The root mean squared error (RMSE) is considered by some to be the best measure of how good a variance estimate is. You often see it quoted as:

$RMSE=\sqrt{\frac{1}{n}\sum_{i=1}^n(\hat{\sigma_i} - \sigma_i)^2}$

Where $\hat{\sigma}$ is the estimate of the volatility while $\sigma$ is the actual volatility.

My question is: what is $\sigma$ in this case? Suppose that $\hat{\sigma}$ is the prior day's realized volatility (i.e. $RV = \sum_{t=0}^N r_t$ where $r_t$ is the 5-minute return), is the actual volatility just the next day's absolute return?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.