HAR Volatility Modeling using Sub-Samples of Data

David KimSpring 2011

Economics 201FS

I have adhered to the Duke Community Standard in completing this assignment.

___________________________

ABSTRACTThis paper looks as varying Heterogeneous Autoregressive models that utilize volatility components that have been defined over different periods of time. This paper first implements the Heterogeneous Auto-regressive model of Realized Volatility. Additional volatility components are then included into the model to implement three additional models. Using high frequency, 1-minute pricing data for four different stocks over the time period from 1997 through 2010, this paper looks to differentiate between the in-sample results of these models. Additionally, the time period is then broken up into three shorter periods to investigate the results that may occur with a smaller data set. These results indicate that Leverage Heterogeneous Auto-Regressive with Continuous volatility and Jumps model is the best model to be used. Additionally, the findings suggest that regressing your volatility measures over shorter periods of time can result in more reasonable results. By utilizing the Bayesian Information Criterion, we are able to utilize a measure easily differentiates the strength between models.

2

I. Introduction

Volatility is extremely important within the stock market and greatly affects the

way that our financial markets operate. There have been a number of proposed models

that hope to improve upon volatility forecasting. This paper hopes to implement a few of

these proposed models and assess their results. Realized variation or volatility is one of

the most common methods of measuring the variance within the market and the first

model utilized makes use of the realized volatility over varying time intervals.

What is striking about many of these models is the simplicity of their structures.

Despite this simplicity, however, these models have been shown to successfully achieve

its purpose in recreating the main features of financial returns. There is no long-memory

volatility within these models, which is usually obtained by using small differences in the

operators, but the model proposed by Corsi (2009) is able to get the same results that are

seen in the empirical and financial data.

II. Volatility Models, Jumps and Leverage

The differing types of HAR models looked at in this paper utilize a couple of

different volatility models, in addition to jumps and leverage, which are then defined over

different periods of time, before being implemented into these models. Here, we define

the realized volatility or variance, the bipower variance, jumps and leverage based on

returns data. First, consider the standard continuous time process that uses a log price,

p (t ), that changes with time

dp (t )=μ ( t ) dt+σ ( t ) dW ( t ) ,(1)

3

where p ( t ) is the log price, μ ( t ) is a continuous and finite variation process, σ ( t ) is a the

volatility of the price movement and W (t )is a standard Brownian motion.

2.1 Returns

Given the log price, p ( t ), we can then use that equation to find the returns for a

stock. Depending on the returns desired, p ( t ) at different times is used to calculate the

intraday geometric returns, which can be calculated using p ( t ), a chosen t days and j

steps within the day.

rt , j=p (t−1+ j△ )−p (t−1+ ( j−1 )△ ), (2)

where j=1 ,2 ,…, M , integer t=1, 2 , …,T . This equation and the possibility for varying

time intervals is useful when working with high-frequency price data because more of the

data can still be used. While including all of the data will produce microstructure noise

that disrupts the results, utilizing larger time intervals allows us to use the data available

while still eliminating some of the noise that impede upon finding results.

2.2 Realized Volatility

While there are a number of ways to calculate variance or volatility using

financial data, but one of the most common ways to do so is using the realized variance

or volatility. The realized variance utilizes the returns equation and sums up the

calculated intraday squared returns,

RV t+1 (△ )=∑j=1

1 /△

rt+ j ∙△ ,△2 ,

(3)

where 1/△will be an integer. The data that we have calculated utilizes 1-minute prices,

but calculates the daily realized variance using 5-minute returns. We can then modify the

4

realized variance values and aggregate them over varying time periods to be used in

volatility forecasting.

2.3 Bipower Volatility

The second type of volatility that was used to calculate our findings was the

standardized realized bipower variation,

BV t+1 (△ )=μ1−2∑

j=2

1 /△

|r t+ j ∙△ ,△||r t+( j−1) ∙△ ,△|,(4)

where μ1is √2π and is the average once the absolute value has been taken of the standard

normally distributed random variable Z. Much of the literature suggests using continuous

variation, but, as bipower variation is continuous, it has been used to get these findings.

The bipower variation allows for two components within quadratic variation and is used

in the calculation of jumps within the pricing data.

2.4 Jumps

Jumps are the results of discontinuities in the pricing process that is seen. Because

the bipower is able to allow for us to separate the quadratic variation process into

separate components, we can use the realized variance and the bipower variance to

calculate the jumps that are found in the pricing data,

RV t+1 (∆ )−BV t+1 (△ )→ ∑t< s ≤t+1

κ2 ( s ) . (5)

Here, the difference between the realized variance and the bipower variance gives us

those discontinuities in the data. To prevent the jumps from becoming negative Andersen,

Bollerslev and Diebold (2007), similarly to Barndorff-Nielsen and Shephard (2004a),

have defined the jumps as

5

J t+1=max [ RV t+1 (△ )−BV t+1 (△ ) ,0 ] , (6)

where the actual empirical measurements have been truncated, which will eliminate any

negative results that are found.

III. Data

3.1 Description

This research used high-frequency stock pricing data was used for four different

stocks. We had access to 1-minute pricing data for a number of stocks and four were

chosen based on the length of their span of available data points. The four stocks

considered in this research were American Electric Power Company (AEP), Baker

Hughes Incorporated (BHI), Entergy Corporation (ETR) and H.J. Heinz Company

(HNZ). All stock data spanned from April 9, 1997 through December 30, 2010 and

includes 3,421 trading days and about 385 1-minute price levels per trading day.

All data was cleaned for obvious discrepancies and was then used to construct the

returns, RV, BV and J components previously discussed. To reduce some of the market

microstructure noise that is present in high-frequency pricing data, as we had access to in

this paper, this paper sampled the prices using 5-minute time intervals.

In addition to implementing various HAR volatility models, this research looks at

the difference between the results from longer data samples and the findings that make

use of smaller data sets. For that reason, for each of the volatility models that has been

implemented on each stock has been a total number of four times for each stock. First,

results have been determined by making use of the entire data set ranging from 1997 to

2010. Additionally, three data sets that range from 1997 to 2002, 2003 to 2006 and 2007

6

to 2010 have been extracted from our total data. This came from the intention of

comparing how the length of the data affected the results of these measurements, as well

as the fact that extracting data points from 2007 to 2010 would help separate the financial

crisis.

IV. HAR Volatility Models

The HAR class of models is one that creates volatility cascades with varying

dependent components. There have been a number of proposed variations on this type of

model which is more manageable because it is a much more simplistic way to look at

results than have been made use of in the past. In addition to being a simplistic model,

there have much of the results have been very strong. This simple model has been able to

create both financial and empirical results that are seen from much more complex

models.

