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Modeling time series when some observations are zero

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  • Harvey, Andrew
  • Ito, Ryoko

Abstract

Sometimes a significant 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 filter 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 fitted to daily rainfall in locations in northern Australia and England and compared with a dynamic zero-augmented model.

Suggested Citation

  • Harvey, Andrew & Ito, Ryoko, 2020. "Modeling time series when some observations are zero," Journal of Econometrics, Elsevier, vol. 214(1), pages 33-45.
    • Handle: RePEc:eee:econom:v:214:y:2020:i:1:p:33-45
    DOI: 10.1016/j.jeconom.2019.05.003
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    References listed on IDEAS

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    1. Nikolaus Hautsch & Peter Malec & Melanie Schienle, 2014. "Capturing the Zero: A New Class of Zero-Augmented Distributions and Multiplicative Error Processes," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 12(1), pages 89-121.
    2. Tommaso Proietti & Eric Hillebrand, 2017. "Seasonal changes in central England temperatures," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(3), pages 769-791, June.
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    5. Tata Subba Rao & Granville Tunnicliffe Wilson & Andrew Harvey & Rutger-Jan Lange, 2017. "Volatility Modeling with a Generalized t Distribution," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(2), pages 175-190, March.
    6. Bauwens, Luc & Giot, Pierre & Grammig, Joachim & Veredas, David, 2004. "A comparison of financial duration models via density forecasts," International Journal of Forecasting, Elsevier, vol. 20(4), pages 589-609.
    7. Newey, Whitney K., 1988. "Adaptive estimation of regression models via moment restrictions," Journal of Econometrics, Elsevier, vol. 38(3), pages 301-339, July.
    8. Tina Hviid Rydberg & Neil Shephard, 2003. "Dynamics of Trade-by-Trade Price Movements: Decomposition and Models," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 1(1), pages 2-25.
    9. Randall A. Lewis & James B. McDonald, 2014. "Partially Adaptive Estimation of the Censored Regression Model," Econometric Reviews, Taylor & Francis Journals, vol. 33(7), pages 732-750, October.
    10. Ito, R., 2016. "Spline-DCS for Forecasting Trade Volume in High-Frequency Finance," Cambridge Working Papers in Economics 1606, Faculty of Economics, University of Cambridge.
    11. Drew Creal & Siem Jan Koopman & André Lucas, 2013. "Generalized Autoregressive Score Models With Applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(5), pages 777-795, August.
    12. McDonald, James B. & Newey, Whitney K., 1988. "Partially Adaptive Estimation of Regression Models via the Generalized T Distribution," Econometric Theory, Cambridge University Press, vol. 4(3), pages 428-457, December.
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    Cited by:

    1. Hiroyuki Kawakatsu, 2019. "Jointly Modeling Autoregressive Conditional Mean and Variance of Non-Negative Valued Time Series," Econometrics, MDPI, vol. 7(4), pages 1-19, December.
    2. Kamil Makieła & Błażej Mazur, 2022. "Model uncertainty and efficiency measurement in stochastic frontier analysis with generalized errors," Journal of Productivity Analysis, Springer, vol. 58(1), pages 35-54, August.
    3. De Rossi, Giuliano & Steliaros, Michael, 2022. "The Shift from Active to Passive and its Effect on Intraday Stock Dynamics," Journal of Banking & Finance, Elsevier, vol. 143(C).
    4. Petra Tomanová & Vladimír Holý, 2021. "Clustering of arrivals in queueing systems: autoregressive conditional duration approach," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(3), pages 859-874, September.
    5. Giuseppe Buccheri & Stefano Grassi & Giorgio Vocalelli, 2021. "Estimating Risk in Illiquid Markets: a Model of Market Friction with Stochastic Volatility," CEIS Research Paper 506, Tor Vergata University, CEIS, revised 08 Nov 2021.
    6. Song, Shijia & Li, Handong, 2023. "A method for predicting VaR by aggregating generalized distributions driven by the dynamic conditional score," The Quarterly Review of Economics and Finance, Elsevier, vol. 88(C), pages 203-214.
    7. Song, Shijia & Li, Handong, 2022. "Predicting VaR for China's stock market: A score-driven model based on normal inverse Gaussian distribution," International Review of Financial Analysis, Elsevier, vol. 82(C).
    8. Domenico Di Gangi & Giacomo Bormetti & Fabrizio Lillo, 2022. "Score Driven Generalized Fitness Model for Sparse and Weighted Temporal Networks," Papers 2202.09854, arXiv.org, revised Mar 2022.

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    More about this item

    Keywords

    Censored distributions; Dynamic conditional score model; Generalized beta distribution; Rainfall; Seasonality; Zero augmented 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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