A fast and stable method to compute the likelihood of time invariant state-space models

Casals, José Francisco Forniés; Sotoca, Sonia; Jerez, Miguel

doi:10.1016/s0165-1765(99)00165-2

Cited by 16 publications

(17 citation statements)

References 6 publications

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“…This allows us to apply an idea due to De Jong (1988) The simplification described above can be extended to any general time invariant model, see Casals et al (1999), so it provides a very efficient way to evaluate the minimally-conditioned likelihood for many common representations such as, e.g., VARMAX or structural time series models.…”

Section: State Decomposition (Sd) Algorithmmentioning

confidence: 99%

“…Under these conditions, one can compute the likelihood by applying a KF with null initial conditions to the sample and then correcting the effect of the arbitrary initialization. When the model matrices are time-invariant and there are no missing values in the sample, one can apply the filter simplification proposed by Casals et al (1999) to improve the stability and computational efficiency of the algorithm.…”

Section: Introductionmentioning

confidence: 99%

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Minimally conditioned likelihood for a nonstationary state space model

Casals

Sotoca

Jerez

2014

Mathematics and Computers in Simulation

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Abstract:Computing the gaussian likelihood for a nonstationary state-space model is a difficult problem which has been tackled by the literature using two main strategies: data transformation and diffuse likelihood. The data transformation approach is cumbersome, as it requires nonstandard filtering. On the other hand, in some nontrivial cases the diffuse likelihood value depends on the scale of the diffuse states, so one can obtain different likelihood values corresponding to different observationally equivalent models. In this paper we discuss the properties of the minimally-conditioned likelihood function, as well as two efficient methods to compute its terms with computational advantages for specific models. Three convenient features of the minimally-conditioned likelihood are: (a) it can be computed with standard Kalman filters, (b) it is scale-free, and (c) its values are coherent with those resulting from differencing, being this the most popular approach to deal with nonstationary data.

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Section: State Decomposition (Sd) Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Minimally conditioned likelihood for a nonstationary state space model

Casals

Sotoca

Jerez

2014

Mathematics and Computers in Simulation

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“…However this representation is equally general, see Hannan and Deistler (1988) for a theoretical discussion and Casals et al (1999) for a procedure to compute the parameters in (6a)-(6b) from any SS model.…”

Section: Ss Modelsmentioning

confidence: 99%

“…Innovations form: Transform the model obtained from Step 1) to the corresponding innovations form. Casals et al (1999) provide an efficient procedure to do it. This transformation has a suitable property: if we choose the strong solution to the Riccati equation, then the eigenvalues of (Φ − EH) will lie in or within the unit circle and there will be no moving average roots outside the unit circle in the resulting VARMAX model.…”

Section: Algorithm #1: From General Ss Model To the Equivalent Standamentioning

confidence: 99%

From general state-space to VARMAX models

Casals

García‐Hiernaux

Jerez

2012

Mathematics and Computers in Simulation

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Fixed coefficients State-Space and VARMAX models are equivalent, meaning that they are able to represent the same linear dynamics, being indistinguishable in terms of overall fit. However, each representation can be specifically adequate for certain uses, so it is relevant to be able to choose between them. To this end, we propose two algorithms to go from general State-Space models to VARMAX forms. The first one computes the coefficients of a standard VARMAX model under some assumptions while the second, which is more general, returns the coefficients of a VARMAX echelon. These procedures supplement the results already available in the literature allowing one to obtain the State-Space model matrices corresponding to any VARMAX. The paper also discusses some applications of these procedures by solving several theoretical and practical problems.

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“…Many time series models, including transfer functions, VAR and VARMAX, can be directly written in the steady-state innovations form (Aoki, 1990;Terceiro, 1990). Also, under weak assumptions any model in the general form (1) can be written in the innovations form (2) (Casals et al, 1999, Theorem 1).…”

Section: State-space Modelsmentioning

confidence: 99%

Fast estimation methods for time-series models in state–space form

Hiernaux¹,

Carro²,

Jerez³

2009

Journal of Statistical Computation and Simulation

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We propose two fast, stable and consistent methods to estimate time series models expressed in their equivalent state-space form. They are useful both, to obtain adequate initial conditions for a maximum-likelihood iteration, or to provide final estimates when maximum-likelihood is considered inadequate or costly. The state-space foundation of these procedures implies that they can estimate any linear fixed-coefficients model, such as ARIMA, VARMAX or structural time series models. The computational and finitesample performance of both methods is very good, as a simulation exercise shows.

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A fast and stable method to compute the likelihood of time invariant state-space models

Cited by 16 publications

References 6 publications

Minimally conditioned likelihood for a nonstationary state space model

Minimally conditioned likelihood for a nonstationary state space model

From general state-space to VARMAX models

Fast estimation methods for time-series models in state–space form

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