Interest rate control variable GARCH I'm building a GARCH model which looks if analysts' reports affect the volatility of certain stocks. I was wondering if it would be logical to include the interest rate in my GARCH model as a sort of control variable for macroeconomic changes.
Maybe a change in volatility doesn't come from the report per se, but underlying changes in monetary policy for instance.
Any help is appreciated!
 A: Research in linking financial market volatility and macroeconomic fundamentals has been a widely studied topic. Different interest rates and related variables have been included in papers from the financial econometrics literature. 
The most common approach is to consider a additive GARCH-X model (here GARCH(1,1) for notional convenience). Denote the "exogenous" variables that you want to include by the vector $x_t$. The model can then be written as:
\begin{align}
r_t =&  \mu + \varepsilon_t =\mu +  \sigma_t z_t \\
\sigma_t^2 =& \omega + \beta \sigma_{t-1}^2 +  \alpha \varepsilon_{t-1}^2 + \gamma^\prime x_{t-1}
\end{align}
where $z_t$ is assumed to be $iid(0,1)$. We lag the exogenous variables one period such that they are included in the information set at time $t$. 
This approach of adding the exogenous variables additively directly to the GARCH equation has different draw backs. One being that the conditional variance may be negative when e.g. rates becomes negative, which is implausible. 
An alternative route would be to consider an multiplicative specification. Then assume that the conditional variance can be written as $\sigma_t^2 = g_t h_t$, where 
\begin{align}
h_t =& \omega + \beta h_{t-1} +  \alpha \left(\varepsilon_{t-1}/\sqrt{g_{t-1}} \right)^2
\end{align}
and 
\begin{equation}
g_t = \gamma^\prime x_{t-1}
\end{equation}
such that the scaled returns follow a "normal" GARCH process while $g_t$ governs the baseline volatility. 
To avoid the possibility of a negative variance due to the exogenous variables, one could assume: 
\begin{equation}
g_t = \exp\left({\gamma^\prime x_{t-1}} \right)
\end{equation}
Another important note is that the relationship between macroeconomic fundamentals often is heavily non-linear. Thus, using models with a smooth transition specification may be nice. You also may have a look at the GARCH-MIDAS model that is used extensively for research in linking macroeconomic variables with volatility. 
A google search will give you a lot of interesting research articles on this topic!
