A constrained maximum-likelihood approach to estimating switching regressions
It is widely known that the likelihood function for the switching-regression model is unbounded if the error variances are unconstrained. This paper shows that a constrained maximum-likelihood formulation makes the likelihood function bounded. Relatively mild constraints are imposed on the parameter...
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| Published in | Journal of econometrics Vol. 48; no. 1; pp. 241 - 262 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Amsterdam
Elsevier B.V
01.04.1991
Elsevier North-Holland Pub. Co Elsevier Sequoia S.A |
| Series | Journal of Econometrics |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0304-4076 1872-6895 |
| DOI | 10.1016/0304-4076(91)90040-K |
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| Abstract | It is widely known that the likelihood function for the switching-regression model is unbounded if the error variances are unconstrained. This paper shows that a constrained maximum-likelihood formulation makes the likelihood function bounded. Relatively mild constraints are imposed on the parameters, and if the true parameters satisfy the constraints, there is a global maximizer of the likelihood function on the constrained parameter space which is consistent, asymptotically normal, and efficient. A well-known EM algorithm is modified in order to compute constrained maximizers of the likelihood function. |
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| AbstractList | A research study shows that a constrained maximum-likelihood formulation makes the likelihood function for the switching-regression model bounded. Relatively mild constraints are imposed on the parameters. A switching-regression model is characterized by switches between 2 regression equations where the timing of the switches is unknown. A well-known difficulty in using maximum likelihood to estimate regressions subject to discrete random switches is that the likelihood function is unbounded if the error variances in the underlying regressions are unconstrained. It is shown that a constrained maximum-likelihood formulation makes the likelihood function bounded. Relatively mild constraints are imposed on the parameters, and if the true parameters satisfy the constraints, there is a global maximizer of the likelihood function on the constrained parameter space that is consistent, asymptotically normal, and efficient. A well-known expectation maximization algorithm is modified in order to compute constrained maximizers of the likelihood function. It is widely known that the likelihood function for the switching-regression model is unbounded if the error variances are unconstrained. This paper shows that a constrained maximum-likelihood formulation makes the likelihood function bounded. Relatively mild constraints are imposed on the parameters, and if the true parameters satisfy the constraints, there is a global maximizer of the likelihood function on the constrained parameter space which is consistent, asymptotically normal, and efficient. A well-known EM algorithm is modified in order to compute constrained maximizers of the likelihood function. |
| Author | Phillips, Robert F. |
| Author_xml | – sequence: 1 givenname: Robert F. surname: Phillips fullname: Phillips, Robert F. organization: George Washington University, Washington, DC 20052, USA |
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| CitedBy_id | crossref_primary_10_1016_j_csda_2009_07_002 crossref_primary_10_1007_s11222_008_9052_4 crossref_primary_10_1016_0165_1889_96_00911_6 crossref_primary_10_1016_j_ijar_2017_09_006 crossref_primary_10_1007_s10260_011_0182_z crossref_primary_10_1016_j_jeconom_2009_06_007 crossref_primary_10_1080_07350015_1994_10524545 crossref_primary_10_1080_00779959909544307 crossref_primary_10_5089_9781451844771_001 crossref_primary_10_3390_econometrics2010001 crossref_primary_10_1080_09603100110086807 crossref_primary_10_1016_j_jhydrol_2005_01_016 crossref_primary_10_1016_0165_1765_92_90135_L crossref_primary_10_1080_07474939908800437 crossref_primary_10_1007_s11269_009_9448_8 crossref_primary_10_1016_S0167_9473_02_00345_6 crossref_primary_10_1007_s00184_022_00873_2 crossref_primary_10_1016_j_spl_2004_11_007 crossref_primary_10_1111_1468_2354_t01_1_00078 crossref_primary_10_1080_03610919808813502 crossref_primary_10_1016_0304_4076_94_90060_4 crossref_primary_10_1080_07474939808800410 |
