volatility forecasting using high frequency data: evidence from stock markets

Economic Modelling 36 (2014) 176–190

Contents lists available at ScienceDirect

Economic Modelling

j ourna l homepage: www.e lsev ie r .com/ locate /ecmod

Volatility forecasting using high frequency data: Evidence fromstock markets☆

Sibel Çelik a,⁎, Hüseyin Ergin b

a Dumlupinar University, School of Applied Sciences, Turkeyb Dumlupinar University, Business Administration, Turkey

☆ This paper is based onmy doctoral dissertation “VolatilEvidence From High Frequency Data of Istanbul Stock ExcDumlupinar University, in 2012.⁎ Corresponding author at: Dumlupinar University,

Insurance and Risk Management Department, Turkey. TelE-mail address: [email protected] (S. Çelik).

0264-9993/$ – see front matter © 2013 Elsevier B.V. All rihttp://dx.doi.org/10.1016/j.econmod.2013.09.038

a b s t r a c t
a r t i c l e i n f o
Article history:Accepted 24 September 2013Available online xxxx

JEL classification:C22G00

Keywords:VolatilityRealized volatilityHigh frequency dataPrice jumps

The paper aims to suggest the best volatility forecasting model for stock markets in Turkey. The findings of thispaper support the superiority of high frequency based volatility forecasting models over traditional GARCHmodels.MIDAS andHAR-RV-CJmodels are found to be the best amonghigh frequency based volatility forecastingmodels.Moreover,MIDASmodel performs better in crisis period. Thefindings of paper are important forfinancialinstitutions, investors and policy makers.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

Volatility plays an important role in theoretical andpractical applica-tions in finance. The availability of high frequency data brings a newdimension to volatility modeling and forecasting of returns on financialassets. First and foremost, nonparametric estimation of volatility of assetreturns becomes feasible and so modeling and forecasting volatilityof asset returns has been a focus for researchers in the literature(Andersen and Bollerslev, 1998; Andersen et al., 2001, 2003b, 2007;Corsi, 2004; Engle and Gallo, 2006; Ghysels et al., 2004, 2005, 2006a,b;Hansen et al., 2010; Shephard and Sheppard, 2010). The empirical find-ings of existing studies support the superiority of high frequency basedvolatility models to popular GARCH models and stochastic volatilitymodels in the literature (Andersen et al., 2003b). Besides, earlier studiespoint to importance of allowing for discontinuities (jumps) in volatilitymodels and pricing derivatives (Andersen et al., 2002; Chernov et al.,2003). Availability of high frequency data is also a turning point inorder to distinguishing jump from continuous part of price process.Empirical findings from recent studies show that incorporating thejumps to volatility models increase the forecasting performance ofmodels supporting the earlier evidence (Andersen et al., 2003b, 2007).

ity Forecasting in StockMarkets:hange” which was completed at

School of Applied Sciences,.: +90 2742652031x4664.

ghts reserved.

This paper aims to suggest the best volatility forecasting model instock markets in Turkey. For this purpose, first, we analyze the datagenerating process and calculate the high frequency based volatilityand examine the return and volatility characteristics. Second, wepropose the best volatility forecasting model by comparing differentvolatility forecasting models.

In doing so, the paper will contribute to the literature in terms offilling five main gaps. First, it suggests the best volatility forecastingmodel from the alternatives including high frequency-based modelsand traditional GARCH models. Second, it reveals the forecastingperformance of volatility models during the periods of structuralchange. Because, recent studies in the literature indicate thatfinancial crisis affect the volatility dynamics deeply (Dungey et al.,2011). Third, it analyses forecasting performance of volatility instock futures markets rather than spot markets. There are threereasons for usage of stock futures markets in this study. Firstly,there are findings in the literature that futures markets respond tonew information faster than spot markets (Stoll and Whaley,1990). Secondly, using futures contracts rather than spot indexes re-duces nonsynchronous trading problems (Wu et al., 2005). Thirdly,using futures contracts provides additional evidence to the existingliterature on spot markets (Wu et al., 2005). Fourth, it comparesthe findings at different frequencies to inference about optimal fre-quency since the sampling selection is important for high frequencydata based studies. Because, while higher sampling frequency maycause bias in realized volatility, lower sampling frequency maycause information loss. Last, it contributes to literature in terms ofpresenting evidence from an Emerging Market.

http://crossmark.crossref.org/dialog/?doi=10.1016/j.econmod.2013.09.038&domain=pdf

http://dx.doi.org/10.1016/j.econmod.2013.09.038

mailto:[email protected]

http://dx.doi.org/10.1016/j.econmod.2013.09.038

http://www.sciencedirect.com/science/journal/02649993

177S. Çelik, H. Ergin / Economic Modelling 36 (2014) 176–190

The paper proceeds as follows. Section 2 introduces dataset of thepaper. Section 3 explains the methodologies used in the paper.Section 4 summarizes the empirical findings. Section 5 concludesthe paper.

2. Data

The dataset comprises of ISE-30 index futures data at intradaily anddaily frequency from 04.02.2005 to 30.04.2010.1 We generate new datasampled at 1-minute interval, 5-minute interval, 10-minute intervaland 15-minute interval. The number of intraday observations ofISE-30 index future are 502, 101, 51 and 34, respectively.

Careful data cleaning is one of the most important point involatility estimation from high frequency data. The importance ofcleaning of high frequency data is emphasized in the literature(Brownless and Gallo, 2006; Dacorogna et al., 2001; Hansen andLunde, 2006).

In this paper, we used following steps for data cleaning process.

1. We delete entries which related to weekends.2. We delete entries of public holidays, which is announced by Istanbul

Stock Exchange and Turkish Derivatives Exchange.3. We delete entries when the Stock Exchanges do not trade full days.4. We delete entries which is not common for Istanbul Stock Exchange

and Turkish Derivatives Exchange from 04.02.2005 to 30.04.2010.

3. Methodology

3.1. Methodologies for volatility modeling and data analysis

3.1.1. GARCH modelThe GARCH models are as follows:

rt ¼ffiffiffiffiffiht

qεt ð1Þ

ht ¼ α0 þXqi¼1

αir2t−i þ

Xpj¼1

β jht− j ð2Þ

p ≥ 0, q N 0, α0 N 0, αi ≥ 0 ∀ i ≥ 1, i = 1,……..p, βj ≥ 0 ∀ j ≥ 1.

3.1.2. Continuous-jump diffusion processThe continuous-time jump diffusion process traditionally used in

asset pricing finance is expressed as:

dpt ¼ μdt þ σ tð ÞdW tð Þ þ γ tð Þdq tð Þ 0 ≤ t ≤ T ð3Þ

where μt is a continuous and locally bounded variation process, σt isstochastic volatility process, Wt denotes a Standard Brownian motion,dqt is a counting process with dqt = 1, corresponding to a jump attime t and dqt = 0 otherwise with jump intensity ψ(t), and γ(t) refersto the size of jumps. The quadratic variation for the cumulative returnprocess, r(t) = p(t) − p(0) is given by,

r; r½ �t ¼Zt0

σ2 sð ÞdsþX

0⊲s≤ t

γ2 sð Þ: ð4Þ

Quadratic variation consists of ∫t

0

σ2 sð Þds continuous and ∑0⊲s≤ t

γ2 sð Þ,jump components. In the absence of jumps, the second term in the rightwill not exist and quadratic variation will equal to integrated volatility(Andersen et al., 2003a).

1 ISE-30 index futures data were taken from Turkish Derivatives Exchange.

3.1.3. Realized volatility, bipower variation and jumpsLet the θ— period returns be denoted by, rt,θ = p(t) − p(t − θ).We

define daily realized volatility by the summing corresponding 1/θ highfrequency intradaily squared returns as follows:

RVtþ1 θð Þ ¼X1=θj¼1

rtþ j:θ;θ2: ð5Þ

In the absence of jumps, realized volatility is the consistent estimateof the integrated volatility. However, in the presence of jumps, we needmore powerful measurement. Barndorff et al. (2004) introduce thevolatility measurement which is powerful in the case of jumps calledbipower variation (henceforth: BV). BV is defined as follows:

BVtþ1 θð Þ ¼ μ1−2X1=θ

j¼2

rtþ j

�� rtþ j−1ð Þ�� ð6Þ

μ1−2 ≅ 0:7979 in Eq. (6).While the realized volatility consists of both continuous and jump

components, BV only includes continuous component. Thus, jumpcomponent may be consistently estimated by,

RVtþ1 θð Þ−BVtþ1 θð Þ ¼X

t≺s≤ tþ1

γ2 sð Þ: ð7Þ

To prevent the right hand-side of Eq. (7) from becoming negative,we impose non-negativity truncation on the jump measurements.

Jtþ1 θð Þ ¼ max RVtþ1 θð Þ−BVtþ1 θð Þ; 0� � ð8Þ

Continuous component is given in Eq. (9).

BVtþ1 θð Þ ¼ RVtþ1 θð Þ− Jtþ1 θð Þ ð9Þ

3.2. Methodologies for volatility forecasting

3.2.1. GARCH modelTo evaluate the forecasting performance of GARCHmodel, first we es-

timate Eqs. (1) and (2). Let htþ1G denote the predicted value for ht. The

forecast error for theGARCHmodel for the observation t + 1 is computedas RVtþ1−htþ1

G based on the existing literature (Alper et al., 2009).

3.2.2. HAR-RV modelHAR-RV model is introduced by Corsi (2004) and denoted as,

RVtþ1 ¼ β0 þ βDRVt þ βWRVt−5;t þ βMRVt−22;t þ εtþ1 ð10Þ

t = 1,2,3…..T. RVt, RVt − 5and RVt − 22 mark daily, weekly and monthlyrealized volatility respectively. Multi-period realized volatility compo-nents such as weekly and monthly realized volatility is calculated as,

RVt;tþh ¼ h−1 RVtþ1 þ RVtþ2 þ ::::þ RVtþh

� � ð11Þ

h ¼ 1;2;… RVt;tþ1 ≡ RVtþ1: ð12Þ

In this paper, we take h = 5 and h = 22 as theweekly andmonthlyvolatility, respectively. Andersen et al. (2003b) state that the distribu-tion of standard deviation and logarithmic form of realized volatilityare close to normal than original form and so using these proxiesincreases performance of volatility forecasting. Therefore, we estimatestandard deviation and logarithmic form of Eqs. (11) and (12).

