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Testing for observation-dependent regime switching in mixture autoregressive models

Mika Meitz, Pentti Saikkonen

arXiv 10 Nov 2017 · Econometrics · publishedJournal of Econometrics (2020) · 2 citations (OpenAlex)

arXiv:1711.03959 · PDF · DOI · OpenAlex · Extracted main text

Abstract

Testing for regime switching when the regime switching probabilities are specified either as constants (`mixture models') or are governed by a finite-state Markov chain (`Markov switching models') are long-standing problems that have also attracted recent interest. This paper considers testing for regime switching when the regime switching probabilities are time-varying and depend on observed data (`observation-dependent regime switching'). Specifically, we consider the likelihood ratio test for observation-dependent regime switching in mixture autoregressive models. The testing problem is highly nonstandard, involving unidentified nuisance parameters under the null, parameters on the boundary, singular information matrices, and higher-order approximations of the log-likelihood. We derive the asymptotic null distribution of the likelihood ratio test statistic in a general mixture autoregressive setting using high-level conditions that allow for various forms of dependence of the regime switching probabilities on past observations, and we illustrate the theory using two particular mixture autoregressive models. The likelihood ratio test has a nonstandard asymptotic distribution that can easily be simulated, and Monte Carlo studies show the test to have satisfactory finite sample size and power properties.

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43
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Kasahara, H., Shimotsu, K (2015) Testing the number of components in normal mixture regression models1.000154100%
2Andrews, D. W (2001) Testing when a parameter is on the boundary of the maintained hypothesis1.000133100%
3Wong, C. S., Li, W. K (2001) On a logistic mixture autoregressive model1.00084100%
4Jeffries, N. O (1998) Logistic mixtures of generalized linear model times series1.00053100%
5Wong, C. S., Li, W. K (2000) On a mixture autoregressive model1.00053100%
6Zhu, H., Zhang, H (2006) Asymptotics for estimation and testing procedures under loss of identifiability0.97112492%
7Andrews, D. W (1999) Estimation when a parameter is on a boundary0.96911391%
8Kasahara, H., Shimotsu, K (2012) Testing the number of components in finite mixture models, unpublished working paper0.874102100%
9Kalliovirta, L., Meitz, M., Saikkonen, P (2015) A Gaussian mixture autoregressive model for univariate time series self0.85113562%
10Hansen, B. E (1996) Inference when a nuisance parameter is not identified under the null hypothesis0.81142100%

Showing the top 10 of 43 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1A mixture autoregressive model based on Student's $t$–distribution0.40511
2Markov Switching0.40511
32003.052210.40511
4Structural Analysis of Vector Autoregressive Models0.40511