Minimum contrast estimation in diffusion processes

This paper is concerned with the asymptotic theory of estimates of an unknown parameter in continuous-time Markov processes, which are described by non-linear stochastic differential equations. The maximum likelihood estimate and the minimum contrast estimate are investigated. For these estimates strong consistency and asymptotic normality are proved. The unknown parameter is assumed to take its values either in an open or in a compact set of real numbers.

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MINIMUM CONTRAST ESTIMATION FOR DISCRETELY OBSERVED DIFFUSION PROCESSES WITH SMALL DISPERSION PARAMETER

Bulletin of informatics and cybernetics ◽

10.5109/12577 ◽

2004 ◽

Vol 36 ◽

pp. 35-49

Author(s):

Masayuki Uchida

Keyword(s):

Diffusion Processes ◽

Dispersion Parameter ◽

Minimum Contrast ◽

Contrast Estimation ◽

Small Dispersion

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Stochastic continuous-time model reference adaptive systems with decreasing gain

Advances in Applied Probability ◽

10.2307/1427023 ◽

1982 ◽

Vol 14 (4) ◽

pp. 763-788 ◽

Cited By ~ 12

Author(s):

Knut Kristian Aase

Keyword(s):

Continuous Time ◽

Adaptive Systems ◽

Strong Consistency ◽

Diffusion Processes ◽

Recursive Estimation ◽

Continuous Time Model ◽

Time Model ◽

Optimality Properties ◽

Model Reference Adaptive ◽

Model Reference Adaptive Systems

Recursive estimation is considered for parameters of certain continuous stochastic models. Several optimality properties are shown to hold for the resulting recursive estimator, where a stochastic approximation viewpoint is taken when deriving statistical properties, like strong consistency and convergence in distribution. Applications are considered throughout, where for example explosion theory for diffusion processes is used as a modeling guide, in a particular application.

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ASYMPTOTIC THEORY FOR A FACTOR GARCH MODEL

Econometric Theory ◽

10.1017/s0266466608090117 ◽

2009 ◽

Vol 25 (2) ◽

pp. 336-363 ◽

Cited By ~ 27

Author(s):

Christian M. Hafner ◽

Arie Preminger

Keyword(s):

Strong Consistency ◽

Asymptotic Theory ◽

Sufficient Conditions ◽

Order Moment ◽

Model Parameters ◽

Conditional Heteroskedasticity ◽

Volatility Spillover ◽

Likelihood Estimator ◽

Consistency And Asymptotic Normality ◽

Quasi Maximum Likelihood

This paper investigates the asymptotic theory for a factor GARCH (generalized autoregressive conditional heteroskedasticity) model. Sufficient conditions for asymptotic stability and existence of moments are established. These conditions allow for volatility spillover and integrated GARCH. We then show the strong consistency and asymptotic normality of the quasi–maximum likelihood estimator (QMLE) of the model parameters. The results are obtained under the finiteness of the fourth-order moment of the innovations.

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Non-linear time series regression

Journal of Applied Probability ◽

10.1017/s0021900200114664 ◽

1971 ◽

Vol 8 (04) ◽

pp. 767-780 ◽

Cited By ~ 15

Author(s):

E. J. Hannan

Keyword(s):

Time Series ◽

Strong Consistency ◽

Linear Time ◽

Stationary Time Series ◽

Compact Set ◽

Time Series Regression ◽

Non Linear ◽

Consistency And Asymptotic Normality ◽

Image Position ◽

Least Squares Estimates

In Jennrich (1969) the modelis considered, wherex(n) is a sequence of i.i.d. (0,σ2) random variables andz(n;θ) is a continuous but possibly non-linear function ofθ∈Θ, Θ being a compact set inRp. We shall use a second subscript when referring to a particular coordinate ofθ0so thatθ0jis thejth coordinate. Jennrich establishes, under suitable conditions onz(n;θ) andx(n), the strong consistency and asymptotic normality of the least squares estimates ofθ.Our main purpose here is to extend these results to the case wherex(n) is generated by a stationary time series.

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THE GLOBAL WEIGHTED LAD ESTIMATORS FOR FINITE/INFINITE VARIANCE ARMA(p,q) MODELS

Econometric Theory ◽

10.1017/s0266466612000059 ◽

2012 ◽

Vol 28 (5) ◽

pp. 1065-1086 ◽

Cited By ~ 12

Author(s):

Ke Zhu ◽

Shiqing Ling

Keyword(s):

Time Series ◽

Asymptotic Normality ◽

Simulation Study ◽

Strong Consistency ◽

Asymptotic Theory ◽

Infinite Variance ◽

Time Series Models ◽

Absolute Deviation ◽

Consistency And Asymptotic Normality ◽

First Time

This paper investigates the global self-weighted least absolute deviation (SLAD) estimator for finite and infinite variance ARMA(p, q) models. The strong consistency and asymptotic normality of the global SLAD estimator are obtained. A simulation study is carried out to assess the performance of the global SLAD estimators. In this paper the asymptotic theory of the global LAD estimator for finite and infinite variance ARMA(p, q) models is established in the literature for the first time. The technique developed in this paper is not standard and can be used for other time series models.