RVtþ1� �1=2 ¼ β0 þ βD RVtð Þ1=2 þ βW RVt−5;t

� 1=2

þ βM RVt−22;t

� 1=2 þ εtþ1 ð13Þ

178 S. Çelik, H. Ergin / Economic Modelling 36 (2014) 176–190

log RVtþ1� � ¼ β0 þ βD log RVtð Þ þ βW log RVt−5;t

� þ βM log RVt−22;t

� þ εtþ1 ð14Þ

3.2.3. HAR-RV-J modelHAR-RV-Jmodel is developed by Andersen et al. (2003b) by including

jump component in HAR-RV model. Daily HAR-RV-J model is expressedin Eq. (15),

RVt;tþ1 ¼ β0 þ βDRVt þ βWRVt−5;t þ βMRVt−22;t þ β j Jt þ εt;tþ1: ð15Þ

Logarithmic and standard deviation formof HAR-RV-Jmodel is givenin Eq. (16) and (17).

RVtþ1� �1=2 ¼ β0 þ βD RVtð Þ1=2 þ βW RVt−5;t

� 1=2

þ βM RVt−22;t

� 1=2β j Jtð Þ1=2 þ εtþ1 ð16Þ

log RVtþ1� � ¼ β0 þ βD log RVtð Þ þ βW log RVt−5;t

� þ βM log RVt−22;t

� þ β j log Jt þ 1ð Þ þ εtþ1 ð17Þ

3.2.4. HAR-RV-CJ modelAndersen et al. (2007) develop HAR-RV-CJ model by including

jump and continuous components separately in HAR-RV model. DailyHAR-RV-CJ model is stated as follows,

RVt;tþ1 ¼ β0 þ βCDCt þ βCWCt−5;t þ βCMCt−22;t þ βjD Jt þ βJW Jt−5;t

þ βJM Jt−22;t þ εt;tþ1: ð18Þ

Multi period jump and continuous components are calculated as inEqs. (19) and (20),

Jt;tþh ¼ h−1 Jtþ1 þ Jtþ2 þ ::::::þ jtþh

� � ð19Þ

Ct;tþh ¼ h−1 Ctþ1 þ Ctþ2 þ ::::::þ Ctþh

� �: ð20Þ

Logarithmic and standard deviation form of HAR-RV-CJ model isgiven in Eqs. (21) and (22).

RVt;tþ1

� 1=2 ¼ β0 þ βCD Ctð Þ1=2 þ βCW Ct−5;t

� 1=2

þ βCM Ct−22;t

� 1=2 þ βjD Jtð Þ1=2 þ βJW Jt−5;t

� 1=2

þ βJM Jt−22;t

� 1=2 þ εt;tþ1 ð21Þ

log RVt;tþ1

� ¼ β0 þ βCD log Ctð Þ þ βCW log Ct−5;t

� þ βCM log Ct−22;t

� þ βjD log Jt þ 1ð Þ

þ βJW log Jt−5;t þ 1�

þ βJM log Jt−22;t þ 1�

þ εt;tþ1 ð22Þ

3.2.5. MIDAS (mixed data sampling) modelMIDAS model is introduced by Ghysels et al. (2004, 2005, 2006a,b).

Univariate MIDAS linear regression is given in Eq. (23),

Yt ¼ δ0 þ δ1Xkmax

k¼0

B k; θð ÞX mð Þt−k=m þ εt : ½23�

Yt and X(m) are one-dimensional processes, B(k,θ) is polynomialweighting function depending on k and θ parameter and Xt

mð Þ issampled m times more frequent than Yt. For example, if t denotes a

22-day monthly sampling and m = 22, model (23) shows a MIDASregression of monthly data (Yt) on past kmax daily data (Xt)

RVtþ1;t ¼ δ0 þ δ1Xkmax

k¼0

B k; θð ÞRV mð Þt−k=m þ εt ð24Þ

m = 1, kmax = 50 and t refers to daily observations.Ghysels et al. (2006a) suggest various alternatives for B(k,θ) polyno-

mial. In this paper, we focus on beta polynomial following Ghysels et al.(2006a). B(k,θ), is denoted as in Eq. (25).

B k; θð Þ ¼ f k=kmax; θ0; θ1� �

Xkmaxk¼1

f k=kmax; θ0; θ1

� � ð25Þ

and,

f x; θ0; θ1ð Þ ¼ xθ0−1 1−xð Þθ1−1Γ θ0 þ θ1ð ÞΓ θ0ð ÞΓ θ1ð Þ : ð26Þ

Γ(.) is gamma function. In beta function, we restrict our attention toθ0 = 1 and estimate θ1 N 1.

3.2.6. Realized GARCH modelRealized GARCH model which is introduced by Hansen et al. (2010)

can be expressed as in Eqs. (27), (28) and (29).

rt ¼ffiffiffiffiffiht

qzt ð27Þ

ht ¼ wþ βht−1 þ γxt−1 ð28Þ

xt ¼ ξþ ϕht þ τ ztð Þ þ ut ð29Þ

rt is return; zt ~ iid(0,1), ut e iid 0;σu2

� �, τ(z) is leverage function, ht =

var(rt|Ft − 1), and Ft = σ(rt,xt,rt − 1,xt − 1,.....).RGARCH model is estimated with maximum likelihood method as

GARCH model. Log likelihood function is given in Eq. (30).

‘ r; x; θð Þ ¼ −12

Xnt¼1

log htð Þ þ rt2=ht þ log σu

2�

þ ut2=σu

2h i

: ð30Þ

We evaluate the forecasting performance of RGARCH model as inGARCH model.

3.3. Evaluation of forecasting performance

We use mean squared error (MSE), mean absolute error (MAE),mean absolute percentage error (MAPE) and Theil's U statistic (TIC) toevaluate performance of volatility forecasting models. Calculation ofthe loss functions is as follows;

RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiN−1

XNi¼1

RVt;tþH−RV̂t;tþH

� 2vuut ð31Þ

MAE ¼ N−1XNi¼1


�� ð32Þ

MAPE ¼ N−1XNi¼1


RVt;tþH

�� ð33Þ

3 We examine the impact of 2007 global crisis on volatility characteristics. In the litera-ture, there are somefindings that global financial crisis give thefirst signal with announce-ment of the problems with the hedge funds of Bear Stearns in July 2007. Some papers use17 July 2007 as a starting date of the globalfinancial crisis (Dungey, 2009). Following thesefindings, we determine three sub-periods (from 04.02.2005 to 16.07.2007 is pre crisis pe-riod, from 17.07.2007 to 30.04.2010 is crisis period and from 17.07.2007 to 30.04.2010 istotal period).

4

Table 1Summary statistics for ISE −30 index futures at 1 minute frequency.

Variable Sampling period Mean Maximum Minimum S.dev Skewness Kurtosis LB

Return Pre-crisis period 1.9100 0.1185 −0.1175 0.0036 0.0562 69.7271 34,906Crisis period 0.3340 0.1071 −0.1080 0.0044 −0.0487 59.8545 77,165Total period 1.0800 0.1185 −0.1175 0.0040 −0.0137 64.8631 115,010

RV Pre-crisis period 0.0006 0.1006 4.3300 0.0120 4.4226 27.8839 1887.80Crisis period 0.0097 0.2637 10.600 0.0195 5.9606 58.6426 776.67Total period 0.0083 0.2637 4.3300 0.0165 6.1654 66.3539 2008.80

RV1/2 Pre-crisis period 0.0648 0.3172 0.0065 0.0503 1.8040 7.5673 1939.60Crisis period 0.0751 0.5136 0.0102 0.0643 1.9433 8.8189 2143.70Total period 0.0702 0.5136 0.0065 0.0584 1.9819 9.1468 4117.40

log(RV) Pre-crisis period −6.0277 −2.2960 −10.0473 1.5362 −0.1492 2.4918 1646.00Crisis period −5.8363 −1.3325 −9.1513 1.6511 0.0407 2.1353 3490.50Total period −5.9263 −1.3325 −10.0473 1.6004 −0.0255 2.3153 5114.80

J Pre-crisis period 278.400 0.0441 0.0000 0.0050 3.7346 20.7028 1438.30Crisis period 175.300 0.0387 0.0000 0.0035 4.6203 4.6203 32.6315Total period 223.800 0.0441 0.0000 0.0043 4.1948 26.1864 2584.70

J1/2 Pre-crisis period 0.0407 0.2101 0.0000 0.0336 1.7732 6.5963 1830.30Crisis period 0.0307 0.1968 0.0000 0.0284 1.8845 7.5504 2033.20Total period 0.0354 0.2101 0.0000 0.0313 1.8465 7.1816 3982.60

log(J + 1) Pre-crisis period 0.0027 0.0432 0.0000 0.0049 3.6922 20.2324 1451.40Crisis period 0.0017 0.0380 0.0000 0.0035 4.5669 31.8685 929.74Total period 0.0022 0.0432 0.0000 0.0043 4.1465 25.5782 2609.70

BV Pre-crisis period 395.000 0.0795 0.0000 844.300 4.9842 33.8822 1777.30Crisis period 803.600 0.2250 7.3000 1640.00 6.3265 64.7405 699.36Total period 611.400 0.2250 0.0000 1340.80 6.9436 82.1317 1795.60

Note: RV, J and BV denote realized volatility, jump component and continuous component respectively. LB is the statistics of Ljung–Box (1979) Q test. Mean returns are multiplied by 106

and, minimum values of RV, mean values of J and mean, minimum and Standard deviation values of BV are multiplied by 105.


