Parameter estimation and bias correction for diffusion processes

Tang, Cheng Yong; Chen, Song Xi

doi:10.1016/j.jeconom.2008.11.001

Cited by 132 publications

(170 citation statements)

References 39 publications

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“…This result echoes the conjecture of Hurwicz (1950) about the bias in the autoregressive (AR) estimate in the discrete time AR(1) model. Second, we show that the bias formula, which mimics that of Marriott and Pope (1954) and Kendall (1954) for the discrete time model and that of Tang and Chen (2009) for continuous time models, is essentially linear in coe¢ cient. Consequently, the bias predicted by the formula does not disappear in the unit root case.…”

Section: Introductionmentioning

confidence: 71%

“…The simpler expression mimics the bias formula derived by Marriott and Pope (1954) for the discrete time AR model and corresponds to the bias formula derived independently by Tang and Chen (2009) for the same model but with unknown mean. The complicated one includes an additional term from the exact evaluation of the Cesaro sums.…”

Section: Discussionmentioning

confidence: 88%

“…The indirect inference method was originally proposed by Smith (1993) and Gouriéroux, Monfort and Renault (1993) and subsequently applied to reduce the bias in the mean reversion estimator by Phillips and Yu (2009a). The bootstrap method was recently proposed to reduce the bias in the mean reversion estimator by Tang and Chen (2009). All three methods are simulation-based, and hence computationally demanding.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Bias in the estimation of the mean reversion parameter in continuous time models

2012

Journal of Econometrics

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Section: Introductionmentioning

confidence: 71%

Section: Discussionmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Bias in the estimation of the mean reversion parameter in continuous time models

2012

Journal of Econometrics

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“…This upward bias in the mean-reversion parameter estimate is well established (see Tang and Chen, 2009;Wang, Phillips, and Yu, 2011). In particular, for values of κ close to zero, i.e., a near unit root situation typical of many financial time series, a bias correction may be preferable (Yu, 2012).…”

Section: Simulation Results: Monthly and Quarterly Datamentioning

confidence: 89%

Estimating dynamic equilibrium models using mixed frequency macro and financial data

Christensen

Posch

Wel

2016

Journal of Econometrics

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. We provide a framework for inference in dynamic equilibrium models including financial market data at daily frequency, along with macro series at standard lower frequency. Our formulation of the macro-finance model in continuous-time conveniently accounts for the difference in observation frequency. We suggest the use of martingale estimating functions (MEF) to infer the structural parameters of the model directly through a nonlinear optimization scheme. This method is compared to regression-based methods and the general method of moments (GMM). We illustrate our approaches by estimating the AK-Vasicek model with mean-reverting interest rates. We provide Monte Carlo evidence on the small sample behavior of the estimators and report empirical estimates using 30 years of U.S. macro and financial data. Terms of use: Documents inJEL-Code: C130, E320, O400.

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“…If δt is not small, the estimators in (3.4) are biased. Therefore, let us also consider the more exact maximum likelihood (ML) estimatorsθ ex := (μ ex ,θ ex ,σ ex ), as discussed in, e.g, [17]. By omitting the assumption δt → 0 and using the Markovian nature of the OU process, these exact ML estimators follow from maximizing the log likelihood function:…”

Section: Unconditional Parametersmentioning

confidence: 99%

Data-driven stochastic representations of unresolved features in multiscale models

Verheul

Crommelin

2016

Communications in Mathematical Sciences

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Abstract. In this study we investigate how to use sample data, generated by a fully resolved multiscale model, to construct stochastic representations of unresolved scales in reduced models. We explore three methods to model these stochastic representations. They employ empirical distributions, conditional Markov chains and conditioned Ornstein-Uhlenbeck processes, respectively. The Kac-Zwanzig heat bath model is used as a prototype model to illustrate the methods. We demonstrate that all tested strategies reproduce the dynamics of the resolved model variables accurately. Furthermore, we show that the computational cost of the reduced model is several orders of magnitude lower than that of the fully resolved model.

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Parameter estimation and bias correction for diffusion processes

Cited by 132 publications

References 39 publications

Bias in the estimation of the mean reversion parameter in continuous time models

Bias in the estimation of the mean reversion parameter in continuous time models

Estimating dynamic equilibrium models using mixed frequency macro and financial data

Data-driven stochastic representations of unresolved features in multiscale models

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