude oil futures models based on high-frequency

data remains limited. Some representative studies are listed as follows.

Haugom et al. (2014) employ the HAR-RV, HAR-RV-IV, HAR-RV-EX and

HAR-RV-IV-EX models to forecast the volatility of WTI crude oil futures.

Sévi (2014) predict the volatility of crude oil futures using the HAR

models (e.g. the HAR-CSJ and HAR-CSJd models). Wen et al. (2016)

develop HAR models with structural breaks to predict volatility in the

WTI crude oil futures market. Ma et al. (2017) propose the HAR models

with regime switching to predict volatility in the WTI crude oil futures

market. The above studies ﬁ nd that the HAR models exhibit good

performance for predicting the volatility of crude oil futures.

2.2. The development of HAR models

Corsi (2009) uses high-freque ncy data to calcula te the realized

volatility (RV, a proxy of volatility), and develops the HAR-RV model.

Corsi (20 09)’s work greatly improves the use of models based on

high-frequency data for forecasting the volatility of ﬁna ncial assets.

Lots of studies (e.g., Andersen et al. 2011; Celik and Ergin 2014; Corsi

2009) show that the predictive ability of HAR-RV model is better than

the GARCH-type, SV-type and ARFIMA-RV models while predicting

the volatility of ﬁnancial assets.

Furthermore, based on the HAR-RV model, some researchers pro-

pose new HAR models to improve the forecasting abilities of model s

for future volatility. Andersen et al. (2007) decompose the RV of HAR-

RV model into continuous sample path variation and discontinuous

jump variation and develop the HAR-RV-J and HAR-C J models. Chen

and Ghysels (2011) decompose the RV of HAR-RV model into positive

realized semivariance and negative realized semivariance. Also, consid-

ering the discontinuous jump variation, they develop the HAR-S-RV-J

model. Addin g leverage effects to the HAR-RV and HAR-CJ models,

371X. Gong, B. Lin / Energy Economics 74 (2018) 370–386

Asai et al. (2012) and Corsi and Renò (2012) develop the LHAR-RV and

LHAR-CJ models, respectively. Patton and Sheppard (2015) argue that

positive and negative realized semivariances, signed jump variation,

and positive and negative signed jump variations have effects on future

volatility; so they propose several new HAR models such as the HAR-

RSV, HAR-RSV-L, and HAR-RV-SJd models. Prokopczuk et al. (2016) pro-

pose the HAR-RV-RJ and HAR-RV-ARJ models. The HAR-RV-RJ model in-

clude s the continuous sample path variation, realized jump, and

realized volatility. The HAR-RV-ARJ model includes the continuous sam-

ple path variation, positive and negative realized jumps, and realized

volatility.

In addition to the HAR models discussed above, some new HAR

models are developed. They include th e HAR-TCJ mod el (Corsi et al.

2010), the HAR-CJN model (Andersen et al. 2011), the HAR-CJ-M

model (Huang et al. 2013), the HAR-CSJ and HAR-CSJd models (Sévi

2014), the HAR-RV-C-type models (Duong and Swanson 2015), the

HARQ model (Bollerslev et al., 2016), the HAR-GASVR(res) and HAR-

GASVR models ( Psaradellis and Sermpinis 2016), the HAR model s

with a dynamic model averaging (DMA) approach (Wang et al.,

2016a, b), the HAR-RV-X, HAR-RV-asset class, HAR-RV-combined and

HAR-RV-average models (Degiannakis and Filis 2017), the TVP-HAR-

RV and TVP-HAR-RV-TCJ models (Wa ng et al. 2017), and the HAR

models with structural breaks (Gong and Lin 2018b).

The above literature shows that the HAR models have good

predictive ability for future volatility in the ﬁnancial market s. How-

ever, the studies that use the HAR models to forecast the volatility

of crude oi l futures are rare. In addition, Aboura and Chevallier

(2013), Haugom et al. (2014) and Ji and Fan (2016) ﬁnd that IFG

(or OVX) affects the volatility of crude oil futures. Thus, adding

investor fear gauge (IFG) to the HAR model s, this paper p roposes

the HAR models with IFG, and test the role of IFG in forecasting

volatility in the cr ude oil market.