TIC ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXNi¼1


� 2

vuutffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXNi¼1

RVt;tþH

� 2

vuut þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXNi¼1

RV̂t;tþH

� 2

vuut: ð34Þ

RVt,t + H andRV̂t;tþH denote actual and predicted values of realizedvolatility, respectively. N is the number of observation. In addition tothese loss functions, we also use Mincer and Zarnowitz regression(1969) in this paper. Mincer–Zarnowitz regression is given inEq. (35).

RVt;tþH ¼ aþ b RV̂t;tþH

� þ ut;tþH ð35Þ

In the regression model, null hypothesis is formed as “a and b equalto 0”. If the forecasting is unbiased, a and b coefficients must equal to 0and 1 respectively and coefficient of b must be significant.

4. Empirical findings

The empirical findings are categorized under four sub-sections.

• We use six different models (GARCH, HAR-RV, HAR-RV-J, HAR-RV-CJ, MIDAS, RGARCH) to determine the best volatility forecastingmodel.

• Wepresent the findings of different transformations of volatility (stan-dard deviation, logarithmic) following Andersen et al. (1999, 2000)and Andersen et al. (2001).2

• We compare the volatility forecasting performance at differentfrequencies to inference about optimal sampling frequency (1 min,5 min, 10 min and 15 min).

2 We examine the standard deviation and logarithmic transformation of realized vola-tility, jumps statistics since Andersen et al. (1999, 2000) and Andersen et al. (2001) indi-cate that the distribution of standard deviation and logarithmic transformations are closeto normal and using these proxies increase performance of volatility forecasting.

• We compare the volatility forecasting performance for differentsample periods to examine the impact of financial crisis on volatilitystructure (pre-crisis period, crisis period and total period).3

Tables 1, 2, 3 and 4 present summary statistics of the variables4 at1-minute, 5-minute, 10-minute and 15-minute frequencies respective-ly. According to return statistics, as expected the mean returns arehigher in pre-crisis period for all frequencies. However, there are noconsistent information about the maximum and minimum values. Thestandard deviation of returns is higher in pre-crisis period for most ofthe frequencies. While returns have positive skewness in pre-crisisperiod, it is negative in crisis period for most of the frequencies. LBstatistics show the evidence of autocorrelation between return series.Mean values of realized volatility and jump statistics are higher inpre-crisis period,5 howevermean values of bipower variation are higherin crisis period for most of the frequencies.

Variables have kurtosis greater than 3 except log(RV) supportingleptokurtic distribution. The higher the frequency, skewness and kurto-sis degree of returns also increase. The distribution of standard devia-tion and logarithmic transformation of variables are close to normal.

Table 5 shows the summary statistics of conditional variance seriesof GARCH(1,1) estimation. The mean returns are higher in pre-crisisperiod. Maximum andminimum values of returns are appeared in crisisperiod. The standard deviation of returns is higher in crisis period. Re-turn series did not distribute normal. The mean conditional variance ishigher in crisis periodwith the value of 0.0005. The conditional varianceseries is rightly skewed and has leptokurtic distribution. Appendices

Return, realized volatility, standard deviation and logarithmic transformation of real-ized volatility, jumps, standard deviation and logarithmic transformation of jumps andbipower variation.

5 Turkish Derivative Exchange has started operating on February 2005 and pre-crisisperiod includes this period. In the first few days, trading volume is low and there is moretime difference between instantaneous price quotations. For this reason, realized volatilityor price jumps may increase in pre-crisis period.

Table 2Summary Statistics for ISE-30 index futures at 5-minute frequency.


Getiri Pre-crisis period 9.4900 0.0980 −0.0987 0.0050 0.0434 44.6137 7845.80Crisis period 1.6600 0.1056 −0.1041 0.0048 −0.1153 43.6467 10292.00Total period 5.3400 0.1056 −0.1041 0.0049 −0.0358 44.2088 17940.00

RV Pre-crisis period 0.0025 0.0412 3.2500 0.0044 3.8137 21.9029 1232.10Crisis period 0.0023 0.0651 6.3900 0.0046 5.9178 59.1149 578.34Total period 0.0024 0.0651 3.2500 0.0045 4.9924 43.1131 1675.10

RV1/2 Pre-crisis period 0.0402 0.2030 0.0057 0.0306 1.8578 7.0060 1634.40Crisis period 0.0381 0.2553 0.0079 0.0302 2.1709 9.8324 1590.00Total period 0.0391 0.2553 0.0057 0.0304 2.0182 8.4350 3213.60

log(RV) Pre-crisis period −6.9039 −3.1888 −10.3342 1.3787 0.1349 2.6138 1464.40Crisis period −7.0161 −2.7304 −9.6581 1.3492 0.4119 2.4306 2465.60Total period −6.9634 −2.7304 −10.3342 1.3638 0.2792 2.5022 3847.20

J Pre-crisis period 80.000 0.0165 0.0000 0.0018 4.5780 29.1127 1835.30Crisis period 37.300 0.0092 0.0000 0.0008 5.1176 39.0344 328.33Total period 57.800 0.0165 0.0000 0.0013 5.5964 44.6346 3207.60

J1/2 Pre-crisis period 0.0204 0.1287 0.0000 0.0198 2.1898 8.8465 1950.50Crisis period 0.0140 0.0964 0.0000 0.0132 2.0643 8.8297 816.22Total period 0.0170 0.1287 0.0000 0.0169 2.3747 10.6375 3328.50

log(J + 1) Pre-crisis period 0.0008 0.0164 0.0000 0.0017 4.5588 28.8745 1840.70Crisis period 0.0003 0.0092 0.0000 0.0008 5.1034 38.8103 329.55Total period 0.0005 0.0164 0.0000 0.0013 5.5710 44.2280 3213.90

BV Pre-crisis period 176.400 0.0439 0.0000 365.000 5.7191 48.5876 683.49Crisis period 200.000 0.0653 4.5000 418.000 7.1255 86.0992 462.04Total period 189.000 0.0653 0.0000 394.000 6.6502 74.7410 1076.40




1–18 present the results of GARCH, HAR-RV, HAR-RV-J, HAR-RV-CJ,MIDAS and RGARCH estimations, lost functions and Mincer Zarnowitztest. Prior evidence shows that the performance of volatility models isthe best at 15-minute frequency sampling for ISE-30 index futuressince lost functions are minimum at 15-minute frequency. Therefore,in this section, we only compare the performance of different volatilitymodels using 15-minute frequency as a base for ISE-30 index futuresrather than comparison of different frequencies.

Tables 6 and 7 present the comparison of forecasting performance ofmodels in pre-crisis and crisis period for ISE-30 index futures. Inpre-crisis period, RMSE, MAE and TIC functions indicate that GARCH

Table 3Summary statistics for ISE-30 index futures at 10-minute frequency.

Variable Sampling period Mean Maximum M

Getiri Pre-crisis period 18.800 0.0980 −Crisis period 3.2800 0.1010 −Total period 10.600 0.1010 −Pre-crisis period 0.0017 0.0234

RV Crisis period 0.0014 0.0271Total period 0.0015 0.0271Pre-crisis period 0.0328 0.1530

RV1/2 Crisis period 0.0308 0.1648Total period 0.0318 0.1648Pre-crisis period −7.2965 −3.7541 −

log(RV) Crisis period −7.3606 −3.6050 −Total period −7.3305 −3.6050 −Pre-crisis period 51.600 0.0149

J Crisis period 30.000 0.0084Total period 40.100 0.0149Pre-crisis period 0.0158 0.1223

J1/2 Crisis period 0.0123 0.0917Total period 0.0139 0.1223Pre-crisis period 0.0005 0.0148

log(J + 1) Crisis period 0.0002 0.0083Total period 0.0004 0.0148Pre-crisis period 121.000 0.0278

BV Crisis period 118.000 0.0229Total period 120.000 0.0278

Note: RV, J and BV denote realized volatility, jump component and continuous component respand, minimum values of RV, mean values of J and mean, minimum and Standard deviation val

model has the worst forecasting performance. Different from the RMSE,MAE and TIC functions, MAPE function support that GARCH andRGARCH models have the best forecasting performance. The best modelis controversial for the pre-crisis period. RMSE supports the superiorityof MIDAS 1/2 model, MAE functions support the superiority of MIDASlog model, according to MAPE function, GARCH model is the best, andTIC function supports the superiority ofHAR-RV-CJmodel.Whenweeval-uate all loss functions together,MIDAS1/2 andMIDAS logmodels seem tobe the best models. Then, HAR-RV-CJ 1/2, MIDAS, HAR-RV-CJ AND HAR-RV-J 1/2 models perform well, respectively. The findings of HAR-RV,HAR-RV-J and HAR-RV-CJ models support that including jump

inimum S.dev Skewness Kurtosis LB

0.0820 0.0057 0.1774 32.7284 3738.500.1033 0.0053 −0.4008 42.5932 3266.000.1033 0.0055 −0.0968 37.4329 6961.502.3100 0.0029 3.4457 17.3832 1621.905.5500 0.0027 4.6476 31.6358 499.542.3100 0.0028 4.0187 23.8416 2014.900.0048 0.0250 1.8493 6.5932 1875.600.0074 0.0228 2.1880 9.1487 1246.400.0048 0.0239 2.0180 7.7793 3137.30

10.6756 1.3468 0.2134 2.7375 1393.209.7991 1.2202 0.5178 2.7240 1901.00

10.6756 1.2812 0.3605 2.7487 3234.000.0000 0.0012 5.8682 49.5795 1260.700.0000 0.0006 5.5597 45.5093 235.430.0000 0.0010 6.5578 64.9379 1944.800.0000 0.0162 2.3975 10.8800 1425.900.0000 0.0121 2.2444 9.9725 467.140.0000 0.0143 2.4699 11.7815 2112.000.0000 0.0012 5.8416 49.1372 1266.600.0000 0.0006 5.5455 45.2689 235.760.0000 0.0010 6.5263 64.2986 1951.101.0800 236.600 5.0856 40.7553 799.063.8800 225.100 4.8162 33.6960 464.411.0800 230.000 4.9583 37.4717 1235.90

ectively. LB is the statistics of Ljung–Box (1979) Q test. Mean returns are multiplied by 106

ues of BV are multiplied by 105.

