Tilted Nonparametric Estimation of Volatility Functions

Peter Phillips and Ke-Li Xu ()

No 1612, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: This paper proposes a novel positive nonparametric estimator of the conditional variance function without reliance on logarithmic or other transformations. The estimator is based on an empirical likelihood modification of conventional local level nonparametric regression applied to squared mean regression residuals. The estimator is shown to be asymptotically equivalent to the local linear estimator in the case of unbounded support but, unlike that estimator, is restricted to be non-negative in finite samples. It is fully adaptive to the unknown conditional mean function. Simulations are conducted to evaluate the finite sample performance of the estimator. Two empirical applications are reported. One uses cross section data and studies the relationship between occupational prestige and income. The other uses time series data on Treasury bill rates to fit the total volatility function in a continuous-time jump diffusion model.

Keywords: Conditional variance function; Empirical likelihood; Conditional heteroskedasticity; Jump diffusion; Local linear estimator; Heteroskedastic nonparametric regression; Volatility (search for similar items in EconPapers)
JEL-codes: C13 C14 C22 (search for similar items in EconPapers)
Pages: 31 pages
Date: 2007-06, Revised 2010-07
New Economics Papers: this item is included in nep-ecm and nep-ets
Note: CFP 1337.
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Published in Journal of Business and Economic Statistics (October 2011), 29(4): 518–528

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