Testing whether the underlying continuous-time process follows a diffusion: An infinitesimal operator-based approach |
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Authors: | Bin Chen Zhaogang Song |
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Institution: | 1. Department of Economics, University of Rochester, Rochester, NY, 14627, United States;2. Monetary and Financial Market Analysis Section, Division of Monetary Affairs, Board of Governors of the Federal Reserve System, Mail Stop 165, 20th Street and Constitution Avenue, Washington, DC 20551, United States |
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Abstract: | We develop a nonparametric test to check whether a process can be represented by a stochastic differential equation driven only by a Brownian motion. Our testing procedure utilizes the infinitesimal operator-based martingale characterization combined with a generalized spectral approach. Such a testing procedure is feasible and convenient because the infinitesimal operator of the diffusion process has a closed-form expression. The proposed test is applicable to both univariate and multivariate processes and has an N(0,1) limit distribution under the diffusion hypothesis. Simulation and empirical studies show that the proposed test has reasonable performance in small samples. |
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Keywords: | C12 C14 C22 |
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