Table 4Summary statistics for ISE-30 index futures at 15-minute frequency.


Getiri Pre-crisis period 28.200 0.0971 −0.1013 0.0059 −0.1153 32.7125 2276.40Crisis period 5.1300 0.0773 −0.0781 0.0056 −0.3673 24.9238 1269.00Total period 16.000 0.0971 −0.1013 0.0058 −0.2385 29.0940 3459.00Pre-crisis period 0.0012 0.0198 0.4000 0.0020 3.9770 24.3354 1100.00

RV Crisis period 0.0010 0.0196 3.6000 0.0018 4.3395 29.8961 691.43Total period 0.0011 0.0198 0.4000 0.0019 4.1706 27.0939 1814.40Pre-crisis period 0.0281 0.1408 0.0020 0.0206 1.8973 7.3149 1493.60Crisis period 0.0273 0.1401 0.0060 0.0185 1.9688 8.0310 1315.70

RV1/2 Total period 0.0277 0.1408 0.0020 0.0195 1.9428 7.7214 2824.50Pre-crisis period −7.5796 −3.9195 −12.4292 1.3141 0.1007 3.0189 1050.90Crisis period −7.5594 −3.9298 −10.2319 1.1606 0.4454 2.6109 1627.60

log(RV) Total period −7.5689 −3.9195 −12.4292 1.2347 0.2497 2.9011 2596.20Pre-crisis period 38.200 0.0152 0.0000 0.0009 7.8913 98.2244 638.07Crisis period 20.900 0.0034 0.0000 0.0004 4.2103 24.1542 293.98

J Total period 29.000 0.0152 0.0000 0.0007 9.1269 144.2630 1233.20Pre-crisis period 0.0135 0.1234 0.0000 0.0140 2.4266 12.3670 832.71Crisis period 0.0105 0.0590 0.0000 0.0098 1.8174 7.3270 334.84

J1/2 Total period 0.0119 0.1234 0.0000 0.0121 2.4280 13.0206 1352.40Pre-crisis period 0.0003 0.0151 0.0000 0.0009 7.8407 97.0506 643.18Crisis period 0.0002 0.0034 0.0000 0.0004 4.2069 24.1184 294.13

log(J + 1) Total period 0.0002 0.0151 0.0000 0.0007 9.0609 142.2805 1241.00Pre-crisis period 85.000 0.0161 0.3000 158.000 4.5044 30.4697 571.91Crisis period 89.100 0.0200 3.3000 159.200 5.1523 43.3425 485.57

BV Total period 87.200 0.0200 0.3000 158.700 4.8501 37.3844 1042.70



Table 5Daily GARCH(1,1) estimations.

Variable Sampling frequency Mean Maximum Minimum S.dev Skewness Kurtosis LB

Return Pre-crisis period 987.000 0.0667 −0.0818 0.0164 −0.1892 4.7524 5312.20Crisis period 180.000 0.0965 −0.0997 0.0245 −0.0108 5.0478 17.4420Total period 558.000 0.0965 −0.0997 0.0211 −0.0720 5.6916 21.7370

GARCH(1,1) Pre-crisis period 0.0002 0.0009 0.0000 0.0001 1.5871 7.1134 2631.9Crisis period 0.0005 0.0023 0.0002 0.0003 1.9888 6.7554 5090.7Total period 0.0004 0.0024 0.0000 0.0003 2.6075 10.8636 10124.0

Note: Mean returns are multiplied by 106.


component in model increase the forecasting performance. In general,GARCH and RGARCH models have the worst forecasting performance.

In crisis period, GARCH model has the worst forecasting perfor-mance according to RMSE and TIC. It is not clear which model is thebest, however MIDAS log and MIDAS 1/2 models perform well thanothers. Than HAR-RV-CJ, HAR-RV-J and HAR-RV models follow MIDASlog and MIDAS 1/2 models. Both in pre-crisis and crisis period, high

Table 6Comparison of models in pre-crisis period for ISE-30 index futures.

RMSE MAE M

Statistic Order Statistic Order

GARCH 2.2520 14 GARCH 1.0020 14 GHAR-RV 1.4600 8 HAR-RV 0.7240 12 HHAR-RV-1/2 1.4641 9 HAR-RV-1/2 0.6640 7 HHAR-RV-LOG 1.5432 12 HAR-RV-LOG 0.6730 9 HHAR-RV-J 1.4460 6 HAR-RV-J 0.7140 11 HHAR-RV-J 1/2 1.4543 7 HAR-RV-J 1/2 0.6550 6 HHAR-RV-J LOG 1.5387 11 HAR-RV-J LOG 0.6680 8 HHAR-RV-CJ 1.4350 4 HAR-RV-CJ 0.7050 10 HHAR-RV-CJ 1/2 1.4390 5 HAR-RV-CJ 1/2 0.6480 4 HHAR-RV-CJ LOG 1.5052 10 HAR-RV-CJ LOG 0.6510 5 HMIDAS 1.3142 2 MIDAS 0.6410 3 MMIDAS 1/2 1.3014 1 MIDAS 1/2 0.5786 2 MMIDAS LOG 1.3667 3 MIDAS LOG 0.5752 1 MRGARCH 1.9965 13 RGARCH 0.8660 13 R

frequency based volatility models have better forecasting performancethan traditional GARCH model.

5. Conclusion

This paper aims to suggest the best volatility forecasting model forstock markets in Turkey. For this purpose, first we analyze the data

APE TIC

Statistic Order Statistic Order

ARCH 96.6846 1 GARCH 0.8450 14AR-RV 269.0611 14 HAR-RV 0.4273 3AR-RV-1/2 185.7400 10 HAR-RV-1/2 0.4556 6AR-RV-LOG 143.2800 6 HAR-RV-LOG 0.5401 10AR-RV-J 265.8059 12 HAR-RV-J 0.4212 2AR-RV-J 1/2 184.0411 8 HAR-RV-J 1/2 0.4511 5AR-RV-J LOG 143.1967 5 HAR-RV-J LOG 0.5408 11AR-RV-CJ 264.0010 11 HAR-RV-CJ 0.4167 1AR-RV-CJ 1/2 185.4271 9 HAR-RV-CJ 1/2 0.4442 4AR-RV-CJ LOG 139.2902 4 HAR-RV-CJ LOG 0.5003 9IDAS 267.1394 13 MIDAS 0.4602 7IDAS 1/2 183.8430 7 MIDAS 1/2 0.4861 8IDAS LOG 137.6848 3 MIDAS LOG 0.5697 12GARCH 98.3694 2 RGARCH 0.6959 13

Table 7Comparison of models in crisis period for ISE-30 index futures.

RMSE MAE MAPE TIC

Statistic Order Statistic Order Statistic Order Statistic Order

GARCH 1.7754 14 GARCH 0.7770 13 GARCH 90.2634 6 GARCH 0.6337 14HAR-RV 1.5310 3 HAR-RV 0.7690 8 HAR-RV 153.6913 11 HAR-RV 0.4244 4HAR-RV-1/2 1.6289 7 HAR-RV-1/2 0.7700 9(10.11) HAR-RV-1/2 112.3600 10 HAR-RV-1/2 0.4525 6HAR-RV-LOG 1.6914 11 HAR-RV-LOG 0.7650 6 HAR-RV-LOG 90.2400 5 HAR-RV-LOG 0.5119 11HAR-RV-J 1.5280 2 HAR-RV-J 0.7680 7 HAR-RV-J 154.4919 12 HAR-RV-J 0.4233 3HAR-RV-J 1/2 1.6310 8 HAR-RV-J 1/2 0.7710 12 HAR-RV-J 1/2 111.8099 8 HAR-RV-J 1/2 0.4527 7HAR-RV-J LOG 1.7046 13 HAR-RV-J LOG 0.7620 5 HAR-RV-J LOG 89.0720 4 HAR-RV-J LOG 0.5183 12HAR-RV-CJ 1.5260 1 HAR-RV-CJ 0.7700 9(10.11) HAR-RV-CJ 154.9862 13 HAR-RV-CJ 0.4225 1(2)HAR-RV-CJ 1/2 1.6311 9 HAR-RV-CJ 1/2 0.7700 9(10.11) HAR-RV-CJ 1/2 112.1514 9 HAR-RV-CJ 1/2 0.4529 8HAR-RV-CJ LOG 1.6958 12 HAR-RV-CJ LOG 0.7580 4 HAR-RV-CJ LOG 88.2141 3 HAR-RV-CJ LOG 0.5114 10MIDAS 1.5512 5 MIDAS 0.7840 14 MIDAS 163.0589 14 MIDAS 0.4225 1(2)MIDAS 1/2 1.5384 4 MIDAS 1/2 0.6963 2 MIDAS 1/2 107.8838 7 MIDAS 1/2 0.4408 5MIDAS LOG 1.5786 6 MIDAS LOG 0.6863 1 MIDAS LOG 85.2514 2 MIDAS LOG 0.4863 9RGARCH 1.6334 10 RGARCH 0.7035 3 RGARCH 84.3969 1 RGARCH 0.5582 13


generating process and calculate the high frequency based volatility andexamine the return and volatility characteristics. Second, we proposethe best volatility forecasting model by comparing different volatilityforecasting models. The findings of this paper support the superiorityof high frequency based volatility forecasting models over traditionalGARCH models. MIDAS and HAR-RV-CJ models are found to be thebest among high frequency based volatility forecasting models. Thefindings of paper is important for financial institutions in Turkey.Because,financial institutions are exposed tomarket risk due to their in-vestments in financial instruments. Especially, the increase in volatilityof securities obligates financial institutions to manage market risk.Measuring market risk and holding capital to cover this risk becomecompulsory for financial institutions. Value at Risk (VAR) is one of themost usedmethod inmeasuringmarket risk. Calculation of VaR requiresthe volatilities of correlations of securities in portfolio. So, calculation ofvolatilities and correlations accurately is important for accuratemeasurement of market risk. The findings from this paper indicatethat if financial institutions use GARCH model to forecast volatility,

Table A1GARCH(1,1) model estimations for ISE-30 index futures.

