138
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Hidden Markov Mixture Autoregressive Models: Stability and Moments

&
Pages 1087-1104 | Received 17 Jan 2011, Accepted 25 May 2011, Published online: 06 Feb 2013

References

  • Alizadeh , S. , Rezakhah , S. Hidden Markov Mixture Autoregressive Models: Parameter Estimation. Available at: http://arxiv.org/pdf/1105.2891v1.pdf.
  • Bartolucci , F. , Farcomeni , A. ( 2010 ). A note on the mixture transition distribution and hidden markov models . J. Time Ser. Anal. 31 ( 2 ): 132 – 138 .
  • Berchtold , A. ( 2003 ). Mixture transition distribution (mtd) modeling of heteroscedastic time series . Computat. Statist. Data Anal. 41 ( 3–4 ): 399 – 411 .
  • Berchtold , A. , Raftery , A. E. (2002). The mixture transition distribution model for high-order markov chains and non-gaussian time series. Statistical Sci. 17(3):328–359 (in English).
  • Billingsley , P. ( 1999 ). Convergence of Probability Measures, Wiley Series in Probability and Statistics . Wiley .
  • Billingsley , P. ( 2008 ). Probability and Measure. , 3rd ed. Wiley India Pvt. Ltd .
  • Bishop , C. M. ( 2006 ). Pattern Recognition and Machine Learning, Information Science and Statistics . Springer .
  • Brockwell , P. J. , Davis , R. A. ( 2009 ). Time Series: Theory and Methods . Springer Series in Statistics , New York : Springer .
  • Datta , K. B. ( 2004 ). Matrix and Linear Algebra . New Delhi : Prentice-Hall of India Pvt. Ltd .
  • Engle , R. F. ( 1982 ). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation . Econometrica 50 ( 4 ): 987 – 1007 .
  • Fan , J. , Yao , Q. Nonlinear Time Series: Nonparametric and Parametric Methods, Springer Series in Statistics . Springer .
  • Francq , C. , Zakoian , J. M. ( 2010 ). GARCH Models: Structure, Statistical Inference and Financial Applications . New York : John Wiley & Sons .
  • Hamilton , J. D. ( 1990 ). Analysis of time series subject to changes in regime . Journal of Econometrics 45 ( 1–2 ): 39 – 70 .
  • Lai , T. L. , Wong , S. P. ( 2001 ). Stochastic neural networks with applications to nonlinear time series. J. Amer. Statist. Assoc. 96(455):968–981 (in English) .
  • Le , N. D. , Martin , R. D. , Raftery , A. E. ( 1996 ). Modeling flat stretches, bursts, and outliers in time series using mixture transition distribution models. J. Amer. Statist. Assoc. 91(436):1504–1515 (in English) .
  • McCulloch , R. E. , Tsay , R. S. ( 1994 ). Statistical analysis of economic time series via markov switching models . J. Time Seri. Anal. 15 ( 6 ): 523 – 539 .
  • Medeiros , M. C. , Veiga , A. ( 2000 ). A hybrid linear-neural model for time series forecasting . Neur. Netw. IEEE Trans. 11 ( 6 ): 1402 – 1412 .
  • Raftery , A. E. ( 1985 ). A model for high-order markov chains . J. Roy. Statist. Society. Seri. B (Methodolo.) 47 ( 3 ): 528 – 539 .
  • Timmermann , A. ( 2000 ). Moments of markov switching models . J. Econometrics 96 ( 1 ): 75 – 111 .
  • Wong , C. S. , Li , W. K. ( 2000 ). On a mixture autoregressive model . J. Roy. Statist. Soc. Ser. B (Statist. Methodol.) 62 ( 1 ): 95 – 115 (in English) .
  • Wong , C. S. , Li , W. K. ( 2001 ). On a mixture autoregressive conditional heteroscedastic model. J. Amer. Statist. Associ. 96(455):982–995 (in English) .
  • Yao , J.-F. , Attali , J.-G. ( 2000 ). On stability of nonlinear ar processes with markov switching. Adv. Appl. Probabi. 32(2):394–407 (in English) .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.