3. Volatility estimation

3.1. Realized volatility

Following Andersen and Bollerslev (1998), we use the realized vola-

tility (RV) to measure volatility in the ﬁnancial market. For a given day t,

the daily realized volatility is computed as the sum of squared intraday

returns r

t, i

at a given sampling frequency 1/M:

i¼1

t;i

ð1Þ

where r

t, i

is the i

return at the given day t.

3.2. Continuous sample path and discontinuous jump variations

When M → ∞, the daily realized volatility RV

denotes a consistent

estimator of daily quadratic variation QV

→

M→∞

t‐1

ds þ

t‐1b s ≤ t

ð2Þ

Following Barndorff-Nielse and Shepherd (2004, 2006), we use the

daily realized bipower variation RBV

to estimate the daily continuous

sample path variation ∫

t‐1

ds:

RBV

¼ z

−2

M−2

i−3

t;i−2



t;i



ð3Þ

where z

¼ EðZ

Þ¼

ﬃﬃﬃﬃﬃﬃﬃﬃ

π=2

, Z

denotes a random variable which follows a

standard normal distributio n. Foll owing Huang and Tauchen (2005)

and Ji and Zhang (2018), this paper uses a Z-statistic to detect the pres-

ence of discontinuous jump variation

−RBV



=RV

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

‐4

þ 2μ

‐2

−5



max 1;

RTQ

RBV



→N 0; 1ðÞ ð4Þ

where μ

ﬃﬃﬃﬃﬃﬃﬃﬃ

2=π

, RTQ

denotes the daily realized tri-power quarticity,

RTQ

¼ Mμ

−3

4=3

M−4

i¼4

t;i−4

4=3

t;i−2

4=3

t;i

4=3

,(μ

4/3

= E(|Z

4/3

2/3

Γ(7/6)Γ(1/2)

−1

When the Z-statistic is signiﬁcant, the difference between the daily

realized volatility RV

and daily realized bipower variation RBV

is too

large and need to be considered as a jump. Thus, based on Eq. (4),we

can obtain the daily discontinuous jump variation J

¼ RV

−RBV



 IZ

NΦ

fg ð5Þ

The daily continuous sample path variation C

¼ RV

 IZ

≤Φ

fgþRBV

 IZ

NΦ

fg ð6Þ

where I(⋅) is a indicator function. Φ

refers to a threshold value from the

standardized normal dis tribution. Following Andersen et al. (2007,

2011), this paper chooses the threshold value of α = 0.99.

3.3. Positive and negative realized semivariances

Barndorff-Nielsen et al. (2010) decompose the daily realized volatility

into daily positive and negative realized semivariances. The daily positive

realized semivariance can be computed as follows.

PRSV

i¼1

t; j

 Ir

t;i

≥0





ð7Þ

The daily negative realized semivariance can be written as follows.

NRSV

i¼1

t;i

 Ir

t;i

b 0





ð8Þ

3.4. Signed jump

The daily signed jump is deﬁned as the difference between d aily

positive and negative realized semivariances (Patton and Sheppard

2015).

¼ PRSV

−NRSV

ð9Þ

Then the daily positive signed jump is deﬁned as:

PSJ

¼ PRSV

−NRSV



 IPRSV

−NRSV

≥0



ð10Þ

And the daily negative signed jump is written as:

NSJ

¼ PRSV

−NRSV



 IPRSV

−NRSV

b 0



ð11Þ

372 X. Gong, B. Lin / Energy Economics 74 (2018) 370–386

3.5. Realized jump

Following Prokopczuk et al. (2016) and Tauchen and Zhou (2011),

the daily realized jump is deﬁned as:

¼ sign R



ﬃﬃﬃﬃﬃ

ð12Þ

where R

denotes the daily return.