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Stochastic continuous-time model reference adaptive systems with decreasing gain

Advances in Applied Probability ◽

10.1017/s0001867800020814 ◽

1982 ◽

Vol 14 (04) ◽

pp. 763-788 ◽

Cited By ~ 1

Author(s):

Knut Kristian Aase

Keyword(s):

Continuous Time ◽

Adaptive Systems ◽

Strong Consistency ◽

Diffusion Processes ◽

Recursive Estimation ◽

Continuous Time Model ◽

Time Model ◽

Optimality Properties ◽

Model Reference Adaptive ◽

Model Reference Adaptive Systems

Recursive estimation is considered for parameters of certain continuous stochastic models. Several optimality properties are shown to hold for the resulting recursive estimator, where a stochastic approximation viewpoint is taken when deriving statistical properties, like strong consistency and convergence in distribution. Applications are considered throughout, where for example explosion theory for diffusion processes is used as a modeling guide, in a particular application.

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Non-linear time series regression

Journal of Applied Probability ◽

10.2307/3212240 ◽

1971 ◽

Vol 8 (4) ◽

pp. 767-780 ◽

Cited By ~ 127

Author(s):

E. J. Hannan

Keyword(s):

Time Series ◽

Strong Consistency ◽

Linear Time ◽

Stationary Time Series ◽

Compact Set ◽

Time Series Regression ◽

Non Linear ◽

Consistency And Asymptotic Normality ◽

Image Position ◽

Least Squares Estimates

In Jennrich (1969) the model is considered, where x(n) is a sequence of i.i.d. (0, σ2) random variables and z(n; θ) is a continuous but possibly non-linear function of θ∈ Θ, Θ being a compact set in Rp. We shall use a second subscript when referring to a particular coordinate of θ0 so that θ0j is the jth coordinate. Jennrich establishes, under suitable conditions on z(n; θ) and x(n), the strong consistency and asymptotic normality of the least squares estimates of θ. Our main purpose here is to extend these results to the case where x(n) is generated by a stationary time series.

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Powers: The No-Successor Problem

Journal of the American Philosophical Association ◽

10.1017/apa.2020.13 ◽

2021 ◽

pp. 1-18

Author(s):

JOHN PEMBERTON

Keyword(s):

Continuous Time ◽

Real Numbers ◽

Causal Relations

Abstract This essay considers the implications for the powers metaphysic of the no-successor problem: As there are no successors in the set of real numbers, one state cannot occur just after another in continuous time without there being a gap between the two. I show how the no-successor problem sets challenges for various accounts of the manifestation of powers. For powers that give rise to a manifestation that is a new state, the challenge of no-successors is similar to that faced on Bertrand Russell's analysis by causal relations. Powers whose manifestation is a processes and powers that manifest through time (perhaps by giving rise to changing through time) are challenged differently. To avoid powers appearing enigmatic, these challenges should be addressed, and I point to some possible ways this might be achieved. A prerequisite for addressing these challenges is a careful focus on the nature and timing of the manifesting and manifestation of powers.

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ASYMPTOTIC THEORY FOR ESTIMATING DRIFT PARAMETERS IN THE FRACTIONAL VASICEK MODEL

Econometric Theory ◽

10.1017/s0266466618000051 ◽

2018 ◽

Vol 35 (1) ◽

pp. 198-231 ◽

Cited By ~ 15

Author(s):

Weilin Xiao ◽

Jun Yu

Keyword(s):

Strong Consistency ◽

Asymptotic Theory ◽

Least Squares Method ◽

Estimation Method ◽

Hurst Parameter ◽

Stationary Case ◽

Vasicek Model ◽

Continuous Record ◽

Recurrent Case ◽

Two Parameters

This article develops an asymptotic theory for estimators of two parameters in the drift function in the fractional Vasicek model when a continuous record of observations is available. The fractional Vasicek model with long-range dependence is assumed to be driven by a fractional Brownian motion with the Hurst parameter greater than or equal to one half. It is shown that, when the Hurst parameter is known, the asymptotic theory for the persistence parameter depends critically on its sign, corresponding asymptotically to the stationary case, the explosive case, and the null recurrent case. In all three cases, the least squares method is considered, and strong consistency and the asymptotic distribution are obtained. When the persistence parameter is positive, the estimation method of Hu and Nualart (2010) is also considered.

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