4.1 The HAR-RV Model

This HAR-RV Model is an additive cascade of partial volatilities that was

proposed by Corsi (2009) and has been shown to produce results that are similar to those

with long-memory properties, despite its simplicity. This model considers three volatility

components that correspond with time lags of one day, one week or one month. For this

model, the data was calculated using the realized volatilities for the daily, weekly and

monthly observed realized volatilities. The realized volatility was the square root of the

realized variance that was introduced earlier in this paper. In order to obtain the weekly

and monthly aggregated volatilities, we used the average lag,

RV t ,t+h=h−1 [RV t+1+RV t+2+…+RV t +h ] , (7)

7

where h=1 ,2 , … and represents the number of days for the lags that are being used. This

data used h=5 and h=22 for the weekly and monthly volatilities, respectively. Those two

lags, in addition to the daily values, are most used with these models due to their natural

convenience in the way that they relate to the data. The final HAR-R model is stated as

RV t ,t+h=β0+β D RV t+ βW RV t−5 ,t+ βM RV t−22 ,t +εt ,t+h, (8)

with t=1 , 2, …, T . Of course, any time lag can be used to calculate these results, but

using lags of 5 days and 22 days to represents weekly and monthly lags is a natural way

to implement this model.

4.2 The HAR-RV-J Model

To include the jump calculation discussed previously, we can include that as

another variable on this model to create the HAR-RV-J model,

RV t ,t+h=β0+β D RV t+ βW RV t−5 ,t+ βM RV t−22 ,t +βJ J t+εt ,t+h. (9)

The jumps are an additional variable that could help explain the results that is readily

available and can thus be included to create a new model. This model produced similar

results to the HAR-RV model. Similar to the findings of Andersen, Bollerslev and

Diebold (2007), the R2’s when the jumps have been included are higher. We can see that

jumps are an additional volatility that is certainly relevant and can assist in replacing

some of the data that is lost by the realized variance to produce stronger results.

4.3 The HAR-RV-CJ Model

A way to include further variables into this model, we continue to incorporate

more variables that are based on variation. These two could again include the jump

8

variation, as well as a continuous variation component. Andersen, Bollerslev and Diebold

(2007) defined the jump and continuous variability measures with lags as

J t ,t+h=h−1 [ J t+1+J t+2+…+J t+h ] , (10)and

C t ,t h=h−1 [C t+1+Ct+2+…+C t +h ] , (11)

which are then incorporated into the HAR-RV-CJ model explained as,

RV t ,t+h=β0+βCD C t+βCW C t−5 , t+βCM Ct−22 ,t+βJD J t+βJW J t−5 ,t+βJM J t−22, t+,εt ,t+h (12)

Because the bipower volatility is a continuous variability measure, this research makes

use of that calculation as the additional continuous variation component. Now, we can

notice that the previous HAR-RV-J model is still included within this model, but has

been broken up which could help break down any potential explanations or indications

that are being made by the results. Instead of the findings being found as one number, by

including this continuous variation component, we can split up those results, which may

help us find more applications for our results.

4.4 The LHAR-CJ Model

Looking at the leverage effect and how it relates to the HAR class of models can

by done by considering asymmetric responses from realized volatility on previous daily

negative returns and comparing the relationship between the two measures. This

particular idea stemming from the Heterogeneous Market Hypothesis from Muller et al.

(1997) can be seen through the aggregated negative returns. Corsi and Renò (2009)

implement this idea in one model. Before the regression, however, they define returns

rt=X t−X t−1. This calculation is then used to find the past aggregated negative returns as

rt

( n)−¿=1n ( rt+ …+rt−n+1) I {¿¿ ¿, (13)

9

which includes the indicator function of all the aggregated negative returns, which are

then averaged over varying time intervals, as has been done in other HAR models. The

final Leverage Heterogeneous Auto-Regressive with Continuous volatility and Jumps

model can be stated as,

log V̂ t ,t+h=β0+βJD log (1+J t )+βJW log (1+J t−5 ,t ) +βJM log (1+J t−22, t )+βCD C t+βCW C t−5 , t+βCM Ct −22, t+βrD rt−¿+βrW rt−5, t

−¿+βrM r t−22 ,t

−¿+ε t ,t+h, ¿¿¿

(14)

This model takes the logarithms of the volatility measures that have been previously

used, realized volatility, bipower volatility and jumps, as well as including the aggregated

past negative returns to create this model. By using a cascade, they are able to look at the

results for daily, weekly and monthly forecasting.

V. Results

Upon inspection, there is definitely a trend that indicates that the addition of more

measures of volatility helps to improve upon the performance of the models that are used.

Tables 1 through Tables 4 include the coefficients for the measured variables, their R2

value and the BIC value that corresponds to each respective coefficient. The most striking

trend is that the addition of the log component to the HAR model within the LHAR-CJ

model greatly is able to reduce the BIC values, which helps to indicate that this model

may be the best in measuring these parameters. Additionally, this is the model that

included the most variables, in addition to being the only model that utilized a log

function to define the same variables that had been used in other models. We can see

from the R2 values that the HAR-RV-J model is able to improve on the HAR-RV model

just by including another, readily available volatility model.

10

5.1 Sub-Sampling Data

The sub-sampling data that was calculated for smaller chunks of time over the

whole period of the data were able to greatly help improve upon all of the models. We

can see that much of the results are more consistent and often have improved values for

the significance measures that have been utilized. The R2 and BIC values were often

higher or lower, respectively, amongst the shorter samples of data that had been extracted

from our original price sets.

By shortening the span of the data, the results have more consistency with the

components that are being regressed upon. Particularly with the recent financial crisis, we

can see how the increase in volatility has often left an impression upon the results in the

overall sample and in the sub-sample from 2007 to 2010. While there was less volatility

throughout 1997 to 2006 within the data, we can see how the change in the financial

industry during the last three years of the data set impacted the models.

5.2 Bayesian Information Criterion

One method that was used to evaluate the findings from these models was the

Bayesian Information Criterion (BIC) (Schwarz, 1978), which is a measure for model

selection within a group of parametric models with varying numbers of parameters. This

is a way to see which of the HAR models has performed the best. This value can be

calculated as

BIC=−2l+K log (n ) , (15)

where K is the number of parameters being estimated, n is the sample size of the group

and l is the maximum log likelihood under the model

11

l=lnP ( D|M , θ̂ , τ̂ , υ̂ ), (16)

where M is the model, that is testing the probability of the data, with the rest of the

variables representing model parameters. To choose the best model using this standard,

you must choose the model that obtains the smallest BIC value. The BIC values are

included for each model at the bottom of the tables that include the coefficients for each

variable. These values have also been represented in Figure 1 as a collection of four stem

plots for each stock broken up into one plot for each the overall sample and the three sub-

samples.

Overwhelmingly, we can see that the leveraged heterogeneous autoregressive

with continuous volatility and jumps (LHAR-CJ) model has the smallest BIC values. In

comparison with the LHAR-CJ model, the other three methods explored within this

research have seemingly similar BIC values. The BIC values of the other three models

were often approximately four times that of the BIC value for the LHAR-CJ model that

incorporated the aggregated past negative returns, in addition to using the log of its other

dependent variables.

When looking at the actual values of the BIC for the different models, the sub-

sampling greatly reduces the level of the BIC for any given model. The BIC for the entire

sample often ranges at a value that is nearly four times as large as the BIC values for any

of the sub-samples that were used.