The daily positive realized jump is written as:

PRJ

¼ max RJ

; 0



ð13Þ

The daily negative realized jump is written as:

NRJ

¼ min RJ

; 0



ð14Þ

4. Volatility forecasting models

We randomly choose six popular HAR models as benchmark volatil-

ity forecasting models in this p aper. These models are the HAR-RV,

LHAR-RV, HAR-CJ, HAR-S-RV-J, HAR-RV-SJd and HAR-RV-ARJ models.

Some of them are the most classica l HAR models (e.g., the HAR-RV

and HAR-CJ mo dels). Some have be en developed in recent ye ars

(e.g., the HAR-RV-SJd and HAR-R V-ARJ models). Thus, these models

are very representative. Considering the investor fear gauge (IFG), we

develop six HAR models with IFG, i.e., the HAR-RV-IFG, LHAR-RV-IFG,

HAR-CJ-IFG, HAR-S-RV-J-IFG, HAR-RV-SJd-IFG, and HAR-RV-ARJ-IFG

models. We now present the linear/original forms of a bove twelve

volatility forecasting models as follows.

4.1. The HAR-RV and HAR-RV-IFG models

The HAR-RV model is proposed by Corsi (2009), which can test the

role of lag realized volatility in forecasting the volatility of ﬁnancial

assets. The HAR-RV model is denoted as follows:

tþH

¼ c þ α

þ α

þ ε

tþH

ð15Þ

where

tþ H

denotes the average realized volatility over the period

[t +1,t + H].

tþ 1

, RV

tþ 5

and RV

tþ22

denotes the 1-day, 1-week and

1-month future realized volati litie s, respectively. RV

, RV

and RV

denotes the daily, weekly and monthly realized volatility, respec-

tively, where RV

=(RV

+ RV

t−1

+ ⋯ + RV

t−4

)/5 and RV

(RV

+ RV

t−1

+ ⋯ + RV

t−21

)/22.

Adding the investor fear gauge (IFG) to Eq. (15), we obtain the HAR-

RV model with IFG (HAR-RV-IFG model). This model can assess the role

of realized volatility and investor fear gauge in forecasting volatility.

This model is expressed as:

tþH

¼ c þ α

þ α

þ λIFG

þ ε

tþ H

ð16Þ

where IFG

is the investor fear gauge.

4.2. The LHAR-RV and LHAR-RV-IFG models

The HAR-RV model with levera ges (LHAR-RV model) is proposed

by adding leverage effects to the HAR-R V mode l (Asai et al. 2012).

This model can examine whether the lag realized volatility and

leverages have e ffects on fore casting the vo latility. It can be

expressed as:

tþH

¼ c þ α

þ α

þ β

þ ε

tþ H

ð17Þ

where L

denotes the daily leverage effect, i.e., L

= R

d−

= R

⋅ I{R

b 0};

= R

w−

=(R

+ R

t−1

+ ⋯ + R

t−4

) ⋅ I{(R

+ R

t−1

+ ⋯ + R

t−4

) b 0}/5

denotes the weekly leverage effect. L

= R

m−

=(R

+ R

t−1

+ ⋯ +

t−21

) ⋅ I{(R

+ R

t−1

+ ⋯ + R

t−21

) b 0}/22 denotes the monthly

leverage effect.

Taking into account investor fear gauge (IFG) on the basis of Eq. (17),

we propo se the LHAR-RV model with IFG (LHAR-RV-IFG model) as

follows.

tþ H

¼ c þ α

þ α

þ β

d−

þ β

w−

þ β

m−

þ λIFG

þ ε

tþ H

ð18Þ

4.3. The HAR-CJ and HAR-CJ-IFG models

Andersen et al. (2007) de compose the realized volatility into the

continuous sample path variation and discontinuous jump variation,

and develop the heterogeneous autoregressive (HAR) model with

continuous sample path and discontinuous jump variations (HAR-CJ

model). This model can examine whether these two volatility compo-

nents contain information contents for forecasting the volatility of

ﬁnancial assets. It is written as:

tþ H

¼ c þ ϕ

þ ϕ

þ φ

þ ε

tþH

ð19Þ

where C

, C

and C

denot e daily, weekly and monthly continuous

sample path variations, where C

=(C

+ C

t−1

+ ⋯ + C

t−4

)/5 and

=(C

+ C

t−1

+ ⋯ + C

t−21

)/22. J

, J

and J

are daily, weekly and

monthly discontinuous jump variations, J

=(J

+ J

t−1

+ ⋯ + J

t−4

)/5

and J

=(J

+ J

t−1

+ ⋯ + J

t−21

)/22.

