Unfortunately, financial markets are not like physical measures, where you know the "true" value of a physical variable but you just access to it thanks to noised sensors. We do not know the "true" volatility, just because there is not such one value...

In statistics you have two kinds of modelling procedures:

• the ones dedicated to estimate the unknown values of parameters of a known structural model. Here you have the usual "confidence intervals" approach.

• the ones for simultaneously inferring from data the shape (i.e. "class") of the model and its parameters. Here you have the usual issues coming from "overfitting", and the usual approaches are "cross validation", "regularization - penalization", "Vapnik-Chervonenkis dimensions", etc.

In finance you are very often in the second case, and especially for volatility: for instance its value is not the same if your underlying model includes jumps or not... what is the "true" one? Moreover (as I commented) at your time scale (1 min) you face the microstructure noise, see my answer here for a brief.

But come back to my generic answer on "knowledge discovery" via statistical modelling: what can you test if you believe you have a good new estimation procedure?

You can test your prediction capability of course, but you will have to face a lot of ugly features of intraday volatility:

• it is not iid, even not ergodic, since it has a seasonality (see Market Microstructure in Practice for intraday seasonalities).

• once you removed the seasonality, it is clustered (we cannot ignore it since Robert Engle's Nobel prize).

• moreover, it is path dependent (I mean, even inside a volatility cluster as defined by Engle)...

Thus if you wan to challenge existing estimation procedure, you will have to remove the first two features and demonstrate on the deseasonalized data, cluster by cluster. Of course you could alternatively try to perform a change of state space to estimate something else than volatility. Like use it to estimate the seasonality or the switching probabilities themselves...

Unfortunately, financial markets are not like physical measures, where you know the "true" value of a physical variable but you just access to it thanks to noised sensors. We do not know the "true" volatility, just because there is not such one value...

In statistics you have two kinds of modelling procedures:

• the ones dedicated to estimate the unknown values of parameters of a known structural model. Here you have the usual "confidence intervals" approach.

• the ones for simultaneously inferring from data the shape (i.e. "class") of the model and its parameters. Here you have the usual issues coming from "overfitting", and the usual approaches are "cross validation", "regularization - penalization", "Vapnik-Chervonenkis dimensions", etc.

In finance you are very often in the second case, and especially for volatility: for instance its value is not the same if your underlying model includes jumps or not... what is the "true" one? Moreover (as I commented) at your time scale (1 min) you face the microstructure noise, see my answer here for a brief.

But come back to my generic answer on "knowledge discovery" via statistical modelling: what can you test if you believe you have a good new estimation procedure?

You can test your prediction capability of course, but you will have to face a lot of ugly features of intraday volatility:

• it is not iid, even not ergodic, since it has a seasonality (see Market Microstructure in Practice for intraday seasonalities).

• once you removed the seasonality, it is clustered (we cannot ignore it since Robert Engle's Nobel prize).

• moreover, it is path dependent (I mean, even inside a volatility cluster as defined by Engle)...

Thus if you wan to challenge existing estimation procedure, you will have to remove the first two features and demonstrate on the deseasonalized data, cluster by cluster. Of course you could alternatively try to perform a change of state space to estimate something else than volatility. Like use it to estimate the seasonality or the switching probabilities themselves...