大阪大学　数理・データ科学教育研究センター
Center for Mathematical Modeling and Data Science,Osaka University

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

金谷信（ウィスコンシン大学マディソン校経済学部）

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4. Non-Parametric Specification Testing for Continuous-Time Markov Processes: Do the Processes Follow Diffusions?

大阪大学 金融・保険セミナーシリーズ 第14回

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

金谷信（ウィスコンシン大学マディソン校経済学部）

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.