Using recently developed limit theory for power and multipower variation, I
evaluate how well filtering algorithms estimate the integrated variance in
Lévy-driven stochastic volatility models. When data is available at only
moderate intra-daily frequencies, realized variance has yet to converge to
the integrated variance making it valuable to specify a model. Particle
filters are the efficient estimator in non-Gaussian models while the Kalman
filter remains the best linear predictor. If the price process does not
include jumps, filters provide nearly exact estimates when using daily
realized variances calculated at only moderate frequencies. Simulation
experiments suggest that, when the true price process includes
finite-activity or infinite-activity jumps, filtered estimates based upon
realized variance may be quite poor.
Considerable improvement can be made by switching to multipower variation at
which point filters can separate quadratic variation into its components.
These findings should be of practical interest for researchers interested in
building state space models using high frequency financial data.
The slideset from this talk can be downloaded from
here.
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