Pre-crisis period AR(1). MA(2)

a0 0.0000**[0.0000]

a1 0.0902***[0.0215]

b1 0.8585[0.0356]

Q(6) 0.877Q(8) 0.492Q(10) 0.420Q(12) 0.602LM(2) 0.833LM(4) 0.266LM(6) 0.444LM(8) 0.495

Note: Standard deviations are in []. Q(n):p-values of for Ljung -Box Qstatistics for n.lag. ARCH-LMsignificance level, respectively.

they cannot obtain accurate results regarding market risk. The findingsof this paper support the superiority of high frequency based volatilityforecasting models. In addition to these findings, we find evidence ofthe impact of structural break periods on the volatility dynamics. Theusage of MIDASmodel in crisis period provides more accuratemeasure-ments for market risk.

The findings of paper are also important for investors. In Turkey,option contracts have not traded in Turkish Derivative Exchange(henceforth: TURKDEX), yet. However, TURKDEX applied for Stock Ex-change Commission to trade with option contracts in February 2011.Thus, the findings of paper are important for investors who will tradeoption contracts in Turkey. To trade with options, investors must fore-cast volatility accurately. According to the findings of paper, investorscan determine the exact value of options by forecasting volatility usinghigh frequency based volatility models.

Lastly, the findings are important for policy makers. Because, policymakers use market volatility as a barometer of fragility of financialmarkets and economy.

Appendix A

Crisis period AR(1). MA(2) Total period AR(1)

0.0000*** 0.0000***[0.0000] [0.0000]0.0834*** 0.0842***[0.0165] [0.0116]0.8838*** 0.8916***[0.0206] [0.0132]0.323 0.3420.400 0.3740.356 0.2110.525 0.3290.139 0.2010.787 0.6060.554 0.2710.699 0.730

(n): p values of LagrangeMultiplier test statistics for n.lag.***, **, and * are 1%, 5%, and 10%

Table A2Forecasting performance evaluation of GARCH(1,1) model for ISE-30 index futures.

Pre-crisis period Crisis period Total period

Frequency 1 min 5 min 10 min 15 min 1 min 5 min 10 min 15 min 1 min 5 min 10 min 15 min

RMSE 13.6300 4.9690 3.2430 2.2520 21.5920 4.9340 2.7830 1.7754 18.2668 4.9404 2.9997 2.0062MAE 6.4460 2.2940 1.4700 1.0020 9.2610 1.9380 1.1170 0.7770 7.9190 2.0920 1.2740 0.8750MAPE 82.3086 77.8298 81.1864 96.6846 76.2150 71.6952 78.3836 90.2634 78.7397 73.6849 79.0971 94.0441TIC 0.9698 0.9224 0.8863 0.8450 0.9551 0.8302 0.7331 0.6337 0.9575 0.8622 0.7929 0.7188

Note: RMSE and MAE values are multiplied by 103.

Table A3Mincer Zarnowitz regression results of GARCH(1,1) model for ISE-30 index futures.



a 0.0079 0.0034 0.0022 0.0015 0.0036 0.0005 0.0002 0.0000 0.0043 0.0015 0.0009 0.0006b (−4.6241) (−3.3969)** (−2.0629)** (−1.3506)* 10.5019*** 3.1706 2.1937*** 1.7177*** 9.0358*** 1.9601*** 1.3091*** 1.0791***R2 0.0020 0.0082 0.0069 0.0061 0.0412 0.0659 0.0930 0.1308 0.0341 0.0211 0.0247 0.0362p 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Note: a and b denote intercept and trend coefficient Mincer and Zarnowitz (1969) regression, respectively. p is the statistic of Wald test of null hypothesis.***, **, and * are 1%, 5%, and 10% significance level, respectively.

Table A4HAR-RV model estimations for ISE-30 index futures.

RV RV 1/2 log(RV)


Pre-crisis periodβ 0 0.0010** 0.0004** 0.0002** 0.0001** 0.0083*** 0.0065** 0.0048** 0.0046*** (−0.9120)*** (−1.4463)*** (−1.5330)*** (−1.9307)***

[0.0004] [0.0002] [0.0001] [0.0000] [0.0030] [0.0025] [0.0018] [0.0017] [0.2377] [0.3665] [0.3982] [0.4741]β d 0.6521*** 0.4345*** 0.4680*** 0.2609** 0.6830*** 0.5205*** 0.5052*** 0.4141*** 0.6454*** 0.5001*** 0.4725*** 0.3966***

[0.0749] [0.1324] [0.0739] [0.1108] [0.0535] [0.0808] [0.0626] [0.0710] [0.0405] [0.0446] [0.0438] [0.0448]β w 0.2718*** 0.3660*** 0.3377*** 0.3683*** 0.1872*** 0.2664*** 0.2942*** 0.2720*** 0.1561*** 0.2524*** 0.2837*** 0.2799***

[0.0920] [0.1396] [0.1295] [0.1360] [0.0623] [0.0760] [0.0793] [0.0869] [0.0583] [0.0638] [0.0647] [0.0724]β m (−0.0869)* (−0.0123) 0.0183 0.1576 (−0.0115) 0.0194 0.0184 0.098 0.0614 0.0546 0.0503 0.0886

[0.0502] [0.0754] [0.0867] [0.1255] [0.0408] [0.0565] [0.0574] [0.0784] [0.0592] [0.0629] [0.0362] [0.0734]R2 0.6728 0.4344 0.4812 0.2989 0.6571 0.4964 0.5139 0.3982 0.5729 0.4485 0.4354 0.3315

Crisis periodβ 0 0.0020*** 0.0005*** 0.0002** 0.0001** 0.0075*** 0.0049*** 0.0040*** 0.0036*** (−0.4473)*** (−0.8739)*** (−1.0857)*** (−1.2069)***

[0.0006] [0.0001] [0.0001] [0.0000] [0.0023] [0.0014] [0.0014] [0.0013] [0.1346] [0.2176] [0.2681] [0.3150]β d 0.6409*** 0.4766*** 0.3447*** 0.3398*** 0.6758*** 0.5212*** 0.4324*** 0.3813*** 0.6675*** 0.5219*** 0.4515*** 0.3498***

[0.0676] [0.0713] [0.1099] [0.0897] [0.0492] [0.0646] [0.0752] [0.0686] [0.0425] [0.0432] [0.0445] [0.0466]β w 0.0384 0.0875 0.1021 0.2177* 0.1170* 0.1787** 0.1550* 0.2454*** 0.1847*** 0.2528*** 0.2225*** 0.2810***

[0.0685] [0.1181] [0.1486] [0.1227] [0.0632] [0.0847] [0.0901] [0.0856] [0.0531] [0.0599] [0.0623] [0.0645]β m 0.1129* 0.2236** 0.3730** 0.2594*** 0.0877** 0.1401** 0.2419*** 0.2020*** 0.0849* 0.1154** 0.1956*** 0.2289***

[0.0666] [0.0990] [0.1490] [0.0919] [0.0438] [0.0607] [0.0810] [0.0642] [0.0439] [0.0521] [0.0623] [0.0659]R2 0.4659 0.3256 0.2624 0.2945 0.643 0.5041 0.4346 0.4274 0.7624 0.6222 0.5459 0.4791

Total periodβ 0 0.0015*** 0.0004*** 0.0002*** 0.0002*** 0.0075*** 0.0056*** 0.0046*** 0.0042*** (−0.5868)*** (−1.0932)*** (−1.2714)*** (−1.4985)***

[0.0003] [0.0001] [0.0000] [0.0000] [0.0018] [0.0013] [0.0012] [0.0010] [0.1192] [0.1925] [0.2262] [0.2648]β d 0.6527*** 0.4709*** 0.4007*** 0.3063*** 0.6807*** 0.5227*** 0.4692*** 0.3978*** 0.6573*** 0.5087*** 0.4625*** 0.3821***

[0.0542] [0.0692] [0.0787] [0.0742] [0.0373] [0.0505] [0.0507] [0.0486] [0.0298] [0.0307] [0.0300] [0.0318]β w 0.1026 0.2097** 0.2553** 0.2863*** 0.1447*** 0.2240*** 0.2405*** 0.2630*** 0.1726*** 0.2574*** 0.2643*** 0.2841***

[0.0632] [0.1010] [0.1093] [0.0944] [0.0470] [0.0575] [0.0621] [0.0611] [0.0392] [0.0423] [0.0436] [0.0489]β m 0.0561 0.1021 0.1452* 0.2039** 0.0505* 0.0777* 0.1088** 0.1448*** 0.0857** 0.0928** 0.1163*** 0.1550***

[0.0530] [0.0734] [0.0868] [0.0835] [0.0306] [0.0437] [0.0513] [0.0545] [0.0347] [0.0399] [0.0431] [0.0487]R2 0.5177 0.3647 0.3454 0.2939 0.6505 0.4985 0.4634 0.4103 0.6822 0.5376 0.4854 0.4003

Note: bd, bw, and bm refer to coefficient of daily, weekly and monthly volatility. Standard deviations are in []. ***, **, and * denote 1%, 5%, and 10% significance level, respectively.


Table A5Forecasting performance evaluation of HAR-RV model for ISE-30 index futures.

