Transcript Presentation 3 - Duke University

Presentation 3
Kunal Jain
March 24, 2010
Economics 201FS
HAR-RV Model

Heterogeneous Autoregressive model of the Realized Volatility
(HAR-RV), Corsi 2003, uses average realized variance over daily,
weekly, and monthly time intervals to build a conditional volatility
model.

h=1 corresponds to daily periods, h=5 corresponds to weekly
periods, h=22 corresponds to monthly periods.
This model uses volatilities realized over a 1-day, 5-day, and 1-month
time interval to build the conditional volatilities.

HAR-RV Model


Model implemented in MatLab
Regression Results (AMZN)
RVt+1



Coefficient
Standard Error
T-Statistic
RVt
.3921
0.0220
17.82*
RVt-5,t
.3638
0.0339
10.73*
RVt-22,t
.1766
0.0282
6.26
constant
.0001
0.0000
0.000
Coefficient sum approximates one.
Constant?
Reject the null hypothesis?
HAR-RV Model- Kernel Density

Residuals- Kernel Density Plot (Observed-Expected)

Non-parametric way of estimating the probability density function of a random
variable- want to resemble a normal distribution.
HAR-RV: Squared Overnight

Including squared overnight returns to look at volatility
RVt+1
Coefficient
Standard Error
T-Statistic
RVt
.3742
.0217
17.24
RVt-5,t
.3542
.0334
10.60
RVt-22,t
.1786
.0277
6.45
BON
.0656
.0067
9.79
Constant
.0001
0.0000
0.000
HAR-RV Model- Kernel Density
*Including overnight returns
HAR-RV Model

Normalizing overnight returns

[Sqrt(RV) & Abs(Overnight)] vs. [RV & Overnight2]
[Sqrt(RV) & Abs(Overnight)]
[RV & Overnight2]
RVt+1


Coefficient
Standard Error
T-Statistic
RVt+1
Coefficient
Standard Error
T-Statistic
RVt
.3742
.0217
17.24
RVt
.3856
.0216
17.85
RVt-5,t
.3542
.0334
10.60
RVt-5,t
.3472
.0326
10.65
RVt-22,t
.1786
.0277
6.45
RVt-22,t
.1886
.0250
7.54
BON
.0656
.0067
9.79
BON
.1012
.0082
12.34
Constant
.0001
0.0000
0.000
Constant
.0011
0.0004
2.75
Normalize outliars -> T-statistic for Overnight
Which one is better?
HAR-RV Model: MedV



Use MedV as a dummy variable in regression
Regression Results with MedV Z-values at 5% significance level (10 minute interval)
T-Distribution with 5 DOF
RVt+1
Coefficient
Standard Error
T-Statistic
RVt
.2731
.0185
14.76
RVt-5,t
.1683
.0286
5.88
RVt-22,t
.1524
.0233
6.54
BMedV
.0030
.0001
30
Constant
.0003
0.0000
-
HAR-RV Model

Regression results with:

Squared Overnight returns


RV & Overnight2
MedV 5% significant Z-statistic dummy variable (10 minute interval)
RVt+1
Coefficient
Standard Error
T-Statistic
RVt
.2508
.0182
13.78
RVt-5,t
.1533
.0280
5.475
RVt-22,t
.1469
.0228
6.44
BON
.0108
.0009
12
BMedV
.0030
.0001
30
Constant
.0002
0
-
Further Research



Significant Levels
STATA integration
More stocks


New Regressors
Integrate Earnings Surprises