VI. Conclusion

I believe that these results create a strong argument in favor of the proposed

LHAR-CJ model by Corsi and Renò. The BIC is a simple method of measuring the

12

strength of different models and the results shown indicate that the leverage

heterogeneous auto regressive with continuous volatility and jumps model have

significantly lower results than that of any of the other models that were tested. Because

of the nature of the BIC, that is a clear indication that the LHAR-CJ is a better method of

forecasting volatility than the other models used were.

As the models were built onto each other, it was interesting to see the additional

benefits that each additional volatility component was included on the different models.

When another variable is included, we could see that the results had a little more

definition. With the inclusion of more variables included in the model’s equation, we can

better understand how the model is being affected by the variable coefficients. Some of

the variables were linked, such as the jumps and the continuous, or bipower, variations

that were used as components on a couple of models. These measures already have links

due to the nature and relationships between the volatility measures used in this research,

but it still helps to split up findings and makes it possible to understand the results a little

bit more deeply. Finally, much of the results of the shorter samples of data that were used

with the same models were able to see much stronger results once the length or span of

the total data was reduced.

13

FIGURESFigure 1: BIC stem plots

Figures 6A – 6D: the BIC values for each of the HAR volatility models has been graphed into a stem plot. Each quadrant includes the BIC value for the HAR-RV, HAR-RV-J, HAR-RV-CJD, HAR-RV-CJW, HAR-RV-CJM, LHAR-CJD, LHAR-CJW, LHAR-CJM models, respectively. There is one group of four for each stock that includes a plot for the entire sample and one for each of the three sub-samples that were used.

14

REFERENCES

Corsi, F. “A Simple Approximate Long-Memory Model of Realized Volatility,” Journal of Financial Econometrics 7:2 (2009), 174 – 196.

Corsi, F. and R. Renò. “HAR Volatility Modeling with Heterogeneous Leverage and Jumps.” Unpublished Paper, Università di Siena, University of Lugano and Swiss Finance Institute. (2009).

Andersen, T. G., T. Bollerslev and F. X. Diebold. “Roughing it Up: Including Jump Components in the Measurement, Modeling, and Forecasting of Return Volatility.” The Review of Economics and Statistics. 89.4 (2007): 701 – 720.

Barndorff-Nielsen, O. E. and N. Shephard. “Measuring the impact of jumps in multivariate price processes using bipower covariation.” Unfinished paper.

Hansen, P. R. and A. Lunde. “Forecasting Volatility using High Frequency Data.” Stanford University.

Muller, U. A., M. M. Dacorogna, R. D. Dave, R. B. Olsen, O. V. Pictet, and J. E. von Weizsacker. “Volatilities of different time resolutions – Analyzing the dynamics of market components.” Journal of Empirical Finance. 4 (1997): 213 – 239.

Posada, D. and T. R. Buckley. “Model Selection and Model Averaging in Phylogenetics: Advantages of Akaike Information Criterion and Bayesian Approaches Over Likelihood Ratio Tests.” Society of Systematic Biologies. 53.5 (2004): 793 – 808.

 

15

Appendix Figure 1: Price Series

Figure 2: Geometric Returns Series (5-minute)

15

Figure 3: Realized Volatility (RV) Series [Annualized]

Figure 4: Bipower Volatility (BV) Series [Annualized]

15

Figure 5: Jumps Series

  