Considering investor fear gauge (IFG) based on Eq. (19),wedevelop

the HAR-CJ model with IFG (HAR-CJ-IFG model):

tþ H

¼ c þ ϕ

þ ϕ

þ φ

þ λIFG

þ ε

tþH

ð20Þ

4.4. The HAR-S-RV-J and HAR-S-RV-J-IFG models

Chen and Ghysels (2011) believe that the positive realized

semivariance, negative realized semivariance and discontinuous jump

variation contain predictive information for the volatility of ﬁnancial

assets. They develop the HAR model with realized semivariances and

discontinuous jump variation (HAR-S-RV-J model):

tþ H

¼ c þ γ

PRSV

þ γ

PRSV

þ γ

PRSV

þ η

NRSV

þ η

NRSV

þ η

NRSV

þ φ

þ ε

tþ H

ð21Þ

where PRSV

, PRSV

and PRSV

denote the daily, weekly and monthly

positive realized semivariances, where PRSV

=(PRSV

+ PRSV

t−1

+ ⋯

+ PRSV

t−4

)/5 and PRSV

=(PRSV

+ PRSV

t−1

+ ⋯ + PRSV

t−21

)/22.

NRSV

, NRSV

and NRSV

denote the daily weekly and monthly

negative realized semivariances, where NRSV

=(NRSV

+ NRSV

t−1

⋯ + NRSV

t−4

)/5 and NRSV

=(NRSV

+ NRSV

t−1

+ ⋯ + NRSV

t−21

)/22.

Considering the investor fear gauge (IFG) on the basis of the HAR-S-

RV-J model, we develop the HAR-S-RV-J model with IFG (HAR-S-RV-J-

IFG model):

tþ H

¼ c þ γ

PRSV

þ γ

PRSV

þ γ

PRSV

þ η

NRSV

þ η

NRSV

þ η

NRSV

þ φ

þ λIFG

þ ε

tþH

ð22Þ

373X. Gong, B. Lin / Energy Economics 74 (2018) 370–386

4.5. The HAR-RV-SJd and HAR-RV-SJd-IFG models

Patton and Sheppard (2015) develop the HAR model with realized

volatility and signed jump (HAR-RV-SJd model). This model includes

the daily continuous sample path variation, daily positive and negative

signed jumps, weekly and monthly realized volatilities:

tþ H

¼ c þ ϕ

þ θ

PSJ

þ ρ

NSJ

þ α

þ ε

tþH

ð23Þ

where PSJ

denotes the daily positive signed jump as deﬁned in Eq. (10).

NSJ

denotes the daily negative signed jump as deﬁned in Eq. (11).

Adding investor fear gauge (IFG) to the HAR-RV-SJd model, we

develop the HAR-RV-SJd model with IFG (HAR-RV-SJd -IFG model):

tþ H

¼ c þ ϕ

þ θ

PSJ

þ ρ

NSJ

þ α

þ λIFG

þ ε

tþ H

ð24Þ

4.6. The HAR-RV-ARJ and HAR-RV-ARJ-IFG models

Prokopczuk et al. (2016) believe that the daily positive realized jump

and daily negative realized jump have asymmetric impacts on volatility.

They develop the HAR model of realized volatility and asymmetric

signed jumps (HAR-RV-ARJ model):

tþ H

¼ c þ ϕ

þ θ

PRJ

þ ρ

NRJ

þ α

þ ε

tþH

ð25Þ

where PRJ

denotes the daily positive realized jump as deﬁned in Eq. (13).

NRJ

denotes the daily negative realized jump as deﬁned in Eq. (14).

