Hi Quantitative Finance Stack Exchange,
It's my first go at GARCH models so give me a chance with my phrasing. I'm looking for an answer to a general question.
First, I understand that you can have a forecasting model to forecast returns and a GARCH model to forecast volatility. Let's proceed with the simplest example:
Forecasting returns:
$$\hat{y_t}=\alpha\cdot y_{t-1} + \epsilon_t$$
GARCH(1,1):
$$\hat{\sigma^2_t}=\beta_1\epsilon_{t-1}+\beta_2\sigma^2_{t-1}$$
Now, I've developed my trading strategy and let's say I found that it works, namely buy when $\hat{y_t} > 0.0020\%$. My question is this. What is the standard way of looking at how GARCH compliments my strategy, if at all?
The way I see it is that both predicts different things. One predicts $\hat{y_t}$ and another predicts $\hat{\sigma^2_{t}}$. Therefore, GARCH is only readily implementable if you somehow found a way to incorporate volatility in your strategy. If my existing strategy $\hat{y_t} > 0.0020\%$ works fine, there isn't a need for GARCH correct?
Thank you for your help, Donny