15

TABLES

Table 1A. Whole Sample and Sub-Sample AEP HAR-RV Regressions

1997 - 2010 1997 - 2002 2003 - 2006 2007 - 2010β0 1.564 2.309 1.637 1.574

0.964 2.165 1.189 3.430 0.720 2.554 0.412 2.737

βD 0.480 0.673 0.264 0.224

0.441 0.519 0.617 0.729 0.190 0.337 0.147 0.301

βW 0.287 0.102 0.287 0.589

0.228 0.345 0.022 0.183 0.154 0.420 0.466 0.712

βM 0.163 0.137 0.344 0.117

0.115 0.211 0.070 0.204 0.232 0.455 0.017 0.217

R2 0.675 0.684 0.547 0.653BIC 21688.412 9103.770 5603.077 6802.133

Table 1C. Whole Sample and Sub-Sample ETR HAR-RV Regressions

1997 - 2010 1997 - 2002 2003 - 2006 2007 - 2010β0 1.244 3.384 1.946 1.341

0.695 1.793 1.855 4.913 0.776 3.116 0.317 2.365βD 0.293 0.337 0.186 0.249

0.253 0.333 0.276 0.398 0.111 0.261 0.172 0.326βW 0.495 0.396 0.355 0.626

0.431 0.560 0.297 0.495 0.215 0.494 0.506 0.746βM 0.155 0.145 0.321 0.066

0.103 0.207 0.056 0.235 0.183 0.459 -0.025 0.158

R2 0.698 0.504 0.360 0.724BIC 21586.728 9391.350 5448.308 6531.673

Table 1B. Whole Sample and Sub-Sample BHI HAR-RV Regressions

1997 - 2010 1997 - 2002 2003 - 2006 2007 - 2010β0 1.948 4.217 4.860 1.900

1.036 2.861 1.782 6.653 2.623 7.097 0.446 3.353βD 0.249 0.237 0.135 0.304

0.209 0.290 0.174 0.299 0.061 0.210 0.227 0.380βW 0.516 0.380 0.604 0.600

0.449 0.583 0.268 0.492 0.470 0.737 0.487 0.713βM 0.183 0.291 0.082 0.044

0.127 0.238 0.188 0.393 -0.047 0.211 -0.039 0.127

R2 0.686 0.494 0.360 0.760BIC 24374.422 10793.259 6411.147 6975.084

Table 1D. Whole Sample and Sub-Sample HNZ HAR-RV Regressions

15

1997 - 2010 1997 - 2002 2003 - 2006 2007 - 2010β0 0.886 3.230 1.514 0.979

0.368 1.404 1.389 5.070 0.615 2.414 0.181 1.776βD 0.266 0.235 0.249 0.342

0.227 0.306 0.175 0.296 0.176 0.321 0.268 0.416βW 0.325 0.220 0.285 0.432

0.256 0.395 0.106 0.333 0.155 0.414 0.314 0.550βM 0.361 0.416 0.348 0.168

0.299 0.423 0.297 0.534 0.225 0.470 0.071 0.265R2 0.642 0.331 0.445 0.687

BIC 20922.856 9494.723 5250.014 5935.805

Table 2A. Whole Sample and Sub-Sample AEP HAR-RV-J Regressions

1997 - 2010 1997 - 2002 2003 - 2006 2007 - 2010β0 1.916 2.792 1.605 1.219

1.314

2.517

1.736

3.848 0.667 2.54

3 0.046 2.392

βD 0.397 0.503 0.268 0.3190.35

40.44

10.44

50.56

1 0.189 0.347 0.226 0.412

βW 0.319 0.158 0.287 0.5470.26

00.37

70.08

20.23

4 0.154 0.420 0.422 0.672

βM 0.178 0.174 0.343 0.0960.13

00.22

60.11

10.23

7 0.231 0.455

-0.004 0.197

βJ 1.386 3.039 -0.257 -1.7921.04

71.72

42.59

93.47

9-

1.8301.31

7-

2.793-

0.792R2 0.681 0.721 0.547 0.658

BIC 21732.785 9074.831 5609.867 6793.489

Table 2C. Whole Sample and Sub-Sample ETR HAR-RV-J Regressions

1997 - 2010 1997 - 2002 2003 - 2006 2007 - 2010β0 1.237 3.457 1.629 1.271

0.668 1.807 1.900 5.01

3 0.457 2.801 0.219 2.323

βD 0.294 0.331 0.260 0.258

0.251 0.337 0.265 0.39

7 0.177 0.343 0.175 0.342

βW 0.495 0.398 0.318 0.624

0.430 0.560 0.298 0.49

7 0.178 0.458 0.504 0.744

βM 0.155 0.143 0.320 0.065

0.103 0.208 0.054 0.23

3 0.183 0.458 -0.027

0.157

βJ -0.016 0.143 -2.385 -0.251-

0.4050.37

3-

0.4200.70

6-

3.565-

1.204-

1.1070.60

5R2 0.698 0.504 0.370 0.724BIC 21511.020 9341.458 5443.698 6531.803

Table 2B. Whole Sample and Sub-Sample BHI HAR-RV-J Regressions

1997 - 2010 1997 - 2002 2003 - 2006 2007 - 2010β0 2.034 4.573 4.843 1.582

1.092 2.975 2.100 7.04

7 2.599 7.088 0.117 3.048

βD 0.245 0.220 0.138 0.332

0.203 0.287 0.155 0.28

6 0.059 0.216 0.254 0.411

βW 0.517 0.386 0.603 0.596

0.450 0.584 0.274 0.49

7 0.469 0.737 0.483 0.708

βM 0.181 0.284 0.082 0.042

0.126 0.237 0.181 0.38

7-

0.0470.21

1-

0.041 0.124

βJ 0.120 0.370 -0.107 -1.182-

0.2070.44

7-

0.0850.82

4-

1.2161.00

3-

2.011-

0.352R2 0.687 0.495 0.361 0.762BIC 24410.560 10789.828 6411.051 6988.944

Table 2D. Whole Sample and Sub-Sample HNZ HAR-RV-J Regressions

15

1997 - 2010 1997 - 2002 2003 - 2006 2007 - 2010β0 0.858 3.485 1.581 0.793

0.325 1.391 1.618 5.35

2 0.672 2.490 0.000 1.586

βD 0.270 0.220 0.238 0.452

0.227 0.312 0.156 0.28

3 0.163 0.314 0.365 0.538

βW 0.324 0.218 0.284 0.362

0.255 0.394 0.105 0.33

2 0.155 0.414 0.242 0.483

βM 0.361 0.412 0.347 0.153

0.299 0.423 0.293 0.53

0 0.225 0.469 0.057 0.250

βJ -0.108 0.631 1.135 -2.017-

0.6020.38

6-

0.1541.41

6-

1.1123.38

1-

2.872-

1.163R2 0.642 0.333 0.446 0.693BIC 21030.217 9495.543 5249.360 5942.442

15

Table 3A. Whole Sample and Sub-Sample AEP HAR-RV-CJ Regressions1997 - 2010 1997 - 2002 2003 - 2006 2007 - 2010

RV(d) RV(w) RV(m) RV(d) RV(w) RV(m) RV(d) RV(w) RV(m) RV(d) RV(w) RV(m)β0 3.284 4.679 9.715 4.942 7.528 13.995 3.141 5.395 10.316 2.476 4.438 11.009

2.672 3.897 3.924 5.434 8.767 10.663 4.004 5.881 6.205 8.852 12.341 15.649 2.052 4.230 4.239 6.551 9.105 11.526 1.131 3.820 2.925 5.951 9.054 12.965βCD 0.383 0.172 0.090 0.482 0.186 0.110 0.231 0.072 0.070 0.252 0.231 0.022

0.343 0.424 0.122 0.221 0.027 0.152 0.429 0.535 0.112 0.260 0.017 0.203 0.157 0.305 -0.006 0.150 -0.012 0.152 0.165 0.339 0.133 0.328 -0.105 0.148βCW 0.353 0.675 0.194 0.220 0.936 0.175 0.310 0.363 0.005 0.621 0.538 0.423

0.285 0.421 0.591 0.758 0.089 0.299 0.126 0.313 0.804 1.068 0.010 0.340 0.172 0.449 0.216 0.510 -0.149 0.159 0.480 0.762 0.380 0.697 0.218 0.627βCM 0.123 -0.016 0.310 0.160 -0.208 0.441 0.264 0.205 0.242 0.025 0.015 0.040

0.059 0.187 -0.094 0.063 0.211 0.408 0.061 0.258 -0.347 -0.069 0.268 0.615 0.144 0.384 0.078 0.333 0.109 0.376 -0.100 0.151 -0.126 0.156 -0.143 0.222βJD 2.500 1.372 0.047 4.311 2.291 0.320 1.787 -0.444 -0.953 -0.452 -0.110 -0.051

2.150 2.850 0.940 1.804 -0.495 0.588 3.863 4.759 1.659 2.923 -0.470 1.110 0.167 3.407 -2.163 1.276 -2.754 0.847 -1.476 0.573 -1.263 1.044 -1.541 1.439βJW -1.208 -6.507 0.703 -1.700 -12.027 -1.556 -1.670 -0.121 3.983 -1.924 -3.382 3.717

-2.172 -0.243 -7.696 -5.318 -0.789 2.195 -3.138 -0.262 -14.054 -9.999 -4.091 0.979 -5.429 2.089 -4.111 3.869 -0.195 8.161 -4.445 0.597 -6.220 -0.545 0.051 7.384βJM 2.009 5.902 -0.076 -1.074 3.672 -8.352 3.914 7.153 3.708 4.006 7.881 1.203

0.696 3.322 4.283 7.520 -2.107 1.955 -3.145 0.998 0.752 6.593 -12.004 -4.700 2.212 5.616 5.347 8.959 1.817 5.600 -0.207 8.219 3.138 12.623 -4.926 7.331R2 0.682 0.517 0.239 0.735 0.472 0.174 0.550 0.483 0.210 0.652 0.558 0.255

BIC 21900.613 22397.218 23231.087 9040.033 9283.403 9602.290 5601.013 5729.649 5835.756 6797.654 6954.371 7341.516

Table 3B. Whole Sample and Sub-Sample BHI HAR-RV-CJ Regressions1997 - 2010 1997 - 2002 2003 - 2006 2007 - 2010

RV(d) RV(w) RV(m) RV(d) RV(w) RV(m) RV(d) RV(w) RV(m) RV(d) RV(w) RV(m)β0 4.186 6.179 13.132 8.008 10.904 19.677 5.547 8.335 20.367 3.546 6.124 12.802

