NONPARAMETRIC ESTIMATION OF VOLATILITY FUNCTIONS: THE LOCAL EXPONENTIAL ESTIMATOR

By Flávio Augusto Ziegelmann. Econometric Theory, 2002

70 citations recorded by the source corpus.

Kernel smoothing techniques free the traditional parametric estimators of volatility from the constraints related to their specific models. In this paper the nonparametric local exponential estimator is applied to estimate conditional volatility functions, ensuring its nonnegativity. Its asymptotic properties are established and compared with those for the local linear estimator. It theoretically enables us to determine when the exponential is expected to be superior to the linear estimator. A very strong and novel result is achieved: the exponential estimator is asymptotically fully adaptive to unknown conditional mean functions. Also, our simulation study shows superior performance of the exponential estimator.

Subfields: Finance, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/099d117927ca0efb634f478b9a8122aa039415cb

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Citations in the corpus

Semi-Parametric Modelling of Correlation Dynamics (2005, methodology): “Of course, other nonparametric estimators such as local polynomials could be used as well, see e.g. Fan and Gijbels (1996), Härdle, Lütkepohl and Chen (1997) and Pagan and Ullah (1999) for reviews, and Fan and Yao (1998) and Ziegelmann (2002) for applications to volatility modelling.”
Tilted Nonparametric Estimation of Volatility Functions With Empirical Applications (2010, unknown): “Ziegelmann (2002) recently obtained a nonnegative nonparametric volatility estimator by fitting an exponential function locally (rather than a linear function as in the local linear estimator) within the general locally parametric nonparametric framework of Hjort and Jones (1996) (see also Yu and…”