What is "Observed realized measure"?

Question

I am working with a Realized GARCH model. I have am having some trouble understanding a concept:

Paper: Realized GARCH: A Complete Model of Returns and Realized Measures of Volatility, Hansen & Haung

"A key feature of the Realized GARCH framework is a measurement equation that relates the observed realized measure to latent volatility".

Or from the rugarch-vignette (R), page 14:

"Unlike the naive augmentation of GARCH processes by a realized measures, the realGARCH model relates the observed realized measure to the latent volatility..."

I am confused to exactly does "observed realized measure" mean?

Answer 1

I presume, that you are familiar with the subject and need clarification only upon the expression in question.

I also preume that you know what volatility is. Volatility is generally unobserved in GARCH models, i.e. it can not be measured directly in which sence it is latent volatility. Usual GARCH model derives an estimate for this latent volatility from squared errors.

In this paper the way to incorporate a different estimatior of the latent volatility is sujested. As it is not entirely accurate to call it an estimator, that refer to it as measure. They consider measures from the family that is commonly referred to as realized measures of volatility, e.g. realized varianse and bipower variance. So we have realized measure to latent volatility. However we can not observe a random variable, which this realized measure actually. Instead we observe one realization of it - an observation. So the numbers that we got from using these procedure are called "observed realized measure to latent variation".

If my explanations were unclear or something else needs to be explained please specify it.