3.177 5.195 5.056 7.303 11.733 14.532 5.530 10.485 8.221 13.587 16.624 22.731 3.355 7.739 5.987 10.683 17.730 23.003 1.874 5.218 4.162 8.086 10.045 15.558βCD 0.214 0.195 0.061 0.197 0.118 0.032 0.106 0.139 -0.032 0.282 0.360 0.136

0.174 0.254 0.151 0.240 0.006 0.116 0.136 0.258 0.052 0.184 -0.043 0.107 0.033 0.179 0.061 0.218 -0.120 0.056 0.206 0.358 0.271 0.449 0.011 0.261βCW 0.535 0.432 0.256 0.390 0.335 0.130 0.626 0.470 0.220 0.626 0.413 0.293

0.467 0.603 0.356 0.507 0.162 0.350 0.277 0.503 0.213 0.457 -0.009 0.269 0.491 0.760 0.326 0.614 0.059 0.382 0.510 0.742 0.277 0.550 0.102 0.485βCM 0.111 0.167 0.267 0.202 0.264 0.371 0.067 0.085 0.119 -0.031 0.007 0.263

0.050 0.171 0.099 0.235 0.183 0.351 0.088 0.317 0.140 0.388 0.230 0.513 -0.071 0.205 -0.063 0.233 -0.047 0.285 -0.132 0.070 -0.112 0.126 0.096 0.430βJD 0.893 0.137 0.447 1.002 0.139 0.322 1.196 0.215 -0.190 0.031 -0.199 0.810

0.526 1.260 -0.272 0.545 -0.063 0.956 0.512 1.491 -0.391 0.669 -0.282 0.925 0.028 2.364 -1.036 1.467 -1.596 1.215 -0.852 0.913 -1.235 0.837 -0.646 2.265βJW -0.729 0.096 2.014 -0.244 0.567 1.517 -1.298 -2.285 3.329 -1.341 0.267 5.126

-1.659 0.201 -0.940 1.132 0.724 3.305 -1.495 1.006 -0.787 1.922 -0.025 3.058 -4.289 1.693 -5.489 0.919 -0.270 6.928 -3.525 0.842 -2.295 2.829 1.527 8.725βJM 3.461 3.929 2.592 2.547 2.764 0.971 1.960 3.733 -9.482 5.169 6.069 -8.110

2.360 4.561 2.703 5.154 1.065 4.118 0.917 4.177 0.998 4.529 -1.038 2.980 -2.936 6.855 -1.511 8.977 -15.371 -3.593 1.326 9.013 1.559 10.580 -14.446 -1.774R2 0.686 0.610 0.395 0.494 0.406 0.224 0.363 0.268 0.043 0.763 0.673 0.348

BIC 24474.290 24957.041 25767.892 10815.667 10974.262 11230.981 6407.324 6523.409 6730.505 6989.614 7251.990 7467.765

Table 3C. Whole Sample and Sub-Sample ETR HAR-RV-CJ Regressions1997 - 2010 1997 - 2002 2003 - 2006 2007 - 2010

RV(d) RV(w) RV(m) RV(d) RV(w) RV(m) RV(d) RV(w) RV(m) RV(d) RV(w) RV(m)β0 2.909 4.134 9.222 6.336 9.308 17.359 2.187 3.705 10.488 2.332 4.191 9.312

2.325 3.492 3.474 4.794 8.365 10.078 4.926 7.746 7.738 10.877 15.493 19.225 0.990 3.383 2.419 4.992 9.120 11.856 0.819 3.845 2.458 5.924 6.913 11.712βCD 0.262 0.161 0.112 0.282 0.048 0.119 0.201 0.103 0.008 0.237 0.314 0.080

0.220 0.303 0.114 0.208 0.051 0.173 0.221 0.344 -0.021 0.117 0.037 0.201 0.121 0.280 0.017 0.188 -0.083 0.099 0.156 0.317 0.222 0.406 -0.047 0.208βCW 0.518 0.553 0.343 0.401 0.584 0.076 0.420 0.331 0.391 0.647 0.477 0.545

0.447 0.589 0.473 0.634 0.238 0.448 0.290 0.511 0.461 0.707 -0.070 0.222 0.272 0.567 0.172 0.489 0.222 0.559 0.516 0.778 0.327 0.627 0.337 0.753βCM 0.075 0.084 0.090 0.101 0.062 0.243 0.241 0.308 -0.219 0.017 0.007 0.016

0.011 0.139 0.012 0.157 -0.004 0.184 -0.008 0.210 -0.059 0.184 0.099 0.387 0.090 0.392 0.145 0.470 -0.392 -0.046 -0.119 0.154 -0.149 0.164 -0.201 0.233βJD 1.200 0.194 0.410 1.511 0.160 0.689 -0.409 -0.649 -0.710 0.830 0.275 -0.142

0.761 1.639 -0.303 0.691 -0.235 1.054 0.896 2.126 -0.525 0.844 -0.124 1.503 -1.599 0.782 -1.930 0.631 -2.071 0.651 -0.053 1.713 -0.737 1.287 -1.543 1.259βJW -0.023 1.028 0.362 0.504 1.693 -0.292 -3.321 -1.164 -5.692 -0.540 -0.183 2.794

-1.088 1.042 -0.177 2.233 -1.201 1.925 -0.967 1.975 0.056 3.331 -2.238 1.654 -6.553 -0.090 -4.638 2.311 -9.387 -1.998 -2.743 1.662 -2.705 2.339 -0.698 6.287βJM 3.368 3.121 3.799 1.183 0.295 -0.604 6.205 5.841 20.933 2.157 4.291 -4.737

2.222 4.515 1.825 4.418 2.117 5.482 -0.443 2.810 -1.515 2.105 -2.755 1.548 1.207 11.203 0.467 11.214 15.220 26.646 -2.469 6.783 -1.007 9.589 -12.073 2.599R2 0.694 0.604 0.331 0.502 0.367 0.100 0.370 0.269 0.117 0.725 0.638 0.301

BIC 21593.874 22201.189 23384.123 9370.091 9585.443 9844.762 5447.625 5576.541 5692.905 6525.009 6667.016 7184.413

Table 3D. Whole Sample and Sub-Sample HNZ HAR-RV-CJ Regressions1997 - 2010 1997 - 2002 2003 - 2006 2007 - 2010

RV(d) RV(w) RV(m) RV(d) RV(w) RV(m) RV(d) RV(w) RV(m) RV(d) RV(w) RV(m)β0 2.014 2.933 5.377 5.742 7.695 12.229 2.813 4.308 6.302 1.182 2.221 5.756

1.417 2.610 2.280 3.587 4.630 6.124 3.858 7.626 5.687 9.702 10.092 14.367 1.722 3.904 3.141 5.474 5.070 7.534 0.355 2.009 1.258 3.185 4.541 6.971βCD 0.240 0.084 0.054 0.202 0.040 0.022 0.219 -0.016 0.045 0.384 0.268 0.121