RV RV1/2 log(RV)


Pre-crisis periodRMSE 6.8990 3.1070 1.8250 1.4600 6.9822 3.1024 1.8475 1.4641 8.0940 3.3513 2.0260 1.5432MAE 3.4060 1.4540 0.9070 0.7240 3.2740 1.3560 0.8630 0.6640 3.5710 1.4130 0.8880 0.6730MAPE 300.2989 240.3733 220.8144 269.0611 204.9100 164.5500 165.9800 185.7400 158.1900 126.5200 128.5600 143.2800TIC 0.2708 0.3773 0.3526 0.4273 0.2882 0.3999 0.3798 0.4556 0.3811 0.4892 0.4726 0.5401

Crisis periodRMSE 14.5220 3.8970 2.3730 1.5310 15.4302 4.1428 2.5178 1.6289 15.9021 4.2572 2.5705 1.6914MAE 6.1150 1.7350 1.1320 0.7690 6.0860 1.7220 1.1120 0.7700 6.2330 1.7070 1.0810 0.7650MAPE 307.3465 201.4046 166.3450 153.6913 129.5600 119.7100 110.7700 112.3600 100.3400 94.5000 87.8500 90.2400TIC 0.3716 0.4356 0.4569 0.4244 0.3830 0.4585 0.4835 0.4525 0.4228 0.5093 0.5323 0.5119

Total periodRMSE 11.5460 3.5330 2.1340 1.4910 11.5290 3.5210 2.1330 1.4900 12.1170 3.6710 2.2210 1.5520MAE 4.7990 1.5940 1.0230 0.7460 4.3890 1.4450 0.9340 0.6780 4.5620 1.4580 0.9250 0.6770MAPE 298.0006 218.7096 194.9467 207.4527 160.9400 139.2800 134.9500 146.2400 124.8100 107.9800 105.6000 114.8600TIC 0.3490 0.4138 0.4153 0.4264 0.3603 0.4347 0.4396 0.4528 0.4156 0.4993 0.5036 0.5196


Table A6Mincer Zarnowitz regression results of HAR-RV model for ISE-30 index futures.

RV RV1/2 log(RV)


Pre-crisis perioda 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000b 1.0000*** 1.0000*** 1.0000*** 0.9999*** 0.9999*** 0.9999*** 1.0000*** 1.0000*** 1.0000*** 1.0000*** 1.0000*** 1.0000***R2 0.6728 0.4344 0.4812 0.2989 0.6571 0.4964 0.5139 0.3982 0.5729 0.4485 0.4354 0.3315p 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999

Crisis perioda 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000b 1.0000*** 0.9999*** 1.0002*** 0.9996*** 1.0000*** 1.0000*** 0.9999*** 1.0000*** 1.0000*** 1.0000*** 1.0000*** 1.0000***R2 0.4659 0.3255 0.2624 0.2943 0.6430 0.5041 0.4346 0.4274 0.7624 0.6222 0.5459 0.4791p 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999

Total perioda 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000b 0.9999*** 0.9999*** 1.0000*** 1.0000*** 1.0000*** 1.0000*** 0.9999*** 1.0000*** 1.0000*** 1.0000*** 1.0000*** 1.0000***R2 0.5177 0.3646 0.3455 0.2939 0.6505 0.4985 0.4634 0.4103 0.6822 0.5376 0.4854 0.4003p 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999

Note: a and b denote intercept and trend Mincer and Zarnowitz (1969) regression, respectively. p is the statistic of Wald test of null hypothesis.***, **, and * are 1%, 5%, and 10% significance level, respectively.


Table A7HAR-RV-J model estimations for ISE-30 index futures.

RV RV1/2 log(RV)


Pre-crisis periodβ 0 0.0011** 0.0004** 0.0002** 0.0001** 0.0089*** 0.0065*** 0.0048** 0.0047*** (−0.9065)*** (−1.6601)*** (−1.4163)*** (−1.7531)***

[0.0005] [0.0001] [0.0001] [0.0000] [0.0032] [0.0024] [0.0019] [0.0017] [0.2734] [0.4574] [0.4547] [0.5026]β d 0.7332*** 0.3745** 0.5221*** 0.3593*** 0.7594*** 0.4562*** 0.5288*** 0.4782*** 0.6460*** 0.4819*** 0.4814*** 0.4104***

[0.0835] [0.1586] [0.0833] [0.1154] [0.0666] [0.1172] [0.0713] [0.0676] [0.0420] [0.0508] [0.0461] [0.0477]β w 0.2702*** 0.3633*** 0.3344** 0.3499*** 0.1873*** 0.2599*** 0.2952*** 0.2692*** 0.1562*** 0.2492*** 0.2862*** 0.2818***

[0.0924] [0.1267] [0.1311] [0.1308] [0.0625] [0.0719] [0.0786] [0.0860] [0.0589] [0.0641] [0.0650] [0.0723]β m (−0.0883)* −0.0384 0.0440 0.1839 −0.0143 0.006 0.0244 0.1094 0.0614 0.0483 0.0532 0.0944

[0.0511] [0.0766] [0.1014] [0.1261] [0.0421] [0.0526] [0.0598] [0.0798] [0.0591] [0.0652] [0.0640] [0.0737]β j (−0.2499) 0.3738 −0.3089 (−0.3532)** −0.137 0.1805 −0.0701 (−0.1672)* (−0.3604) 42.2085 −33.8259 (−60.4054)*

[0.2145] [0.4674] [0.3170] [0.1533] [0.1235] [0.1715] [0.1055] [0.0900] [14.1241] [52.5367] [54.1382] [36.4452]R2 0.6754 0.4420 0.4881 0.3128 0.6586 0.5013 0.5148 0.4051 0.5729 0.4495 0.4358 0.3326

Crisis periodβ 0 0.0020*** 0.0004*** 0.0002** 0.0001** 0.0081*** 0.0049*** 0.0038** 0.0035*** (−0.3345)** (−0.7007)** (−0.8001)*** (−0.9683)***

[0.0005] [0.0001] [0.0001] [0.0000] [0.0022] [0.0014] [0.0014] [0.0013] [0.1465] [0.3043] [0.2903] [0.3218]β d 0.3927** 0.4202*** 0.4093*** 0.3068*** 0.4753*** 0.5086*** 0.5430*** 0.4023*** 0.6866*** 0.5455*** 0.4918*** 0.3740***

[0.1669] [0.0940] [0.1358] [0.0995] [0.1185] [0.0765] [0.0914] [0.0736] [0.0491] [0.0488] [0.0481] [0.0525]β w −0.0023 0.0736 0.1028 0.2002 0.0934 0.1785** 0.1508* 0.2494*** 0.1877*** 0.2533*** 0.2218*** 0.2881***

[0.0678] [0.1215] [0.1467] [0.1298] [0.0634] [0.0853] [0.0887] [0.0828] [0.0523] [0.0595] [0.0625] [0.0628]β m 0.1239* 0.2149** 0.3730** 0.2548*** 0.0958** 0.1377** 0.2486*** 0.2056*** 0.0778* 0.1125** 0.1901*** 0.2256***

[0.0645] [0.1047] [0.1493] [0.0897] [0.0434] [0.0644] [0.0822] [0.0641] [0.0440] [0.0515] [0.0617] [0.0652]β j 1.5675* 0.5366 (−0.3378) 0.2856 0.5097* 0.0406 (−0.2710)** (−0.0725) (−12.2303) (−61.5435) (−109.7300)* (−129.9306)

[0.8256] [0.7523] [0.3655] [0.4885] [0.2698] [0.2042] [0.1209] [0.1184] [12.2064] [85.9177] [63.6082] [153.09559]R2 0.4774 0.3300 0.2655 0.2970 0.6483 0.5042 0.4426 0.4282 0.7627 0.6230 0.5484 0.4806

Note: bd, bw, bm and bj refer to coefficient of daily, weekly and monthly volatility and jump component. Standard deviations are in []. ***, **, and * denote 1%, 5%, and 10% significance level, respectively.

185S.Çelik,H

.Ergin/Econom

icModelling

36(2014)

176–190

Table A9Mincer Zarnowitz regression results of HAR-RV-J model for ISE-30 index futures.

RV RV1/2 log(RV)





Table A8Forecasting performance evaluation of HAR-RV-J model for ISE-30 index futures.

RV RV1/2 log(RV)






Table A10HAR-RV-CJ model estimations for ISE-30 index futures.

RV RV1/2 log(RV)


Pre-crisis periodβ 0 0.0010** 0.0005*** 0.0003*** 0.0002*** 0.0088*** 0.0066*** 0.0055*** 0.0048*** (−2.7332)*** (−2.6043)*** (−3.1073)*** (−3.4672)***

[0.0004] [0.0001] [0.0001] [0.0000] [0.0031] [0.0024] [0.0017] [0.0017] [0.3895] [0.4993] [0.5028] [0.6370]β cd 0.7645*** 0.3613** 0.1363 0.3451*** 0.6049*** 0.4310*** 0.1468 0.4266*** 0.4320*** 0.4073*** 0.4110*** 0.3333***

[0.0836] [0.1592] [0.3152] [0.1041] [0.0573] [0.1017] [0.0996] [0.0656] [0.0479] [0.0490] [0.0400] [0.0382]β cw 0.2517* 0.4489** 0.9974* 0.4228*** 0.2011** 0.2305** 0.1928 0.3228*** 0.1977*** 0.2005*** 0.2601*** 0.2766***

[0.1500] [0.1755] [0.5457] [0.1348] [0.0878] [0.0917] [0.1877] [0.0876] [0.0710] [0.0676] [0.0623] [0.0662]β cm (−0.1930)* (−0.1882)* 0.4168 −0.1229 (−0.1551)** −0.0946 0.4039 −0.1250 −0.1021 0.0159 −0.0953 −0.0627

[0.1069] [0.1096] [0.6319] [0.1401] [0.0784] [0.1017] [0.2550] [0.1150] [0.0700] [0.0831] [0.0726] [0.0804]β jd 0.4119** 0.6869 0.4606*** −0.0162 0.3647*** 0.3833*** 0.4861*** 0.0804 53.9009*** 110.1767 13.5898 40.1341

