Conditional Variance in GARCH Model?

[Aditya-16]

  Dear all,
 
 I would like to ask about the GARCH model. I have read few articles about stock returns modelling with GARCH. I am confused about the definition of conditional variance. What does it forecast? Is it the conditional variance of the returns or the conditional variance of the returns' residuals? What is the definition and the measure of volatility in the GARCH model?
 
 Thank you in advance
 
 Best Regards,
 
 Aditya
 
       
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[michal miklovic]

Hi,

It is usually assumed that stock returns have the following structure:
R(t) = mean(t) + sigma(t)*z(t)
where R(t) is the return, mean(t) can be estimated by, e.g., arma models and sigma(t) is modeled by garch. z(t) is assumed to have zero mean and unit variance, i.e. z(t) ~ D(0,1). The term sigma(t)*z(t) stands for random shocks to returns, which have zero mean and conditional variance equal to sigma(t)^2. Thus, R(t) has conditional mean equal to mean(t) and conditional variance equal to sigma(t)^2.
sigma(t) is an estimate of true volatility, which is not observable. Therefore, sigma(t) is used as a measure of volatility in garch models.

Hope this helps.

Best regards,

Michal



----- Original Message ----
From: Aditya <learningaddict83@...>
To: r-sig-finance@...
Sent: Wednesday, April 23, 2008 1:15:16 PM
Subject: [R-SIG-Finance] Conditional Variance in GARCH Model?

  Dear all,

I would like to ask about the GARCH model. I have read few articles about stock returns modelling with GARCH. I am confused about the definition of conditional variance. What does it forecast? Is it the conditional variance of the returns or the conditional variance of the returns' residuals? What is the definition and the measure of volatility in the GARCH model?

Thank you in advance

Best Regards,

Aditya
 
     
---------------------------------

    [[alternative HTML version deleted]]

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