0.200 0.280 0.040 0.127 0.004 0.103 0.143 0.261 -0.023 0.103 -0.045 0.088 0.149 0.290 -0.092 0.059 -0.035 0.125 0.299 0.469 0.169 0.366 -0.003 0.246βCW 0.307 0.298 0.242 0.165 0.145 0.203 0.267 0.337 0.073 0.431 0.394 0.349

0.234 0.379 0.219 0.377 0.151 0.332 0.049 0.281 0.022 0.269 0.071 0.334 0.134 0.400 0.194 0.479 -0.078 0.223 0.301 0.561 0.242 0.545 0.159 0.540βCM 0.330 0.432 0.379 0.360 0.457 0.288 0.241 0.244 0.304 0.159 0.245 0.238

0.258 0.401 0.354 0.511 0.290 0.469 0.223 0.498 0.310 0.603 0.131 0.444 0.084 0.398 0.076 0.413 0.126 0.481 0.050 0.269 0.118 0.373 0.077 0.399βJD 0.725 0.251 -0.034 1.140 0.426 -0.108 2.958 2.138 0.673 -0.384 -0.776 -0.324

0.182 1.268 -0.344 0.846 -0.714 0.646 0.274 2.005 -0.496 1.348 -1.090 0.874 0.603 5.312 -0.381 4.656 -1.987 3.334 -1.244 0.475 -1.777 0.225 -1.587 0.939βJW 1.152 0.789 3.667 2.403 1.751 4.625 1.837 1.316 6.104 -1.158 -0.796 0.944

-0.195 2.498 -0.686 2.265 1.980 5.354 0.312 4.494 -0.476 3.979 2.252 6.997 -4.039 7.713 -4.969 7.601 -0.536 12.744 -3.283 0.966 -3.271 1.678 -2.177 4.066βJM 3.896 5.483 3.009 2.330 3.736 -1.856 10.719 19.230 11.936 -0.065 0.613 -3.966

2.225 5.566 3.653 7.314 0.916 5.101 -0.319 4.980 0.913 6.559 -4.862 1.150 0.077 21.362 7.847 30.612 -0.089 23.961 -4.373 4.243 -4.405 5.631 -10.296 2.364R2 0.637 0.564 0.428 0.331 0.241 0.137 0.447 0.359 0.225 0.690 0.579 0.323

BIC 21010.908 21339.456 22098.640 9512.864 9687.620 9807.862 5246.627 5359.648 5368.986 5938.353 6115.014 6379.729

Table 4A. Whole Sample and Sub-Sample AEP LHAR-CJ Regressions

1997 - 2010 1997 - 2002 2003 - 2006 2007 - 2010RV(d) RV(w) RV(m) RV(d) RV(w) RV(m) RV(d) RV(w) RV(m) RV(d) RV(w) RV(m)

β 0.751 0.588 1.093 0.931 0.384 1.179 0.949 0.327 0.893 0.470 1.172 1.012

0.504 0.999 0.249 0.926 0.725 1.461 0.519 1.34

3 -0.179 0.948 0.531 1.827 0.309 1.589 -

0.452 1.106 0.085 1.701 -0.042 0.98

2 0.355 1.990 0.137 1.887

βCD 0.023 0.081 -0.020 0.082 0.048 0.027 0.205 -0.168 -0.264 -0.082 -0.051 0.079-

0.086 0.133 -0.068 0.231 -0.183 0.14

2 -0.089 0.254 -0.187 0.28

2 -0.243 0.297 -0.309 0.719 -

0.794 0.458 -0.913 0.385 -0.323 0.16

0 -0.437 0.334 -0.333 0.492

βCW -0.033 -0.135 0.368 0.001 -0.313 -0.122 0.850 0.504 0.219 0.095 0.211 0.941-

0.223 0.158 -0.395 0.126 0.085 0.65

1 -0.332 0.333 -0.767 0.14

1 -0.644 0.401 -0.110 1.811 -

0.666 1.673 -0.994 1.432 -0.386 0.57

7 -0.558 0.980 0.118 1.764

βCM 0.503 0.267 0.110 0.234 0.202 0.410 0.030 -0.008 0.144 0.257 0.204 -0.766

0.286 0.719 -0.029 0.564 -0.211 0.43

2 -0.177 0.645 -0.359 0.76

4 -0.236 1.056 -0.451 0.511 -

0.594 0.578 -0.464 0.751 -0.232 0.74

7 -0.578 0.985 -1.603 0.070

βJD 0.374 0.173 0.170 0.321 0.012 0.217 0.198 0.043 -0.006 0.536 0.186 0.161

0.265 0.482 0.025 0.321 0.009 0.331 0.140 0.50

2 -0.235 0.260 -0.067 0.502 -

0.022 0.418 -0.224 0.311 -0.284 0.27

1 0.346 0.727 -0.117 0.49

0 -0.164 0.486

βJW 0.354 0.598 0.062 0.259 0.782 0.248 0.331 0.465 0.125 0.270 0.589 -0.096

0.174 0.533 0.352 0.844 -0.206 0.329 -0.033 0.55

0 0.383 1.181 -0.210 0.707 -

0.085 0.748 -0.042 0.973 -0.401 0.65

1 -0.013 0.554 0.137 1.04

1 -0.580 0.388

βJM -0.002 0.041 0.386 0.106 0.127 0.165 0.085 0.367 0.549 0.023 -0.175 0.587-

0.166 0.162 -0.183 0.266 0.142 0.63

0 -0.170 0.382 -0.250 0.50

4 -0.269 0.599 -0.358 0.528 -

0.173 0.906 -0.011 1.109 -0.234 0.28

0 -0.585 0.236 0.148 1.027

βrD 0.001 -0.002 -0.003 0.001 -0.001 -0.001 0.041 0.007 0.008 0.003 0.005 0.000-

0.001 0.002 -0.004 0.000 -0.005 0.00

0 -0.001 0.003 -0.004 0.00

2 -0.004 0.002 0.012 0.070 -0.028 0.042 -0.028 0.04

4 -0.008 0.013 -0.012 0.02

2 -0.018 0.018

βrW 0.005 0.001 -0.008 -0.008 -0.004 -0.046 0.048 0.060 0.088 0.024 0.047 -0.012-

0.021 0.031 -0.035 0.037 -0.047 0.03

0 -0.046 0.031 -0.057 0.04

8 -0.107 0.014 -0.048 0.144 -

0.057 0.177 -0.034 0.209 -0.026 0.07

3 -0.033 0.126 -0.097 0.073

βrM 0.037 0.075 0.098 0.052 0.064 0.131 0.018 -0.166 -0.132 0.005 0.066 0.083-

0.014 0.088 0.005 0.144 0.022 0.174 -0.026 0.12

9 -0.042 0.170 0.009 0.252 -

0.193 0.228 -0.422 0.090 -0.398 0.13

3 -0.077 0.086 -0.065 0.19

7 -0.056 0.223

R2 0.739 0.560 0.442 0.708 0.544 0.330 0.668 0.506 0.363 0.781 0.522 0.396BIC -296.487 427.920 1338.086 -353.185 -77.234 231.420 -145.274 3.865 145.736 65.202 329.032 763.663

