What is the timing of inferred garch volatility?

When I infer volatility from a GARCH model, such as

v=infer(model,x)

where x is indexed over time (1:T), is the output volatility also indexed over (1:T)? I ask because when I plot the inferred volatility, it appears to be off by one period (it appears to be indexed from (0:T-1)).

Answer 1

[Roger Wohlwend]

The volatility is also indexed over (1:T). GARCH models are not perfect. If volatilty changes suddenly from low to high (or the other way around) GARCH models react in generel one period after the change occurs. The same is true for ARMA models. It is in the nature of these models that significant changes in the modeled variable take them by surprise, and the models react one period too late. That is why the fit is better if you move the volatility backwards one period (i.e. from 1:T to 0:T-1). However, that is not acceptable.