Garch Model Application in Sas
Chapter
Chapter 12
Autoregressive Conditional
Heteroscedasticity (ARCH) and Generalized ARCH
(GARCH) Models
Section
Section 12.1
Introduction
ARCH and GARCH Models
• ARCH and GARCH models are designed to model heteroscedasticity
(unequal variance) of the error term with the use of timeseries data
• Objective is to model and forecast volatility
Example: Understand the risk of holding an asset; useful in financial situations
• ARCH -- Autoregressive Conditional Heteroscedasticity
• GARCH -- Generalized ARCH
Engle, R. “Autoregressive Conditional Heteroscedasticity with
Estimates of the Variance of UK Inflation,” Econometrica 50
(1982):987-1008.
Engle noticed that in some time series, particularly those involving financial data, large and small residuals tend to come in clusters, suggesting that the variance of an error may depend on the size of the preceding error.
3
ARCH-GARCH Models
Recent development in financial econometrics require the use of models and techniques that are able to model the attitude of investors not only towards expected returns, but towards risk (or uncertainty) as well. This fact requires models that are capable of dealing with the volatility (variance) of the series. Such models are the ARCH-family of models.
In
In other words, we observe that large changes in stock returns seem to be followed by other large changes and vice versa. This phenomenon is what financial analysts call volatility clustering.
In such cases it is clear that the assumption of homoskedasticity
(or constant variance) is very limiting, and in such instances it is preferable to examine patterns that allow the variance to depend upon its history.
4
Section
Section 12.2
The ARCH(q) Model
The ARCH(q) Model
The ARCH(q) model will simultaneously examine the mean and the variance of a series according to the following specification:
Yt = a + β ′X t + u t ut =
ht e t
e t ~ IN ( 0 ,1) u t I Ω t ~ iid N ( 0 ,
Chapter 12
Autoregressive Conditional
Heteroscedasticity (ARCH) and Generalized ARCH
(GARCH) Models
Section
Section 12.1
Introduction
ARCH and GARCH Models
• ARCH and GARCH models are designed to model heteroscedasticity
(unequal variance) of the error term with the use of timeseries data
• Objective is to model and forecast volatility
Example: Understand the risk of holding an asset; useful in financial situations
• ARCH -- Autoregressive Conditional Heteroscedasticity
• GARCH -- Generalized ARCH
Engle, R. “Autoregressive Conditional Heteroscedasticity with
Estimates of the Variance of UK Inflation,” Econometrica 50
(1982):987-1008.
Engle noticed that in some time series, particularly those involving financial data, large and small residuals tend to come in clusters, suggesting that the variance of an error may depend on the size of the preceding error.
3
ARCH-GARCH Models
Recent development in financial econometrics require the use of models and techniques that are able to model the attitude of investors not only towards expected returns, but towards risk (or uncertainty) as well. This fact requires models that are capable of dealing with the volatility (variance) of the series. Such models are the ARCH-family of models.
In
In other words, we observe that large changes in stock returns seem to be followed by other large changes and vice versa. This phenomenon is what financial analysts call volatility clustering.
In such cases it is clear that the assumption of homoskedasticity
(or constant variance) is very limiting, and in such instances it is preferable to examine patterns that allow the variance to depend upon its history.
4
Section
Section 12.2
The ARCH(q) Model
The ARCH(q) Model
The ARCH(q) model will simultaneously examine the mean and the variance of a series according to the following specification:
Yt = a + β ′X t + u t ut =
ht e t
e t ~ IN ( 0 ,1) u t I Ω t ~ iid N ( 0 ,