Table 4B. Whole Sample and Sub-Sample BHI LHAR-CJ Regressions1997 - 2010 1997 - 2002 2003 - 2006 2007 - 2010

RV(d) RV(w) RV(m) RV(d) RV(w) RV(m) RV(d) RV(w) RV(m) RV(d) RV(w) RV(m)β 0.689 0.561 1.891 0.794 0.404 1.739 0.578 1.120 2.466 0.712 -0.500 1.781

0.335 1.044 0.160 0.962 1.386 2.396 0.222 1.365 -

0.193 1.000 1.058 2.420 -0.319 1.475 0.275 1.965 1.443 3.489 -0.386 1.809 -

1.992 0.993 -0.293 3.855

βCD 0.034 -0.001 0.018 0.020 -0.028 0.005 -0.038 -0.126 -0.085 0.059 0.223 0.163-

0.028 0.097 -0.072 0.069 -0.071 0.10

7 -0.057 0.097 -0.108 0.053 -

0.087 0.097 -0.268 0.191 -0.343 0.090 -0.347 0.176 -

0.088 0.206 0.022 0.423 -0.115 0.442

βCW -0.060 -0.029 0.162 -0.122 0.001 0.060 0.227 -0.375 0.459 0.107 -0.353 -0.054-

0.194 0.073 -0.179 0.122 -0.027 0.35

2 -0.293 0.048 -0.177 0.180 -

0.144 0.263 -0.262 0.716 -0.836 0.086 -0.099 1.017 -

0.241 0.455 -0.826 0.121 -0.711 0.604

βCM 0.194 0.112 0.046 0.235 0.038 0.060 0.048 0.162 -0.695 0.178 -0.280 -0.196

0.038 0.350 -0.064 0.288 -0.176 0.26

8 0.025 0.445 -0.182 0.257 -

0.285 0.216 -0.550 0.647 -0.402 0.726 -1.378 -0.013 -

0.341 0.697 -0.986 0.426 -1.176 0.785

βJD 0.145 0.219 -0.088 0.076 0.078 -0.207 0.130 0.059 -0.208 0.296 0.844 0.414

0.033 0.256 0.093 0.345 -0.246 0.070 -0.080 0.232 -

0.085 0.241 -0.393 -0.021 -0.116 0.377 -

0.173 0.291 -0.489 0.072 0.024 0.568 0.474 1.214 -0.100 0.929

βJW 0.366 0.223 0.278 0.276 0.167 0.400 0.473 0.362 0.225 0.240 -0.263 -0.189

0.185 0.547 0.019 0.428 0.020 0.535 0.000 0.552 -

0.122 0.455 0.071 0.729 0.068 0.878 -0.020 0.744 -0.237 0.688 -

0.124 0.604 -0.758 0.232 -0.877 0.498

15

βJM 0.277 0.398 0.256 0.411 0.651 0.342 0.212 0.259 0.263 0.230 0.612 0.294

0.100 0.453 0.199 0.597 0.005 0.507 0.122 0.701 0.349 0.953 -

0.003 0.687 -0.181 0.605 -0.112 0.629 -0.185 0.712 -

0.178 0.638 0.057 1.168 -0.478 1.066

βrD 0.003 0.000 0.002 0.004 0.001 0.002 0.005 0.007 0.009 0.003 -0.002 0.003

0.001 0.006 -0.003 0.002 -0.001 0.00

6 0.002 0.007 -0.002 0.004 -

0.002 0.005 -0.005 0.015 -0.002 0.017 -0.003 0.021 -

0.003 0.009 -0.009 0.006 -0.008 0.013

βrW 0.011 0.017 0.009 0.002 0.008 0.026 0.012 0.034 -0.038 0.016 0.023 0.000

0.003 0.019 0.007 0.026 -0.003 0.021 -0.011 0.015 -

0.005 0.022 0.010 0.042 -0.034 0.058 -0.009 0.077 -0.090 0.014 0.005 0.027 0.008 0.038 -0.020 0.021

βrM 0.004 0.005 0.029 0.016 0.019 0.010 -0.008 -0.024 -0.034 -0.019 -0.021 0.067-

0.012 0.020 -0.013 0.023 0.007 0.05

2 -0.005 0.036 -0.002 0.040 -

0.014 0.035 -0.086 0.069 -0.096 0.049 -0.122 0.054 -

0.054 0.016 -0.069 0.027 0.000 0.133

R2 0.651 0.563 0.334 0.502 0.473 0.292 0.385 0.330 0.100 0.759 0.610 0.228BIC -524.623 113.014 987.465 -140.039 81.561 336.365 -290.532 -133.992 94.492 -189.966 125.500 484.528

Table 4C. Whole Sample and Sub-Sample ETR LHAR-CJ Regressions1997 - 2010 1997 - 2002 2003 - 2006 2007 - 2010

RV(d) RV(w) RV(m) RV(d) RV(w) RV(m) RV(d) RV(w) RV(m) RV(d) RV(w) RV(m)β 0.524 0.817 1.302 1.092 1.372 2.130 0.863 1.180 1.897 0.156 0.872 1.735

0.263 0.785 0.506 1.128 0.900 1.704 0.542 1.64

3 0.730 2.015 1.335 2.925 0.016 1.711 0.093 2.266 0.823 2.97

1 -0.403 0.715 0.236 1.50

8 0.818 2.651

βCD 0.072 0.043 0.049 0.064 0.095 -0.033 0.269 -0.269 -0.410 -0.007 -0.071 -0.029-

0.038 0.182 -0.088 0.174 -0.121 0.21

8 -0.103 0.230 -0.100 0.28

9 -0.274 0.208 -0.308 0.847 -

1.010 0.472 -1.142 0.322 -0.174 0.16

0 -0.261 0.119 -0.303 0.244

βCW 0.088 0.105 0.255 0.252 0.301 0.353 -0.099 -0.252 -0.192 -0.100 -0.310 0.077-

