Specification testing in discretized diffusion models: Theory and practice

Gao, Jiti; Casas, Isabel

doi:10.1016/j.jeconom.2008.09.006

Cited by 16 publications

(9 citation statements)

References 23 publications

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“…We target more on the misspecification of the diffusion part and work on a semi‐parametric model where only the diffusion function is parametrized and where the drift part is left unspecified. Generally, one can consider parametric (both the drift and diffusion terms are specified; ), semi‐parametric (either the drift or diffusion is specified; ), or non‐parametric (neither is specified) setting to specify the diffusion models.…”

Section: Stochastic Differential Equation Modelmentioning

confidence: 99%

Test for dispersion constancy in stochastic differential equation models

Lee

Guo

2011

Appl Stoch Models Bus & Ind

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In this paper, we propose a constancy test for volatility in It Oo processes based on discretely sampled data. The test statistic constitutes an integration of the Ljung-Box test statistic and the kurtosis statistic in the Jarque-Bera test. It is shown that under regularity conditions, the proposed test asymptotically follows a chi-square distribution under the null hypothesis of constant volatility. To evaluate the test, empirical sizes and powers were examined through a simulation study. Analysis of real data including ultra-high frequency transaction data and interest rates was also conducted for illustration.

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Section: Stochastic Differential Equation Modelmentioning

confidence: 99%

Test for dispersion constancy in stochastic differential equation models

Lee

Guo

2011

Appl Stoch Models Bus & Ind

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“…1 for asymptotic theory and applicable to both low and high …quency data. In contrast, other procedures using the discretization scheme of a continuous time model only apply to high frequency data and henthfore a little restricted(for example, see Gao and Casas(2008) and Fan and Zhang(2003)). …”

Section: Test Procedures Based On Multivariate Generalized Spectral Dementioning

confidence: 99%

“…3 In recent years, there have been some researches which check the generic properties of a continuous time process and which are naturally nonparmatric, including the tests of markov property(Ait-Sahalia, 1997; Chen and Hong 2008b), of jumps(Ait-Sahalia into two categories: the …rst is focused on the speci…cation testing of either the drift term or the di¤usion term, but not both; the second is concentrated on speci…cation of both drift and di¤usion terms which determine the whole dynamics of the process. Corradi and White(1999), Li(2007), Kristensen(2008a,b) Fan and Zhang(2003), and Gao and Casas(2008), for example, belong to the …rst category. The test I will propose belongs to the second category.…”

Section: Introductionmentioning

confidence: 99%

A martingale approach for testing diffusion models based on infinitesimal operator

Song¹

2011

Journal of Econometrics

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“…Others focus on the diffusion function only (e.g., Li (2007), Corradi and White (1999)). For those who test the drift function in a semiparametric setup (Kristensen (2008a), Gao and Casas (2008)), a parametric form of the diffusion function is assumed and thus these tests are subject to misspecification of the diffusion function. Kristensen (2008b) and Bandi and Phillips (2007) suggest nonparametric methods which could be used to test the drift specification but they do not pursue it.…”

Section: Introductionmentioning

confidence: 99%

Is the Drift of the Interest Rate Process Linear? A New Approach and Evidence

Hong,

Lee,

Song

2009

SSRN Journal

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Continuous-time models are important for investigating interest rate term structure and pricing fixed income derivatives. Economic theory often provides little guidance on the choice of the form of continuous-time models, and existing one-factor and multi-factor continuous-time interest rate models often assume a linear drift, among other things. Some studies, based smoothed nonparametric kernel estimation, suggest that the drift of the interest rate process is nonlinear, particularly at high interest rate levels. However, this has been doubted as an artifact of smoothed nonparametric estimation in comparison with highly persistent interest rate data. Whether the drift of the interest rate process is linear or nonlinear remains an unsolved issue in the literature. In this paper, we take a new approach to re-address this important issue by first considering a general continuous-time regression for the interest rate process and then testing it via a generalized spectral derivative approach of Hong and Lee (2005) which is tailored to the continuous-time setting. Our method avoids the undesirable features of smoothed nonparametric estimation for highly persistent financial time series data. Unlike the existing approaches to testing linearity in drift, we allow for stochastic volatility and jumps, which have been well documented for the interest rate process in the literature. An empirically realistic simulation study shows that the generalized spectral derivative provides reliable inference in finite samples for continuous-time models. Based on the widely used 7-day Eurodollar rates, we document strong evidence that the interest rate process has a nonlinear drift and such evidence is robust to the presence of level effect, stochastic volatility, jumps, and different methods of drift parameter estimation. We further document that such popular nonlinear drift models as Aït-Sahalia's (1996a) nonlinear drift model and Ahn and Gao's (1991) Inverse-Feller drift model can capture some nonlinear drift dynamics of the short rate, and Aït-Sahalia's nonlinear model outperforms Ahn and Gao's nonlinear drift model due to its flexibility to capture asymmetric mean-reverting feature. However, they are still firmly rejected, indicating room for further improving the modelling of the drift function of the interest rate.

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Specification testing in discretized diffusion models: Theory and practice

Cited by 16 publications

References 23 publications

Test for dispersion constancy in stochastic differential equation models

Test for dispersion constancy in stochastic differential equation models

A martingale approach for testing diffusion models based on infinitesimal operator

Is the Drift of the Interest Rate Process Linear? A New Approach and Evidence

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