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Interval-valued Time Series Models: Estimation based on Order Statistics. Exploring the Agriculture Marketing Service Data

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  • Gloria Gonzalez-Rivera

    () (Department of Economics, University of California Riverside)

  • Wei Lin

    () (Capital University of Economics and Business)

Abstract

The current regression models for interval-valued data ignore the extreme nature of the lower and upper bounds of intervals. We propose a new estimation approach that considers the bounds of the interval as realizations of the max/min order statistics coming from a sample of n_t random draws from the conditional density of an underlying stochastic process {Y_t}. This approach is important for data sets for which the relevant information is only available in interval format, e.g., low/high prices. We are interested in the characterization of the latent process as well as in the modeling of the bounds themselves. We estimate a dynamic model for the conditional mean and conditional variance of the latent process, which is assumed to be normally distributed, and for the conditional intensity of the discrete process {n_t}, which follows a negative binomial density function. Under these assumptions, together with the densities of order statistics, we obtain maximum likelihood estimates of the parameters of the model, which are needed to estimate the expected value of the bounds of the interval. We implement this approach with the time series of livestock prices, of which only low/high prices are recorded making the price process itself a latent process. We find that the proposed model provides an excellent fit of the intervals of low/high returns with an average coverage rate of 83%. We also offer a comparison with current models for interval-valued data.

Suggested Citation

  • Gloria Gonzalez-Rivera & Wei Lin, 2015. "Interval-valued Time Series Models: Estimation based on Order Statistics. Exploring the Agriculture Marketing Service Data," Working Papers 201505, University of California at Riverside, Department of Economics.
  • Handle: RePEc:ucr:wpaper:201505
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    References listed on IDEAS

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    1. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
    2. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Applications to Poisson Models," Econometrica, Econometric Society, vol. 52(3), pages 701-720, May.
    3. Ivana Komunjer & Michael T. Owyang, 2012. "Multivariate Forecast Evaluation and Rationality Testing," The Review of Economics and Statistics, MIT Press, vol. 94(4), pages 1066-1080, November.
    4. Paulo Rodrigues & Nazarii Salish, 2015. "Modeling and forecasting interval time series with threshold models," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 9(1), pages 41-57, March.
    5. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464, August.
    6. Jarque, Carlos M. & Bera, Anil K., 1980. "Efficient tests for normality, homoscedasticity and serial independence of regression residuals," Economics Letters, Elsevier, vol. 6(3), pages 255-259.
    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.
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    Cited by:

    1. repec:eee:econom:v:206:y:2018:i:2:p:414-446 is not listed on IDEAS
    2. Gloria Gonzalez-Rivera & Wei Lin, 2016. "Extreme Returns and Intensity of Trading," Working Papers 201607, University of California at Riverside, Department of Economics.

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