0.120 0.297 -0.143 0.354 -0.066 0.57

6 -0.019 0.524 -0.016 0.61

8 -0.039 0.745 -0.964 0.765 -

1.361 0.856 -1.288 0.904 -0.502 0.30

2 -0.768 0.147 -0.583 0.736

βCM 0.123 0.322 0.225 -0.254 -0.136 -0.313 1.333 1.698 4.015 -0.020 0.531 0.141-

0.119 0.364 0.034 0.610 -0.147 0.598 -0.622 0.11

4 -0.566 0.293 -0.845 0.218 -

0.634 3.300 -0.825 4.221 1.521 6.50

9 -0.496 0.457 -0.011 1.07

3 -0.641 0.922

βJD 0.243 0.142 0.074 0.099 0.067 -0.022 0.270 0.088 0.066 0.429 0.218 0.097

0.137 0.350 0.015 0.269 -0.090 0.238 -0.052 0.25

1 -0.110 0.243 -0.241 0.197 0.047 0.493 -

0.198 0.375 -0.217 0.350 0.214 0.64

3 -0.026 0.461 -0.254 0.448

βJW 0.364 0.389 0.108 0.298 0.252 0.008 0.277 0.159 0.172 0.182 0.519 -0.103

0.186 0.542 0.178 0.601 -0.166 0.381 0.023 0.57

4 -0.069 0.573 -0.389 0.406 -

0.129 0.683 -0.361 0.680 -0.343 0.68

7 -0.142 0.506 0.151 0.88

8 -0.634 0.428

βJM 0.209 0.173 0.366 0.277 0.249 0.398 0.085 0.267 -0.062 0.350 -0.030 0.420

0.049 0.368 -0.017 0.364 0.120 0.61

2 -0.030 0.583 -0.108 0.60

7 -0.044 0.841 -0.370 0.541 -

0.317 0.851 -0.639 0.515 0.093 0.60

7 -0.322 0.263 -0.001 0.841

βrD 0.005 -0.001 -0.002 0.005 -0.005 -0.004 0.030 0.002 0.030 0.010 0.015 0.014

0.000 0.010 -0.007 0.004 -0.009 0.00

6 -0.001 0.011 -0.012 0.00

2 -0.013 0.004 -0.017 0.077 -

0.058 0.063 -0.030 0.089 -0.001 0.02

2 0.002 0.028 -0.004 0.033

βrW -0.004 0.020 0.000 0.020 0.054 0.038 0.039 0.060 0.070 -0.018 0.004 -0.025-

0.023 0.015 -0.003 0.042 -0.029 0.02

9 -0.011 0.051 0.018 0.09

0 -0.006 0.083 -0.095 0.172 -

0.111 0.231 -0.099 0.239 -0.044 0.00

7 -0.025 0.033 -0.067 0.017

βrM 0.037 0.029 0.109 0.013 0.011 -0.013 -0.195 -0.004 0.039 0.072 0.022 0.299-

0.009 0.083 -0.026 0.083 0.038 0.18

0 -0.049 0.076 -0.062 0.08

4 -0.103 0.076 -0.433 0.043 -

0.310 0.301 -0.262 0.341 -0.001 0.14

5 -0.061 0.105 0.179 0.418

R2 0.753 0.663 0.476 0.513 0.388 0.124 0.515 0.279 0.369 0.823 0.751 0.506BIC -169.604 576.972 1574.092 -282.431 -7.002 244.017 -52.007 116.448 250.290 5.559 288.920 703.865

Table 4D. Whole Sample and Sub-Sample HNZ LHAR-CJ Regressions1997 - 2010 1997 - 2002 2003 - 2006 2007 - 2010

RV(d) RV(w) RV(m) RV(d) RV(w) RV(m) RV(d) RV(w) RV(m) RV(d) RV(w) RV(m)β 0.307 0.593 0.965 0.741 1.579 1.940 0.926 0.542 1.963 0.064 0.409 1.416

0.020 0.595 0.294 0.891 0.596 1.333 -0.099 1.58

0 0.785 2.372 1.056 2.825 0.213 1.639 0.076 1.664 1.044 2.88

2 -0.474 0.602 -0.160 0.97

9 0.563 2.270

βCD 0.206 0.091 0.007 0.248 0.129 -0.034 0.847 -0.528 0.065 -0.034 0.081 -0.059

15

0.071 0.342 -0.051 0.232 -0.167 0.18

2 0.077 0.419 -0.033 0.29

1 -0.215 0.146 0.156 1.538 -1.297 0.242 -0.825 0.95

6 -0.399 0.332 -0.305 0.46

8 -0.638 0.521

βCW -0.074 0.053 0.693 -0.078 -0.150 0.567 -0.488 0.628 1.414 0.451 -0.083 0.674-

0.361 0.213 -0.245 0.351 0.325 1.06

1 -0.452 0.296 -0.503 0.20

4 0.173 0.961 -1.627 0.652 -

0.641 1.896 -0.053 2.882 -0.370 1.27

3 -0.953 0.787 -0.630 1.978

βCM 0.092 0.368 -0.200 -0.106 0.663 -0.136 1.738 1.167 2.543 0.041 -0.234 -0.356-

0.229 0.413 0.034 0.702 -0.612 0.212 -0.605 0.39

3 0.191 1.134 -0.662 0.390 -

0.389 3.864 -1.201 3.535 -0.196 5.28

2 -0.588 0.670 -0.900 0.43

2 -1.354 0.643

βJD 0.159 -0.004 -0.023 0.167 -0.078 -0.086 0.062 0.038 0.091 0.308 0.188 -0.054

0.041 0.277 -0.127 0.119 -0.175 0.12

8 -0.015 0.348 -0.250 0.09

3 -0.277 0.105 -0.136 0.260 -

0.183 0.258 -0.164 0.347 0.054 0.56

3 -0.081 0.458 -0.458 0.349

βJW 0.295 0.332 0.168 0.038 0.191 0.201 0.394 0.077 -0.031 0.317 0.517 0.269

0.103 0.487 0.132 0.532 -0.079 0.414 -0.277 0.35

3 -0.107 0.489 -0.131 0.533 0.081 0.707 -

0.272 0.426 -0.435 0.372 -0.098 0.73

1 0.078 0.956 -0.389 0.927

βJM 0.434 0.436 0.496 0.566 0.324 0.234 0.126 0.510 0.042 0.343 0.159 0.285

0.252 0.616 0.247 0.625 0.263 0.729 0.182 0.95

0 -0.040 0.687 -0.171 0.639 -

0.292 0.544 0.044 0.976 -0.496 0.581 0.021 0.66

5 -0.181 0.500 -0.226 0.796

βrD 0.006 0.002 0.015 0.010 0.007 0.019 0.026 -0.060 -0.003 -0.012 0.001 0.009-

0.005 0.017 -0.009 0.013 0.002 0.02

9 -0.005 0.024 -0.007 0.02

1 0.004 0.035 -0.035 0.087 -

0.128 0.008 -0.082 0.075 -0.033 0.00

8 -0.021 0.023 -0.024 0.042

βrW 0.029 0.055 -0.007 0.012 0.039 -0.041 -0.025 -0.012 -0.041 0.116 0.094 0.153-

0.006 0.064 0.018 0.091 -0.052 0.038 -0.030 0.05

5 -0.001 0.080 -0.086 0.005 -

0.213 0.162 -0.221 0.197 -0.283 0.20

1 0.022 0.210 -0.005 0.19

4 0.004 0.302

βrM -0.004 0.003 0.045 0.010 -0.019 0.062 -0.058 0.066 0.157 -0.156 0.036 -0.104-

0.073 0.065 -0.068 0.075 -0.043 0.13

3 -0.074 0.093 -0.098 0.06

0 -0.026 0.150 -0.296 0.180 -

0.199 0.331 -0.150 0.463 -0.391 0.07

9 -0.213 0.284 -0.477 0.269

R2 0.710 0.686 0.545 0.350 0.349 0.259 0.649 0.542 0.426 0.772 0.709 0.378BIC 29.839 593.560 1300.614 95.707 260.707 448.011 -96.651 38.850 106.941 -69.418 190.874 468.526

15