Tilted Nonparametric Estimation of Volatility Functions with Empirical Applications
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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.
Phillips, Peter C.B. and Xu, Ke-Li, "Tilted Nonparametric Estimation of Volatility Functions with Empirical Applications" (2007). Cowles Foundation Discussion Papers. 1908.