Testing the Parametric Specification of the Diffusion Function in a Diffusion Process

Abstract

A new consistent test is proposed for the parametric specification of the diffusion function in a diffusion process without any restrictions on the functional form of the drift function. The data are assumed to be sampled discretely in a time interval that can be fixed or lengthened to infinity. The test statistic is shown to follow an asymptotic normal distribution under the null hypothesis that the parametric diffusion function is correctly specified. Monte Carlo simulations are conducted to examine the finite-sample performance of the test, revealing that the test has good size and power.

Specification testing in discretized diffusion models: Theory and practice

“…As a result, such nonparametric estimators of the drift and diffusion functions can only be consistent when ∆ → 0. Naturally, the condition of ∆ → 0 is certainly needed when tests are constructed based on (2.3) (see Li 2007).…”

“…In the field of continuous-time model specification, some closely related studies include Aït-Sahalia (1996a), who proposes a simple methodology for testing whether the marginal density function of {r t } belongs to a parametric family of density functions; Corradi and White (1999), who establish an asymptotically normal test for the diffusion function; Fan and Zhang (2003), who propose a simultaneous test procedure for the specification of both the drift and diffusion functions; Gao and King (2004), who propose an improved test for a parametric specification of the marginal density function; Kristensen (2004), in which a semiparametric diffusion model is considered and tested; Corradi and Swanson (2005), who propose using a bootstrap specification test; Hong and Li (2005), who establish an asymptotically consistent test for specifying the transitional density function of {r t } parametrically; Arapis and Gao (2006), who consider testing for a parametric specification of the drift function; Chen, Gao and Tang (2008), who develop an empirical likelihood method to establish an adaptive test for the parametric specification of the transitional density function; and Li (2007), who discusses a nonparametric test for the parametric specification of the diffusion function in a diffusion process.…”

Consistent nonparametric specification tests for stochastic volatility models based on the return distribution

“…The stochastic volatility model we consider here is essentially a (partially observed) two dimensional diffusion process, so our test is related to the vast literature of nonparametric test for diffusion models, such as Aït-Sahalia (1996), Hong and Li (2005), Corradi and Swanson (2005), Li (2007), Chen et al (2008), , Kristensen (2011) and Aït-Sahalia and Park (2012), among others. However, the unobservability of the volatility process in Model (1) makes the aforementioned research not applicable.…”

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

“…In fact, the author applies the results of the paper to nonparametric speci…cation testing of Markov processes (Kanaya, 2014). They may be used for deriving asymptotic distributions results in speci…cation testing problems of volatility components as found in Li (2007) and Corradi and Distaso (2010), as well as in derivative-security pricing problems as in Aït-Sahalia (1996a) and Kristensen (2008).…”