Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. It only takes a minute to sign up.
Sign up to join this community
I found excellent notes on ARCH and GARCH models here. On page 3 it is given that:
Standard time series models:
\begin{eqnarray*} Y_{t} & = & E\left(Y_{t}|\Omega_{t-1}\right)+\epsilon_{t}\\ E\left(Y_{t}|\Omega_{t-1}\right) & = & \mu_{t}\left(\theta\right)\\ E\left(Y_{t}|\Omega_{t-1}\right) & = & E\left(\epsilon_{t}^{2}|\Omega_{t-1}\right)=\sigma^{2} \end{eqnarray*}
What does this $\Omega$ means here? Any help will be highly appreciated. Thanks
Roughly speaking, $\Omega_{t-1}$ is all the information available up to time $t-1$. For example, it can be considered as the observed values of your time series i.e. $Y_0, Y_1, Y_2, ..., Y_{t-1}$. If I want to be more precise, it is the $\sigma$-algebra generated by all these random variables i.e. $\Omega_{t-1}=\sigma\{Y_0, Y_1, Y_2, ..., Y_{t-1}\}$.
