Hi, I am trying to calculate the forecast standard error for a long-term volatility forecast of a time series.

I am simply using the unbiased estimator of the historical volatility of the time series as my forecast. The historical time series is monthly frequency with approximately 360 data points and I would like to forecast future long-term volatility over the next 5-10 years (60-120 data points).

I believe the standard error of the monthly volatility estimator is \frac{1}{\sqrt{2T}}\sigma (where T is the total number of historical data points, and \sigma is the true historical monthly volatility.

My assumption is that I simply need to multiple this by \sqrt{S} (where S is the number of future data points for the forecast). Is this correct?