| Cites_doi | 10.1214/aos/1176349557 10.2307/1912950 10.1214/aoms/1177697731 10.2307/2286266 10.2307/2286267 10.2307/2284373 10.2307/1914031 10.1080/00949658608810872 10.2307/2285939 10.1214/aos/1176346060 10.2307/2286268 10.1214/aoms/1177698520 10.1093/biomet/41.1-2.56 10.2307/1913910 10.2307/2326563 |
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| Keywords | Regression equation Regression model Asymptotic normality Gaussian distribution Maximum likelihood Timing EM algorithm Switching Variance |
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| References | Wu (BIB22) 1983; 11 Yakowitz, Spragins (BIB23) 1968; 39 Kiefer (BIB12) 1980; 48 Quandt (BIB15) 1972; 67 White (BIB21) 1984 Amemiya (BIB1) 1973; 41 Chanda (BIB3) 1954; 41 Hosmer (BIB8) 1978; 73 Quandt, Ramsey (BIB17) 1978; 73 Amemiya (BIB2) 1985 Rao (BIB18) 1973 Johnson, Kotz (BIB10) 1970 Hathaway (BIB6) 1985; 13 Kiefer (BIB11) 1978; 46 Jennrich (BIB9) 1969; 40 Phillips (BIB14) 1989 Hartley (BIB5) 1978; 73 Hartley (BIB4) 1977 Kon, Jen (BIB13) 1978; 33 Swamy, Mehta (BIB19) 1975; 70 Theil (BIB20) 1971 Quandt (BIB16) 1983; Vol. 1 Hathaway (BIB7) 1986; 23 Hartley (10.1016/0304-4076(91)90040-K_BIB4) 1977 Yakowitz (10.1016/0304-4076(91)90040-K_BIB23) 1968; 39 Amemiya (10.1016/0304-4076(91)90040-K_BIB2) 1985 White (10.1016/0304-4076(91)90040-K_BIB21) 1984 Hosmer (10.1016/0304-4076(91)90040-K_BIB8) 1978; 73 Jennrich (10.1016/0304-4076(91)90040-K_BIB9) 1969; 40 Swamy (10.1016/0304-4076(91)90040-K_BIB19) 1975; 70 Amemiya (10.1016/0304-4076(91)90040-K_BIB1) 1973; 41 Quandt (10.1016/0304-4076(91)90040-K_BIB16) 1983; Vol. 1 Kiefer (10.1016/0304-4076(91)90040-K_BIB11) 1978; 46 Phillips (10.1016/0304-4076(91)90040-K_BIB14) 1989 Wu (10.1016/0304-4076(91)90040-K_BIB22) 1983; 11 Kiefer (10.1016/0304-4076(91)90040-K_BIB12) 1980; 48 Quandt (10.1016/0304-4076(91)90040-K_BIB17) 1978; 73 Johnson (10.1016/0304-4076(91)90040-K_BIB10) 1970 Theil (10.1016/0304-4076(91)90040-K_BIB20) 1971 Hathaway (10.1016/0304-4076(91)90040-K_BIB6) 1985; 13 Hartley (10.1016/0304-4076(91)90040-K_BIB5) 1978; 73 Quandt (10.1016/0304-4076(91)90040-K_BIB15) 1972; 67 Kon (10.1016/0304-4076(91)90040-K_BIB13) 1978; 33 Hathaway (10.1016/0304-4076(91)90040-K_BIB7) 1986; 23 Rao (10.1016/0304-4076(91)90040-K_BIB18) 1973 Chanda (10.1016/0304-4076(91)90040-K_BIB3) 1954; 41 |
| References_xml | – year: 1971 ident: BIB20 article-title: Principles of econometrics – year: 1984 ident: BIB21 article-title: Asymptotic theory for econometricians – year: 1985 ident: BIB2 article-title: Advanced econometrics – volume: 33 start-page: 457 year: 1978 end-page: 475 ident: BIB13 article-title: Estimation of time-varying systematic risk and performance for mutual fund portfolios: An application of switching regression publication-title: Journal of Finance – volume: 23 start-page: 211 year: 1986 end-page: 230 ident: BIB7 article-title: A constrained EM algorithm for univariate normal mixtures publication-title: Journal of Statistical Computation and Simulation – volume: 39 start-page: 209 year: 1968 end-page: 214 ident: BIB23 article-title: On the identifiability of finite mixtures publication-title: Annals of Mathematical Statistics – volume: 46 start-page: 427 year: 1978 end-page: 434 ident: BIB11 article-title: Discrete parameter variation: Efficient estimation of a switching regression model publication-title: Econometrica – volume: 48 start-page: 1065 year: 1980 end-page: 1069 ident: BIB12 article-title: A note on switching regressions and logistic discrimination publication-title: Econometrica – volume: 41 start-page: 56 year: 1954 end-page: 61 ident: BIB3 article-title: A note on the consistency and maxima of the roots of likelihood