A martingale approach for testing diffusion models based on infinitesimal operator

Song, Zhaogang

doi:10.1016/j.jeconom.2010.12.005

Cited by 9 publications

(2 citation statements)

References 67 publications

(62 reference statements)

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“…Our approach is based on well-known empirical process theory. Specification tests for continuous-time models based on stochastic or empirical processes have been proposed in many previous studies, such as Dette & von Lieres und Wilkau (2003), Dette & Podolskij (2008), Podolskij & Ziggel (2008), Kutoyants (2010), Negri & Nishiyama (2009, 2011, Monsalve-Cobis, González-Manteiga & Febrero-Bande (2011), and Chen, Zheng & Pan (2015). 1 However, most of those tests treat the drift, volatility and jump term separately; few consider joint specification testing for both the drift and volatility functions in a diffusion model.…”

Section: Introductionmentioning

confidence: 99%

“…In addition, most of the joint tests of diffusion models use nonparametric or semiparametric smoothing techniques, which do not account for the different convergence rates of parameter estimators. Some examples of this can be found in Aït-Sahalia (1996), Gallant & Tauchen (1996), Gao & King (2004), Hong & Li (2005), Chen, Gao & Tang (2008), Aït-Sahalia, Fan & Peng (2009), Chen & Hong (2010), Chen & Gao (2011), Song (2011), andAït-Sahalia &Park (2012). Another disadvantage of these tests is that they require a smoothing parameter, and thus the results may be affected by the parameter selection.…”

Section: Introductionmentioning

confidence: 99%

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Empirical‐process‐based specification tests for diffusion models

2022

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We develop two joint tests for the parametric drift and volatility functions of a diffusion model based on empirical processes. One key feature of our joint tests is that they account for different convergence rates of parameter estimators. The tests are of classical Kolmogorov–Smirnov and Cramér–von Mises types, and are asymptotically distribution free. The proposed tests have nontrivial power against a class of local alternatives with different convergence rates for the drift and volatility terms. Monte Carlo simulations show that the tests perform quite well in finite samples and outperform the nonparametric test of Hong and Li. The new tests are applied to EUR/USD exchange rate data and generate some interesting empirical findings that are consistent with our theoretical results and simulation studies.

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