Intraday volatility prediction and estimation

GARCH has been shown to be a reasonable estimator of variance for daily or longer period returns. Some have adapted GARCH to use intraday returns to improve daily returns. GARCH does very poorly in estimating intra-day variance, however.

The GARCH model is based on the empirical observation that there is strong autocorrelation in the square of returns for lower frequencies (such as daily). This can be easily seen by observing clustering and "smooth-ish" decay of squared returns on main daily series.

Intra-day squared returns, however, have many jumps, with little in the way of autocorrelated decay pattern. Here is a sample of squared returns for EUR/USD. There are many spikes followed by immediate drops in return (as opposed to smoother decay). There does appear to be a longer-term pattern, though, allowing for a model.

With expanded processing power and general access to tick data, research has begun to focus on intra-day variance estimation. In particular, expressing variance in terms of price duration has become an emergent theme. Andersen, Dobrev, and Schaumburg are among a growing community developing this in a new direction.

At this point have disqualified GARCH as a useful measure for my work, but am investigating a formulation of a duration based measure.