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Modeling time series with zero observations

Author

Listed:
  • Andrew Harvey

    (Faculty of Economics, Cambridge University)

  • Ryoko Ito

    (Dept of Economics and Nuffield College, Oxford University)

Abstract

We consider situations in which a signi?cant proportion of observations in a time series are zero, but the remaining observations are positive and measured on a continuous scale. We propose a new dynamic model in which the conditional distribution of the observations is constructed by shifting a distribution for non-zero observations to the left and censoring negative values. The key to generalizing the censoring approach to the dynamic case is to have (the logarithm of) the location/scale parameter driven by a ?lter that depends on the score of the conditional distribution. An exponential link function means that seasonal effects can be incorporated into the model and this is done by means of a cubic spline (which can potentially be time-varying). The model is ?tted to daily rainfall in northern Australia and compared with a dynamic zero-augmented model.

Suggested Citation

  • Andrew Harvey & Ryoko Ito, 2017. "Modeling time series with zero observations," Economics Papers 2017-W01, Economics Group, Nuffield College, University of Oxford.
  • Handle: RePEc:nuf:econwp:1701
    as

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    File URL: https://www.nuffield.ox.ac.uk/economics/papers/2017/CensorAus5d_Submit.pdf
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    References listed on IDEAS

    as
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    11. Gneiting, Tilmann & Ranjan, Roopesh, 2011. "Comparing Density Forecasts Using Threshold- and Quantile-Weighted Scoring Rules," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(3), pages 411-422.
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    Cited by:

    1. Leopoldo Catania & Roberto Di Mari & Paolo Santucci de Magistris, 2019. "Dynamic discrete mixtures for high frequency prices," Discussion Papers 19/05, University of Nottingham, Granger Centre for Time Series Econometrics.

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    More about this item

    Keywords

    Censored distributions; dynamic conditional score model; generalized beta distribution; rainfall; seasonality; zero aug- mented model.;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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