equations publication-title: Biometrica – year: 1970 ident: BIB10 article-title: Continuous univariate distributions - 1 – year: 1977 ident: BIB4 article-title: On the estimation of a general switching regression model via maximum likelihood methods publication-title: Discussion paper no. 415 – volume: 73 start-page: 730 year: 1978 end-page: 752 ident: BIB17 article-title: Estimating mixtures of normal distributions and switching regressions (with comments) publication-title: Journal of the American Statistical Association – volume: 40 start-page: 633 year: 1969 end-page: 643 ident: BIB9 article-title: Asymptotic properties of non-linear least squares estimators publication-title: Annals of Mathematical Statistics – year: 1989 ident: BIB14 article-title: A constrained maximum likelihood approach to estimating switching regressions publication-title: Discussion paper no. 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ident: 10.1016/0304-4076(91)90040-K_BIB19 article-title: Bayesian and non-Bayesian analysis of switching regressions and of random coefficient regression models publication-title: Journal of the American Statistical Association doi: 10.2307/2285939 – year: 1970 ident: 10.1016/0304-4076(91)90040-K_BIB10 – year: 1977 ident: 10.1016/0304-4076(91)90040-K_BIB4 article-title: On the estimation of a general switching regression model via maximum likelihood methods – volume: 11 start-page: 95 year: 1983 ident: 10.1016/0304-4076(91)90040-K_BIB22 article-title: On the convergence properties of the EM algorithm publication-title: Annals of Statistics doi: 10.1214/aos/1176346060 – volume: 73 start-page: 741 year: 1978 ident: 10.1016/0304-4076(91)90040-K_BIB8 article-title: Comment on ‘Estimating mixtures of normal distributions and switching regressions’ publication-title: Journal of the American Statistical Association doi: 10.2307/2286268 – year: 1989 ident: 10.1016/0304-4076(91)90040-K_BIB14 article-title: A constrained maximum likelihood approach to estimating switching regressions – volume: 39 start-page: 209 year: 1968 ident: 10.1016/0304-4076(91)90040-K_BIB23 article-title: On the identifiability of finite mixtures publication-title: Annals of Mathematical Statistics doi: 10.1214/aoms/1177698520 – volume: 41 start-page: 56 year: 1954 ident: 10.1016/0304-4076(91)90040-K_BIB3 article-title: A note on the consistency and maxima of the roots of likelihood equations publication-title: Biometrica doi: 10.1093/biomet/41.1-2.56 – volume: 46 start-page: 427 year: 1978 ident: 10.1016/0304-4076(91)90040-K_BIB11 article-title: Discrete parameter variation: Efficient estimation of a switching regression model publication-title: Econometrica doi: 10.2307/1913910 – year: 1985 ident: 10.1016/0304-4076(91)90040-K_BIB2 – volume: 33 start-page: 457 year: 1978 ident: 10.1016/0304-4076(91)90040-K_BIB13 article-title: Estimation of time-varying systematic risk and performance for mutual fund portfolios: An application of switching regression publication-title: Journal of Finance doi: 10.2307/2326563 |
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| Snippet | It is widely known that the likelihood function for the switching-regression model is unbounded if the error variances are unconstrained. This paper shows that... A research study shows that a constrained maximum-likelihood formulation makes the likelihood function for the switching-regression model bounded. Relatively... A switching-regression model is characterized by switches between 2 regression equations where the timing of the switches is unknown. A well-known difficulty... |
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| SubjectTerms | Algorithms Econometrics Economic models Economic statistics Economic theory Estimating techniques Exact sciences and technology Mathematics Probability and statistics Regression analysis Sciences and techniques of general use Statistics Studies Switching Utility functions |
| Title | A constrained maximum-likelihood approach to estimating switching regressions |
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