Estimating Continuous-Time Models on the Basis of Discrete Data via an Exact Discrete Analog

McCrorie, J. Roderick

doi:10.1017/s0266466608090452

Cited by 17 publications

(11 citation statements)

References 89 publications

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“…Due to Fasen-Hartmann and Scholz [21, Theorem 3.1] a canonical form for cointegrated state space processes already exists and can be used to construct a model class satisfying Assumption C and Assumption D. Further details are presented in Fasen-Hartmann and Scholz [20]. Moreover, criteria to overcome the aliasing effect (see Blevins [10], Hansen and Sargent [25], McCrorie [40,41], Phillips [42,43], Schlemm and Stelzer [51]) are given there.…”

Section: Identifiabilitymentioning

confidence: 99%

Quasi-maximum likelihood estimation for cointegrated continuous-time linear state space models observed at low frequencies

Fasen‐Hartmann¹,

Scholz²

2019

Electron. J. Statist.

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In this paper, we investigate quasi-maximum likelihood (QML) estimation for the parameters of a cointegrated solution of a continuous-time linear state space model observed at discrete time points. The class of cointegrated solutions of continuous-time linear state space models is equivalent to the class of cointegrated continuous-time ARMA (MCARMA) processes. As a start, some pseudo-innovations are constructed to be able to define a QML-function. Moreover, the parameter vector is divided appropriately in long-run and short-run parameters using a representation for cointegrated solutions of continuous-time linear state space models as a sum of a Lévy process plus a stationary solution of a linear state space model. Then, we establish the consistency of our estimator in three steps. First, we show the consistency for the QML estimator of the long-run parameters. In the next step, we calculate its consistency rate. Finally, we use these results to prove the consistency for the QML estimator of the short-run parameters. After all, we derive the limiting distributions of the estimators. The long-run parameters are asymptotically mixed normally distributed, whereas the short-run parameters are asymptotically normally distributed. The performance of the QML estimator is demonstrated by a simulation study.

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Section: Identifiabilitymentioning

confidence: 99%

Quasi-maximum likelihood estimation for cointegrated continuous-time linear state space models observed at low frequencies

Fasen‐Hartmann¹,

Scholz²

2019

Electron. J. Statist.

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“…Bergstrom, Nowman and Wymer (1992) and Bergstrom and Nowman (2007) use prior bounds on the parameters as a means of achieving identification, in the way researchers do for large-scale structural VAR models today. The results of Hansen and Sargent (1983) show that without importing a priori restrictions beyond the problem in hand, identification can only be local; see Appendix 1 of McCrorie (2009) for some examples. In practice, one has jointly to solve the aliasing identification problem and the classical identification problem of avoiding observational equivalence through model and estimator choice.…”

Section: Identificationmentioning

confidence: 99%

Continuous Time Modelling Based on an Exact Discrete Time Representation

Chambers

McCrorie

Thornton

2018

Continuous Time Modeling in the Behavioral and Related Sciences

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This chapter provides a survey of methods of continuous time modelling based on an exact discrete time representation. It begins by highlighting the techniques involved with the derivation of an exact discrete time representation of an underlying continuous time model, providing specific details for a second-order linear system of stochastic differential equations. Issues of parameter identification, Granger causality, nonstationarity, and mixed frequency data are addressed, all being important considerations in applications in economics and other disciplines. Although the focus is on Gaussian estimation of the exact discrete time model, alternative time domain (state space) and frequency domain approaches are also discussed. Computational issues are explored and two new empirical applications are included along with a discussion of applications in the field of macroeconometric modelling.

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“…We briefly outline some other known sufficient conditions for identification below. In the interest of brevity, we refer readers interested in estimation methods to recent surveys by Sørensen (2004), Fan (2005), Aït-Sahalia (2007), Bandi and Phillips (2009), McCrorie (2009), and Phillips and Yu (2009.…”

Section: Identification and Aliasing In Continuous Time Modelsmentioning

confidence: 99%

Identifying Restrictions for Finite Parameter Continuous Time Models With Discrete Time Data

Blevins

2015

Econom. Theory

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This paper revisits the question of parameter identification when a linear continuous time model is sampled only at equispaced points in time. Following the framework and assumptions of Phillips (1973), we consider models characterized by first-order, linear systems of stochastic differential equations and use a priori restrictions on the model parameters as identifying restrictions. A practical rank condition is derived to test whether any particular collection of at least n/2 general linear restrictions on the parameter matrix is sufficient for identification. We then consider extensions to incorporate prior restrictions on the covariance matrix of the disturbances, to identify the covariance matrix itself, and to address identification in models with cointegration. IDENTIFICATION AND ALIASING IN CONTINUOUS TIME MODELSThis paper develops identification results for first-order, linear systems of stochastic differential equations of the formin the case where observations of y(t) are only available at discrete, equispaced points in time separated by intervals of length h. Here, y(t) is a stationary n × 1 random vector, A is a parameter matrix whose elements are real numbers, and ζ(dt) is a vector of white noise innovations with covariance matrix dt. The exact discrete time process y t = y(th) corresponding to the continuous time system in (1) is the vector autoregressive (VAR) process

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Estimating Continuous-Time Models on the Basis of Discrete Data via an Exact Discrete Analog

Cited by 17 publications

References 89 publications

Quasi-maximum likelihood estimation for cointegrated continuous-time linear state space models observed at low frequencies

Quasi-maximum likelihood estimation for cointegrated continuous-time linear state space models observed at low frequencies

Continuous Time Modelling Based on an Exact Discrete Time Representation

Identifying Restrictions for Finite Parameter Continuous Time Models With Discrete Time Data

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