Whittle estimation for continuous-time stationary state space models with finite second moments

Fasen‐Hartmann, Vicky; Mayer, Celeste

doi:10.1007/s10463-021-00802-6

Cited by 4 publications

(2 citation statements)

References 39 publications

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“…The basic ideas of such an approach are given in Bardet et al (2008), Dahlhaus (1988) and Dahlhaus and Polonik (2002). Fasen-Hartmann and Mayer (2021a) prove that the Whittle estimator for state space models with finite fourth moment is a consistent and asymptotically normally distributed estimator without using the empirical spectral process. However, their Whittle function is defined by a sum which approximates the integral.…”

Section: Assumption Bmentioning

confidence: 99%

Empirical spectral processes for stationary state space processes

Fasen‐Hartmann¹,

Mayer²

2022

Preprint

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In this paper, we consider function-indexed normalized weighted integrated periodograms for equidistantly sampled multivariate continuous-time state space models which are multivariate continuous-time ARMA processes. Thereby, the sampling distance is fixed and the driving Lévy process has at least a finite fourth moment. Under different assumptions on the function space and the moments of the driving Lévy process we derive a central limit theorem for the function-indexed normalized weighted integrated periodogram. Either the assumption on the function space or the assumption on the existence of moments of the Lévy process is weaker. Furthermore, we show the weak convergence in both the space of continuous functions and in the dual space to a Gaussian process and give an explicit representation of the covariance function. The results can be used to derive the asymptotic behavior of the Whittle estimator and to construct goodness-of-fit test statistics as the Grenander-Rosenblatt statistic and the Cramér-von Mises statistic. We present the exact limit distributions of both statistics and show their performance through a simulation study.

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Section: Assumption Bmentioning

confidence: 99%

Empirical spectral processes for stationary state space processes

Fasen‐Hartmann¹,

Mayer²

2022

Preprint

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“…V , e.g., by quasi maximumlikelihood estimation as in Schlemm and Stelzer (2012a) or Whittle estimation as in Fasen-Hartmann and Mayer (2022), yielding the parameter estimators A 1 , . .…”

Section: Andmentioning

confidence: 99%

Cointegrated continuous-time linear state-space and MCARMA models

Fasen‐Hartmann

Scholz²

2019

Stochastics

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In this paper we define and characterize cointegrated solutions of continuous-time linear state-space models. A main result is that a cointegrated solution of a continuous-time linear state-space model can be represented as a sum of a Lévy process and a stationary solution of a linear state-space model. Moreover, we prove that the class of cointegrated multivariate Lévy-driven autoregressive moving-average (MCARMA) processes, the continuous-time analogues of the classical vector ARMA processes, is equivalent to the class of cointegrated solutions of continuous-time linear state space models. Necessary conditions for MCARMA processes to be cointegrated are given as well extending the results of Comte [11] for MCAR processes. The conditions depend only on the autoregressive polynomial if we have a minimal model. Finally, we investigate cointegrated continuous-time linear state-space models observed on a discrete time-grid and calculate their linear innovations. Based on the representation of the linear innovations we derive an error correction form. The error correction form uses an infinite linear filter in contrast to the finite linear filter for VAR models.

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A note on estimation of α-stable CARMA processes sampled at low frequencies

Fasen‐Hartmann¹,

Mayer²

2022

Journal of Statistical Planning and Inference

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Whittle estimation for continuous-time stationary state space models with finite second moments

Cited by 4 publications

References 39 publications

Empirical spectral processes for stationary state space processes

Empirical spectral processes for stationary state space processes

Cointegrated continuous-time linear state-space and MCARMA models

A note on estimation of α-stable CARMA processes sampled at low frequencies

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