Asymptotic properties of autoregressive regime-switching models

Olteanu, Mădălina

doi:10.1051/ps/2011153

Cited by 6 publications

(9 citation statements)

References 27 publications

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“…This method requires careful study of all parametric paths, for proving convergence of the parameterized densities toward the true one. Using the work by Olteanu and Rynkiewicz (2012), which has been developed for times series data, we study the asymptotic distribution of the marginal LRT (MLRT), when the number of mixture regimes is overestimated. When the state variables are not i.i.d., then the LRT is diverging even for simple hidden Markov models (see Gassiat and Keribin, 2000).…”

Section: Unknown Number Of Regimesmentioning

confidence: 99%

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Mixtures of Nonlinear Poisson Autoregressions

Doukhan

Fokianos

2020

Journal Time Series Analysis

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We study nonlinear mixtures of integer-valued ARCH type models for count time series data. We investigate the theoretical properties of these processes and we prove ergodicity and stationarity, under minimal assumptions. The model can be generalized by including a GARCH component but we show that such inclusion can be accommodated by an ARCH model whose number of lagged variables tend to infinity. This work complements some previous studies in this area and improves on existing results by developing asymptotic properties of the maximum likelihood estimator. Furthermore, we discuss the estimation problem when the number of mixtures regimes is overestimated and we prove theoretically that proper likelihood penalization enables asymptotic estimation of the true number of mixture regimes. A real data example illustrates the methodology.

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Section: Unknown Number Of Regimesmentioning

confidence: 99%

“…Since (Y t ) t∈ℕ is a -mixing process, we need to check the assumption (B) of Olteanu and Rynkiewicz (2012), Thm. 1 to prove the result.…”

Section: A4 Proof Of Theorem 34mentioning

confidence: 99%

Mixtures of Nonlinear Poisson Autoregressions

Doukhan

Fokianos

2020

Journal Time Series Analysis

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“…It is, however, straightforward to verify that the SI condition is NOT satisfied by the Gaussian mixture models in mean–variance and hence the gmar models in . Olteanu & Rynkiewicz, () established the selection consistency of the bic under some strong assumptions including the mixing probabilities

π_{k}

in having a positive lower bound. This assumption somewhat conflicts with the order‐selection issue.…”

Section: Theoretical Propertiesmentioning

confidence: 99%

Regularization and selection in Gaussian mixture of autoregressive models

2017

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Gaussian mixtures of autoregressive models can be adopted to explain heterogeneous behaviour in mean, volatility, and multi‐modality of the conditional or marginal distributions of time series. One important task is to infer the number of autoregressive regimes and the autoregressive orders. Information‐theoretic criteria such as aic or bic are commonly used for such inference, and typically evaluate each regime/autoregressive combination separately in order to choose an optimal model. However the number of combinations can be so large that such an approach is computationally infeasible. In this article we first develop a computationally efficient regularization method for simultaneous autoregressive‐order and parameter estimation when the number of autoregressive regimes is pre‐determined. We then propose a regularized Bayesian information criterion (rbic) to select the number of regimes. We study asymptotic properties of the proposed methods, and investigate their finite sample performance via simulations. We show that asymptotically the rbic does not underestimate the number of autoregressive regimes, and provide a discussion on the current challenges in investigating whether and under what conditions the rbic provides a consistent estimator of the number of regimes. We finally analyze U.S. gross domestic product growth and unemployment rate data to demonstrate the proposed methods. The Canadian Journal of Statistics 45: 356–374; 2017 © 2017 Statistical Society of Canada

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“…For sake of simplicity we consider identically distributed independent variables, but all the following results can be easily generalized to geometrically mixing stationary sequence of random variables as in [Oltanu M., Rynkiewicz, J. (2012)] or [Gassiat(2002)].…”

Section: Asymptotic Distribution Of the Ssementioning

confidence: 99%

“…Note that, it is also the case for the generalized score function S θ of [Liu and Shao(2003)], in particular in the case of finite mixture models under loss of identifiability. Hopefully, we can show the Donsker property of the set S by an other method which can be applied also to generalized score function in the framework of likelihood ratio test as in [Oltanu M., Rynkiewicz, J. (2012)].…”

Section: Donsker Property For Smentioning

confidence: 99%

Asymptotics for Regression Models Under Loss of Identifiability

Rynkiewicz

2016

Sankhya A

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Abstract. This paper discusses the asymptotic behavior of regression models under general conditions. First, we give a general inequality for the difference of the sum of square errors (SSE) of the estimated regression model and the SSE of the theoretical best regression function in our model. A set of generalized derivative functions is a key tool in deriving such inequality. Under suitable Donsker condition for this set, we give the asymptotic distribution for the difference of SSE. We show how to get this Donsker property for parametric models even if the parameters characterizing the best regression function are not unique. This result is applied to neural networks regression models with redundant hidden units when loss of identifiability occurs.

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Asymptotic properties of autoregressive regime-switching models

Abstract: Abstract. The Mathematics Subject Classification. 62M10, 62F5, 62F12.

Cited by 6 publications

References 27 publications

Mixtures of Nonlinear Poisson Autoregressions

Mixtures of Nonlinear Poisson Autoregressions

Regularization and selection in Gaussian mixture of autoregressive models

Asymptotics for Regression Models Under Loss of Identifiability

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