Adding the inve stor fe ar gau ge (IFG) to Eq. (25), we develop the

HAR-RV-ARJ model with IFG (HAR-RV-ARJ -IFG model):

tþ H

¼ c þ ϕ

þ θ

PRJ

þ ρ

NRJ

þ α

þ λIFG

þ ε

tþH

ð26Þ

Table 2

Cross correlations of RV

t+H

and IFG

H 0 1 5 10 15 20 25 30

Correlation coefﬁcient 0.577*** 0.563*** 0.549*** 0.536*** 0.522*** 0.513*** 0.509*** 0.485***

Fig. 1. Time series of the daily RV and IFG over the period May 10, 2007–June 30, 2016.

Table 1

Summary statistics for volatility components, leverages, and IFG.

Mean Std. Dev. Skewness Kurtosis Q(5) Q(10) Q(20) Q(30)

5.713 10.706 10.192 191.841 1641.9*** 3101.0*** 5766.8*** 8419.7***

5.710 7.610 3.997 25.535 8096.2*** 13785*** 24497*** 34664***

5.691 6.685 2.806 11.147 11100*** 21673*** 40718*** 56929***

3.266 4.332 3.928 25.170 5979.1*** 11321*** 21015*** 29003***

3.266 3.829 3.014 13.874 10218*** 19060*** 34890*** 47989***

3.264 3.641 2.879 12.273 11183*** 21906*** 41158*** 57287***

2.447 8.346 13.925 308.773 156.2*** 277.1*** 545.6*** 993.10***

2.444 4.474 5.473 44.445 4902.7*** 6401.3*** 9747.5*** 14013***

2.427 3.193 2.798 10.743 10710*** 20378*** 36858*** 50290***

PRSV

2.877 8.192 17.773 485.740 366.16*** 629.75*** 1251.8*** 2069.4***

PRSV

2.876 4.785 6.245 58.556 5820.6*** 8273.7*** 13885*** 19963***

PRSV

2.869 3.693 3.165 13.850 10903*** 21071*** 38851*** 53111***

NRSV

2.836 5.807 8.150 105.450 758.8*** 1805.2*** 3409.2*** 4850.4***

NRSV

2.834 3.695 3.260 16.596 7196.8*** 12972*** 22744*** 31441***

NRSV

2.822 3.197 2.664 10.359 10958*** 21328*** 39652*** 55286***

PSJ

1.545 7.585 20.519 600.655 36.612*** 51.711*** 137.57*** 404.88***

NSJ

−1.504 4.986 −9.485 134.801 62.041*** 295.98*** 545.32*** 773.24***

PRJ

0.426 1.022 4.505 38.505 24.955*** 33.049*** 103.24*** 173.88***

NRJ

−0.457 1.003 −3.126 16.969 40.523*** 118.11*** 231.88*** 305.64***

−0.864 1.483 −2.706 12.850 10876*** 21172*** 40149*** 782.58***

−0.386 0.660 −2.592 12.137 116.39*** 256.99*** 535.96*** 4067.6***

−0.201 0.346 −2.440 10.071 2605.0*** 2793.0*** 3447.9*** 25350***

IFG

37.780 14.674 1.246 5.121 8720.9*** 14775*** 22046*** 57029***

Note: Asterisks denote statistical signiﬁcance at the 1% (***), 5% (**) and 10% (*) levels. Q(5), Q(10), Q(20) and Q(30) denote the Ljung-Box Q-statistics.

374 X. Gong, B. Lin / Energy Economics 74 (2018) 370–386

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weixin_58834806

2022-04-22

我像问一下“#import <C:/MCS/MulCom>”当作的MulCom是什么呢，我运行的时候显示未找到C:/MCS/R-MAE.ox (11): 'C:/MCS/MulCom' header file for import not found
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2024-01-17

实在是宝藏资源、宝藏分享者！感谢大佬~
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2023-03-28

资源内容详细，总结地很全面，与描述的内容一致，对我启发很大，学习了。
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2022-04-20

用户下载后在一定时间内未进行评价，系统默认好评。
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2023-12-14

资源内容详尽，对我有使用价值，谢谢资源主的分享。