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	SHIN KANAYA Ph.D. & Job Market Candidate at Department of Economics University of Wisconsin-Madison 1180 Observatory Drive Madison, WI 53706 Phone: 608-262-4389 E-mail: skanaya@wisc.edu
Summary List Curriculum Vitae Dissertation Abstract Teaching (Econ 710 Spring 2006)	Fields: Econometric Theory, Financial Econometrics, Empirical Finance & Microeconometrics

Job Market Paper

"Non-Parametric Specification Testing for Continuous-Time Markov Processes: Do the Processes Follow Diffusions?"
[pdf]

Abstract I propose a new non-parametric testing procedure to determine whether or not an underlying continuous-time process is a diffusion. While many papers in economics and finance presuppose that the dynamics of economic variables are described by diffusion processes, an empirical validation of the diffusion hypothesis is rarely found. I develop a new theorem which non-parametrically and fully identifies diffusion processes within a class of univariate stationary Markov processes through their infinitesimal generators - functional operators computed via derivatives of the conditional expectations with respect to time. I construct test statistics based on this theorem and derive their asymptotic distributions. I also propose a simulation-based technique to approximate the asymptotic distributions, since the distributions of the original statistics depend upon a large number of unknown parameters and functions. Monte-Carlo simulations are conducted to study the finite-sample size and power properties of the test. I apply the proposed method to short-term interest rates and foreign exchange rates to examine the validity of the diffusion hypothesis.

Work in Progress

"Semi-Parametric Maximum-Likelihood Estimation for Diffusion Processes"

Abstract In this paper, I consider a new semi-parametric estimator of ergodic diffusion processes, where the drift function is specified parametrically and the diffusion function is unknown. I propose a two-stage estimation strategy. In the first stage, the diffusion function is estimated by the nonparametric kernel method. New uniform convergence results of the nonparametric estimators, which are developed in an accompanying paper, are used to derive the asymptotic properties of the parametric drift function estimator in the second stage, where a semi-parametric log-likelihood is constructed by means of the Girsanov theorem. Given a discretely recorded sample with the infill and long-span assumptions, I show that the proposed estimator is √T-consistent with an asymptotic normal distribution under fairly weak conditions, and that its asymptotic variance attains the Cramer-Rao bound. A simulation study examines the finite-sample properties of the proposed estimator.

"Uniform Convergence of Kernel-Based Nonparametric Estimators for Diffusion Processes:
A Damping Function Approach"

Abstract This paper proposes new nonparametric kernel-based estimators for diffusion processes, introducing a new technical device, called a damping function. This device allows me to derive sharp uniform convergence rates (over the infinite interval) of the estimator with minimal requirements on the process: the existence of the moments or the boundedness of relevant functions is unnecessary. The proofs proceed by exploiting the mixing and path-continuity properties of the process and using empirical process theory. The obtained results are useful for the non/semi-parametric estimation/testing of diffusion processes.

"Estimation of Stochastic Volatility Models by Nonparametric Filtering" (with D. Kristensen)

Abstract A new estimation method of stochastic volatility models is proposed based on the nonparametric filter of the instantaneous volatility process of Kristensen (2006). We propose to use standard estimation methods for fully observed diffusion processes but with the filtered volatility process replacing the latent process. The proposed estimators will carry biases due to the use of the filtered volatility instead of the actual volatility, but under regularity conditions this vanishes asymptotically and our estimators inherit the asymptotic properties of the infeasible estimators based on observations of the volatility process. Our estimation strategy is applicable both to parametric and nonparametric stochastic volatility models, and we give theoretical results for both. A simulation study examines the finite-sample properties of the proposed estimators.

References

Professor Bruce E. Hansen (Primary Advisor) Department of Economics University of Wisconsin-Madison Madison, WI 53706 Phone: 608-263-3880 Fax: 608-263-3876 Email: bhansen@ssc.wisc.edu	Professor Dennis Kristensen Economics Department Columbia University New York, NY 10027 Phone: 212-854-5489 Fax: 212-854-8059 Email: dk2313@columbia.edu
Professor Jack R. Porter Department of Economics University of Wisconsin-Madison Madison, WI 53706 Phone: 608-263-3870 Fax: 608-262-2033 Email: jrporter@ssc.wisc.edu

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Modification: December 4, 2007