Adaptive likelihood estimator of conditional variance function

Abstract

Modelling volatility in the form of conditional variance function has been a popular method mainly due to its application in financial risk management. Among others, we distinguish the parametric GARCH models and the nonparametric local polynomial approximation using weighted least squares or gaussian likelihood function. We introduce an alternative likelihood estimate of conditional variance and we show that substitution of the error density with its estimate yields similar asymptotic properties, that is, the proposed estimate is adaptive to the error distribution. Theoretical comparison with existing estimates reveals substantial gains in efficiency, especially if error distribution has fatter tails than Gaussian distribution. Simulated data confirm the theoretical findings while an empirical example demonstrates the gains of the proposed estimate.

Keywords:

• likelihood function
• nonparametric conditional variance
• adaptive estimate
• kernel smoothing

AMS Subject Classification:

• 62G05
• 62G08
• 62G20

Acknowledgements

The author wishes to thank the editor and the two anonymous reviewers for their valuable comments.

Disclosure statement

No potential conflict of interest was reported by the author.