[0.1952] [0.4421] [0.0832] [0.1353] [0.0928] [0.1382] [0.0640] [0.0747] [12.7606] [75.4510] [83.0085] [52.6831]β jw 0.3161 0.0701 0.2334** 0.1899 0.0268 0.0960 0.2372*** −0.0280 −4.3873 63.1599 128.2485 −13.2792

[0.2461] [0.3524] [0.1184] [0.2140] [0.1103] [0.1706] [0.0766] [0.1399] [18.8104] [76.7143] [140.9519] [131.2560]β jm 0.1261 0.3718 −0.2252 0.7988** 0.2007 0.1883 (−0.2205)** 0.4366* 55.4885** 91.9659 278.2234** 512.5047***

[0.2213] [0.3772] [0.1437] [0.3869] [0.1235] [0.1966] [0.1036] [0.2236] [21.6847] [72.2047] [139.3791] [166.7180]R2 0.6774 0.4427 0.5013 0.3231 0.6663 0.5083 0.5306 0.4130 0.5495 0.4475 0.4508 0.3451

Crisis periodβ 0 0.0020*** 0.0004*** 0.0002** 0.0001** 0.0089*** 0.0051*** 0.0041*** 0.0033** 0.0074 (−0.7220) (−1.3959)** (−1.3613)**

[0.0005] [0.0001] [0.0001] [0.0000] [0.0026] [0.0015] [0.0014] [0.0013] [0.3015] [0.5502] [0.5954] [0.6018]β cd 0.3939** 0.3953*** 0.4100*** 0.2995*** 0.4419*** 0.4611*** 0.4708*** 0.3764*** 0.6305*** 0.4972*** 0.4483*** 0.3508***

[0.1611] [0.0930] [0.1307] [0.1018] [0.1054] [0.0741] [0.0816] [0.0699] [0.0502] [0.0448] [0.0453] [0.0435]β cw −0.0525 −0.1061 0.0646 0.1710 0.1985 0.1055 0.1454 0.2673*** 0.2650*** 0.3052*** 0.2521*** 0.2996***

[0.2136] [0.1989] [0.2190] [0.1923] [0.1906] [0.1306] [0.1161] [0.0958] [0.0674] [0.0722] [0.0644] [0.0702]β cm 0.0372 −0.3285 0.0469 0.0644 −0.1798 −0.2838 −0.0624 0.0057 0.0810 0.0860 0.1080 0.1691**

[0.1753] [0.3739] [0.3099] [0.1988] [0.2083] [0.1825] [0.1595] [0.1264] [0.0632] [0.0731] [0.0782] [0.0861]β jd 1.9389*** 1.0020 0.0391 0.6083 0.6863*** 0.2308 −0.0202 0.0957 8.0711 9.1339 −3.6900 3.4833

[0.6403] [0.6743] [0.3162] [0.4670] [0.2228] [0.1899] [0.1023] [0.1099] [13.3596] [89.7454] [62.1034] [134.1308]β jw 0.2375 1.1577 0.0972 0.3972 −0.2119 0.2130 0.0053 0.0046 (−36.9601)* −148.9403 −135.6412 −180.0954

[0.95664] [1.0715] [0.6378] [0.8037] [0.3977] [0.2986] [0.1948] [0.2023] [19.1483] [146.5756] [139.2924] [210.9465]β jm 0.5059 3.2394 1.8265 0.9850 0.6074 1.0391* 0.7574* 0.5000 −0.6457 150.0480 393.5288 427.8552

[0.9347] [2.7242] [1.6734] [0.8885] [0.4785] [0.5422] [0.3901] [0.2616] [28.9910] [219.1152] [279.0345] [334.3564]R2 0.4775 0.3435 0.2729 0.2987 0.6492 0.5108 0.4446 0.4307 0.7600 0.6211 0.5504 0.4843

Note: bcd, bcw, bcm, bjd, bjw andbjm refer to coefficient of daily, weekly andmonthly realized volatility anddaily, weekly andmonthly volatility of jump component. Standard deviations are in []. ***, **, and * denote 1%, 5%, and 10% significance level,respectively.

187S.Çelik,H

.Ergin/Econom

icModelling

36(2014)

176–190

Table A11Forecasting performance evaluation of HAR-RV-CJ model for ISE-30 index futures.

RV RV1/2 log(RV)





Table A12Mincer Zarnowitz regression results of HAR-RV-CJ model for ISE-30 index futures.

RV RV1/2 log(RV)





Table A13MIDAS model estimations for ISE-30 index futures.

Pre-crisis period

RV RV 1/2 log(RV)


δ0 0.0008*** 0.0004*** 0.0002*** 0.0002 0.0087*** 0.0072*** 0.0062 0.0070*** (−1.1244)*** (−1.5577)*** (−1.9281)*** (−2.4603)[0.0003] [0.0001] [0.0000] [0.0000] [0.0021] [0.0016] [0.0013] [0.0013] [0.2027] [0.2908] [0.3300] [0.4081]

δ1 0.8585*** 0.7799*** 0.7829*** 0.6737 0.8558*** 0.7985*** 0.7847 0.7167*** (−0.8176)*** (−0.7800)*** (−0.7424)*** (−0.6830)[0.0267] [0.0408] [0.0386] [0.0590] [0.0277] [0.0380] [0.0387] [0.0479] [0.0322] [0.0407] [0.0438] [0.0523]

θ1 65.2647*** 33.1299*** 39.221*** 24.0431 58.3145*** 36.2033*** 38.9717 33.0106*** 52.8492*** 34.5749*** 37.1982*** 31.2564[10.0644] [4.3986] [5.6056] [4.8772] [8.3599] [4.9140] [5.7401] [5.6495] [7.7428] [5.1378] [6.2586] [5.8892]

d.1 0.7368 0.4918 0.5513 0.3880 0.6965 0.5228 0.5491 0.4906 0.6606 0.5066 0.5324 0.4720d2-5 0.2622 0.4789 0.4333 0.5348 0.3015 0.4562 0.4353 0.4798 0.3359 0.4683 0.4487 0.4923d6-20 0.0009 0.0292 0.0152 0.0771 0.0020 0.0211 0.0157 0.0296 0.0036 0.0251 0.0189 0.0357d N 20 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000q(10) 45.462*** 8.9157 20.467** 15.0250 4.7810 7.1418 12.8080 12.3330 5.2989 8.0329 8.4627 4.6665R2 0.6701 0.4210 0.4551 0.2270 0.6516 0.4689 0.4572 0.3261 0.5644 0.4294 0.3820 0.2758

Crisis period

RV RV 1/2 log(RV)

δ0 0.0033*** 0.0009*** 0.0005*** 0.0003*** 0.0122 0.0072*** 0.0063*** 0.0050*** (−0.4512)*** (−0.7783)*** (−1.0138)*** (−1.0425)***[0.0005] [0.0001] [0.0001] [0.0000] [0.0026] [0.0016] [0.0014] [0.0012] [0.1237] [0.1986] [0.2435] [0.2804]

δ1 0.6778*** 0.6162*** 0.6571*** 0.7160*** 0.8408 0.8129*** 0.7973*** 0.8190*** (−0.9229)*** (−0.8890)*** (−0.8619)*** (−0.8619)***[0.0000] [0.0441] [0.0543] [0.0492] [0.0266] [0.0348] [0.0399] [0.0394] [0.0205] [0.0280] [0.0328] [0.0369]

θ1 300.0000*** 70.9186*** 31.4527*** 27.9357*** 67.7139 38.2562*** 29.7154*** 25.0723*** 45.4564*** 31.6774*** 27.5798*** 20.6298***[0.0000] [18.4621] [7.1961] [5.2347] [10.6542] [6.0584] [5.0135] [3.8945] [5.8949] [4.4266] [4.1705] [3.3104]

d.1 0.9979 0.7656 0.4740 0.4349 0.7497 0.5424 0.4550 0.4008 0.6051 0.4765 0.4307 0.3438d2-5 0.0021 0.2338 0.4909 0.5142 0.2496 0.4407 0.5028 0.5301 0.3871 0.4894 0.5164 0.5452d6-20 0.0000 0.0005 0.0349 0.0509 0.0007 0.0169 0.0421 0.0691 0.0078 0.0341 0.0529 0.1110d N 20 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000q(10) 20.345** 28.938*** 18.201* 18.073* 25.516*** 17.741* 10.135 9.8383 22.503** 14.5350 16.186* 12.7410R2 0.4588 0.3079 0.2475 0.2983 0.6392 0.5044 0.4322 0.4402 0.7717 0.6364 0.5517 0.4935

Note: Values in the table show the MIDAS model estimation based on Beta polynomial and kmax = 50. Values in parentheses indicate standard errors. ***, **, and * are 1%, 5%, and 10%significance level, respectively. d.1 is the weight of first day, d2-5, shows weight of days between 2 and 5; d6-20, shows weight of days between 6 and 20; d N 20 weights after 20thday. q(10) is Ljung–Box (1979) statistics of residuals fromMIDAS model.


Table A14Forecasting performance evaluation of MIDAS model for ISE-30 index futures.

RV RV 1/2 log(RV)





Table A15Mincer Zarnowitz regression results of MIDAS model for ISE-30 index futures.

RV RV1/2 log(RV)





Table A16RGARCH model estimations for ISE-30 index futures.


