In all seriousness, are you just trying to find out if the given current prices are expensive or not?
That's right ... I should not be trying to predict the past with better accuracy. Not the point ... IDK but the annualized 21 days lookback seems to fit best with current IV. I believe the VIX has also a 1M time window (Going forward) ? What's best describes the next 21 days ? The last 21 days ? Everything being equals. I've tried with longer lookback periods and the HV / IV was completely out of whack especially without the exponentially weighted averages. Thought about using VIX and stocks beta. I understand that I should not waste too much time on this.
That is tougher than it seems. I am after that as well, You tend to think that HV and IV could give you a benchmark to measure expensiveness, but then you have to include other factors like events, monetary policies, state of the market, and so on... The task is huge. Maybe we could put something together. But it is going to take a while.
The benefits might not be worth the costs. Maybe there are easier approaches to make enough. A volatility model definitely takes multiples inputs such as sport betting (Maybe). Just arbing IV with IVs (time & space) might be a better approach. Knowing the future realized volatility would greatly help a trader. Can't say the same about HV.