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A Truncated Mixture Transition Model for Interval-valued Time Series

Author

Listed:
  • Gloria Gonzalez-Rivera

    (Department of Economics, University of California Riverside)

  • Yun Luo

Abstract

We propose a model for interval-valued time series (ITS), e.g. the collection of daily intervals of high/low stock returns over time, that specifies the conditional joint distribution of the upper and lower bounds of the interval as a mixture of truncated bivariate normal distribution. This specification guarantees that the natural order of the interval (upper bound not smaller than lower bound) is preserved. The model also captures the potential conditional heteroscedasticity and non-Gaussian features in ITS. The standard EM algorithm, when applied to the estimation of mixture models with truncated distribution, does not provide a closed-form solution in M step. We propose a new EM algorithm that solves this problem. We establish the consistency of the maximum likelihood estimator. Monte Carlo simulations show the new EM algorithm has good convergence properties. We apply the model to the interval-valued IBM daily stock returns and it exhibits superior performance over competing methods.

Suggested Citation

  • Gloria Gonzalez-Rivera & Yun Luo, 2020. "A Truncated Mixture Transition Model for Interval-valued Time Series," Working Papers 202005, University of California at Riverside, Department of Economics.
    • Handle: RePEc:ucr:wpaper:202005
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    References listed on IDEAS

    as
    1. Amemiya, Takeshi, 1973. "Regression Analysis when the Dependent Variable is Truncated Normal," Econometrica, Econometric Society, vol. 41(6), pages 997-1016, November.
    2. Lee, Gyemin & Scott, Clayton, 2012. "EM algorithms for multivariate Gaussian mixture models with truncated and censored data," Computational Statistics & Data Analysis, Elsevier, vol. 56(9), pages 2816-2829.
    3. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
    4. Lima Neto, Eufrásio de A. & de Carvalho, Francisco de A.T., 2010. "Constrained linear regression models for symbolic interval-valued variables," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 333-347, February.
    5. Luc Bauwens & Sébastien Laurent & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109, January.
    6. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
    7. Gloria González-Rivera & Wei Lin, 2013. "Constrained Regression for Interval-Valued Data," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(4), pages 473-490, October.
    8. Hassan, Mohamed Yusuf & Lii, Keh-Shin, 2006. "Modeling Marked Point Processes via Bivariate Mixture Transition Distribution Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1241-1252, September.
    9. Kalliovirta, Leena & Meitz, Mika & Saikkonen, Pentti, 2016. "Gaussian mixture vector autoregression," Journal of Econometrics, Elsevier, vol. 192(2), pages 485-498.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    interval-valued data; mixture transition model; EM algorithm; truncated normal distribution.;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C34 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Truncated and Censored Models; Switching Regression Models

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