arXiv 10 Nov 2017 · Econometrics · publishedJournal of Econometrics (2020) · 2 citations (OpenAlex)
arXiv:1711.03959 · PDF · DOI · OpenAlex · Extracted main text
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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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Kasahara, H., Shimotsu, K (2015) Testing the number of components in normal mixture regression models | 1.000 | 15 | 4 | 100% |
| 2 | Andrews, D. W (2001) Testing when a parameter is on the boundary of the maintained hypothesis | 1.000 | 13 | 3 | 100% |
| 3 | Wong, C. S., Li, W. K (2001) On a logistic mixture autoregressive model | 1.000 | 8 | 4 | 100% |
| 4 | Jeffries, N. O (1998) Logistic mixtures of generalized linear model times series | 1.000 | 5 | 3 | 100% |
| 5 | Wong, C. S., Li, W. K (2000) On a mixture autoregressive model | 1.000 | 5 | 3 | 100% |
| 6 | Zhu, H., Zhang, H (2006) Asymptotics for estimation and testing procedures under loss of identifiability | 0.971 | 12 | 4 | 92% |
| 7 | Andrews, D. W (1999) Estimation when a parameter is on a boundary | 0.969 | 11 | 3 | 91% |
| 8 | Kasahara, H., Shimotsu, K (2012) Testing the number of components in finite mixture models, unpublished working paper | 0.874 | 10 | 2 | 100% |
| 9 | Kalliovirta, L., Meitz, M., Saikkonen, P (2015) A Gaussian mixture autoregressive model for univariate time series self | 0.851 | 13 | 5 | 62% |
| 10 | Hansen, B. E (1996) Inference when a nuisance parameter is not identified under the null hypothesis | 0.811 | 4 | 2 | 100% |
Showing the top 10 of 43 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | A mixture autoregressive model based on Student's $t$–distribution | 0.405 | 1 | 1 |
| 2 | Markov Switching | 0.405 | 1 | 1 |
| 3 | 2003.05221 | 0.405 | 1 | 1 |
| 4 | Structural Analysis of Vector Autoregressive Models | 0.405 | 1 | 1 |