1 min 5 min 10 min 15 min 1 min 5 min 10 min 15 min 1 min 5 min 10 min 15 min

ω −1.9978* −1.8621 −1.4320* −1.2732 −1.2039 −0.1728 −0.1624 −0.1991 −1.2761 −1.1966* −0.8404* −0.8027[1.0333] [1.4548] [0.8223] [0.6798] [7.4903] [0.2806] [0.1875] [0.3207] [1.9396] [0.7251] [0.4688] [0.5509]

β 0.5846*** 0.5490* 0.6196*** 0.6678*** 0.5334 0.9072*** 0.9061*** 0.8830*** 0.6154 0.5927*** 0.6947*** 0.7066***[0.2029] [0.2944] [0.1800] [0.1507] [2.4079] [0.1139] [0.0759] [0.1256] [0.4977] [0.1989] [0.1356] [0.1603]

γ1 0.3795*** 0.2834*** 0.3090*** 0.2697*** 0.4763* 0.3851*** 0.3374*** 0.2613*** 0.4393*** 0.3224*** 0.3198*** 0.2628***[0.0425] [0.0490] [0.0483] [0.0438] [0.2531] [0.0622] [0.0456] [0.0522] [0.0729] [0.0335] [0.0327] [0.0314]

γ2 −0.1720 −0.0379 −0.0921 −0.0866 −0.1064 −0.3107** −0.2630*** −0.1704 −0.1718 −0.0502 −0.1154 −0.0698[0.1081] [0.1573] [0.1152] [0.0927] [1.9624] [0.1349] [0.0874] [0.1242] [0.3661] [0.1318] [0.0987] [0.1073]

ξ 2.0013*** 1.8362*** 1.7529*** 1.8133*** 1.2610 1.2465* 1.2610* 1.2863 1.4375** 1.4953*** 1.4930*** 1.5195***[0.6038] [0.6941] [0.6024] [0.6351] [2.2153] [0.7000] [0.6863] [0.9786] [0.6900] [0.4189] [0.4211] [0.5060]

ϕ 1.0328*** 1.1122*** 1.1452*** 1.1756*** 0.9904*** 1.1072*** 1.1430*** 1.1699*** 0.9955*** 1.1164*** 1.1536*** 1.1795***[0.0770] [0.0855] [0.0738] [0.0779] [0.2624] [0.0942] [0.0918] [0.1316] [0.0852] [0.0538] [0.0541] [0.0650]

τ1 0.0252 0.0064 −0.0228 0.0002 −0.0225 −0.0485* −0.0695** −0.0304 −0.0053 −0.0332 −0.0559*** −0.0233[0.0410] [0.0354] [0.0328] [0.0330] [0.0378] [0.0266] [0.0274] [0.0260] [0.0246] [0.0210] [0.0210] [0.0202]

τ2 −0.002 0.0573*** 0.0853*** 0.1177*** 0.0083 0.0711*** 0.1065*** 0.1242*** 0.0111 0.07285*** 0.1045*** 0.1211***[0.0186] [0.0194] [0.0196] [0.0206] [0.0130] [0.0170] [0.0162] [0.0138] [0.9857] [0.0108] [0.0118] [0.0108]

σu2 1.1568*** 0.9622*** 0.8952*** 0.9681*** 0.6935** 0.6854*** 0.6567*** 0.6614*** 0.8863*** 0.7918*** 0.7494*** 0.7907***

[0.0876] [0.0922] [0.0761] [0.0756] [0.2923] [0.0516] [0.0474] [0.0461] [0.0950] [0.0473] [0.0403] [0.0404]

Note: The table shows the estimation results of RGARCH(1,2) model. Return is calculated as the difference between logarithmic open and close prices Standard deviations are given in [].***, **, and * are 1%, 5%, and 10% significance level, respectively.


Table A17Forecasting performance evaluation of RGARCH model for ISE-30 index futures.



RMSE 13.2475 4.6184 2.8799 1.9965 20.1428 4.5137 2.5687 1.6334 17.4051 4.4834 2.6308 1.7552MAE 6.1906 2.0789 1.2771 0.8660 8.4684 1.7209 1.0005 0.7035 7.4078 1.8473 1.0892 0.7487MAPE 82.4976 73.0814 79.3547 98.3694 74.1826 62.8130 68.7578 84.3969 78.4074 69.1313 76.7731 95.9831TIC 0.9206 0.8168 0.7286 0.6959 0.8270 0.7030 0.6395 0.5582 0.8717 0.7320 0.6465 0.5946

Note: RMSE and MAE values are multiplied by103.

Table A18Mincer Zarnowitz regression results of RGARCH model for ISE-30 index futures.



a −0.0056 −0.0001 −0.0007 −0.0004 −0.0006 −0.0005 −0.0003 −0.0002 −0.0024 −0.0007 −0.0004000 −0.0003b 24.0964 8.4004*** 5.3188*** 4.0366*** 7.0544*** 3.4775*** 2.6090*** 2.1027*** 11.1519*** 4.4857*** 3.2071*** 2.5863***R2 0.5926 0.4902 0.5389 0.4124 0.4754 0.3618 0.3128 0.3273 0.5282 0.4342 0.4416000 0.3939p 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000



References

Alper, C. Emre, Fendoğlu, Salih, Saltoğlu, Burak, 2009. MIDAS Volatility Forecast Perfor-mance Under Market Stress: Evidence From Emerging and Developed Stock Markets(Manuscript).

Andersen, Torben G., Bollerslev, Tim, 1998. Answering the skeptics: Yes, standard volatil-ity models do provide accurate forecasts. Int. Econ. Rev. 39, 885–905.

Andersen, Torben G., Bollerslev, Tim, Diebold, Francis X., Labys, Paul, 1999. “RealizedVolatility and Correlation”, “(Understanding, Optimizing, Using and Forecast-ing). (Manuscript) Northwestern University, Duke University and University ofPennsylvania.

Andersen, Torben G., Bollerslev, Tim, Diebold, Francis X., Labys, Paul, 2000. Exchange ratereturns standardized by realized volatility are (nearly) Gaussian. Multinatl. Finance J.4, 159–179.

Andersen, Torben G., Bollerslev, Tim, Diebold, Francis X., Ebens, Heiko, 2001. The distribu-tion of realized stock return volatility. J. Financ. Econ. 61 (1), 43–76.

Andersen, Torben G., Benzoni, Luca, Lund, Jesper, 2002. Estimating jump-diffusions for eq-uity returns. J. Financ. 57, 1239–1284.

Andersen, Torben G., Bollerslev, Tim, Diebold, Francis X., 2003a. Some like it smooth andsome like it rough: untangling continuous and jump components in measuringmodelling and forecasting asset return volatility. CFS Working Paper, No: 2003/35.

Andersen, Torben G., Bollerslev, Tim, Diebold, Francis X., Labys, Paul, 2003b. Modeling andforecasting realized volatility. Econometrica 71, 579–625.

Andersen, Torben G., Tim, Bollerslev, Diebold, Francis X., 2007. Roughing it up: includingjump components in the measurement, modeling and forecasting of return volatility.Rev. Econ. Stat. 89 (4), 701–720.

Barndorff, Nielsen, Ole, E., Shephard, Neil, 2004. Power and bipower variation with sto-chastic volatility and jumps. J. Financ. Econ. 2, 1–37.

Brownless, Christian T., Gallo, GiampieroM., 2006. Financial econometric analysis at ultra-high frequency: data handling concerns. Comput. Stat. Data Anal. 51, 2232–2245.

Chernov, Mikhail, Gallant, A. Ronald, Ghysels, Eric, Tauchen, George, 2003. Alternativemodels for stock price dynamics. J. Econ. 116, 225–257.

Corsi, Fulvio, 2004. A Simple Long Memory Model of Realized Volatility. (Manuscript)University of Southern Switzerland.

Dacorogna, Michel M., Gencay, Ramazan, Muller, Ulrich, Olsen, Richard B., Pictet, OlivierV., 2001. An Introduction to High-Frequency Finance. Academic Pres, San Diego.

Dungey, Mardi, 2009. The tsunami: measures of contagion in the 2007–08 credit crunch.Cesifo Forum 9 (4), 33–34.

Dungey, Mardi, Holloway, Jet, Abdullah, Yalama, 2011. Observing the Crisis:Characterising the Spectrum of Financial Markets With High Frequency Data, 2004-2008 (Manuscript).

Engle, Robert F., Gallo, Giampiero, 2006. A multiple indicators model for volatility usingintra-daily data. J. Econ. 131, 3–27.

Ghysels, Eric, Santa Clara, Pento, Valkanov, Rossen, 2004. The MIDAS touch: mixed datasampling regression models. UNC and UCLA Discussion Paper.

Ghysels, Eric, Santa Clara, Pento, Valkanov, Rossen, 2005. There is a risk-return tradeoffafter all. J. Financ. Econ. 76, 509–548.

Ghysels, Eric, Santa Clara, Pento, Valkanov, Rossen, 2006a. Predicting volatility: gettingthe most out of return data sampled at different frequencies. J. Econ. 131, 59–95.

Ghysels, E., Pento, S.C., Valkanov, R., 2006b. “MIDAS Regressions: Further Results and NewDirections”, Mimeo, University of North Carolina, Chapel Hill, NC.

Hansen, Peter R., Lunde, Asger, 2006. Realized variance and market microstructure noise.J. Bus. Econ. Stat. 24 (2), 127–161.

Hansen, Peter R., Zhuo, Huang, Shek, Howard H., 2010. Realized GARCH: A Joint Model forReturns and Realized Measures of Volatility (Manuscript).

Mincer, Jacob, Zarnowitz, Victor, 1969. The Evaluation of Economic Forecasts. In: Mincer,J. (Ed.), Economic Forecasts and Expectations National Bureau of Economic Research,New York.

Shephard, Neil, Sheppard, Kevin, 2010. Realising the future: forecasting with highfrequency based volatility (HEAVY) models. J. Appl. Econ. 25, 197–231.

Stoll, Hans R., Whaley, Robert E., 1990. The dynamics of stock index and stock indexfutures returns. J. Financ. Quant. Anal. 25, 441–468.

Wu, Chunchi, Li, Jinliang, Zhang, Wei, 2005. Intradaily periodicity and volatility spilloversbetween international stock index futures markets. J. Futur. Mark. 25 (6), 553–585.

http://refhub.elsevier.com/S0264-9993(13)00398-2/rf0105



























































volatility forecasting using high frequency data: evidence from stock markets

Documents