A note on Phillips (1991): "A constrained maximum likelihood approach to estimating switching regressions"
Phillips [Phillips R.F., 1991. A constrained maximum likelihood approach to estimating switching regressions.Â Journal of Econometrics 48, 241-262] proposed a constrained maximum-likelihood approach to estimating the parameters in a switching regression model. In this note, we propose a new approach which leads to a proof of a more general result than Phillips's. Specifically, we prove that the Constrained MLE (CMLE) is still strongly consistent when the constant c decreases to 0 at the rate of as n increases to [infinity], with [alpha]>1. We also suggest a suitable [alpha], hence cn, for practice based on simulation results.
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- Naik, Prasad A. & Shi, Peide & Tsai, Chih-Ling, 2007. "Extending the Akaike Information Criterion to Mixture Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 244-254, March.
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- Smith, Aaron D. & Naik, Prasad A. & Tsai, Chih-Ling, 2005. "Markov-Switching Model Selection Using Kullback-Leibler Divergence," Working Papers 11976, University of California, Davis, Department of Agricultural and Resource Economics.
- Phillips, Robert F., 1991. "A constrained maximum-likelihood approach to estimating switching regressions," Journal of Econometrics, Elsevier, vol. 48(1-2), pages 241-262.
- Hartley, Michael J & Mallela, Parthasaradhi, 1977. "The Asymptotic Properties of a Maximum Likelihood Estimator for a Model of Markets in Disequilibrium," Econometrica, Econometric Society, vol. 45(5), pages 1205-1220, July.
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