I'm new to GARCH, but I've got daily data of TV Ratings. I've been trying to forecast this for future, and a quick background - the data is non-stationary, has high seasonality (weekly, monthly & yearly).
I've tried UCM, but forecasts for weekly data using UCM are easier to handle, and daily level of forecasts aren't making the cut. Which is when I turned to GARCH to see if I can quickly get some high level estimates into the future.
I'm stuck with trying to get the forecasts for both the "conditional mean" and the "conditional variance" for t periods in the future. I've got the estimates for the GARCH(1,1) model, but I'm stuck trying to forecast the series into the future.
y(t) = constant + AR(1)coeff*y(t-1) + u(t) h(t) = ARCH0 + ARCH1*u(t-1) + GARCH1*h(t-1)
But I haven't been able to implement this to get the predicted conditional mean & variance values, and haven't really found a perfect step-by-step guide anywhere yet! I'm new to GARCH, so, I'm guessing this might be pretty basic, but any help would be much appreciated.