IDEAS home Printed from https://ideas.repec.org/p/nuf/econwp/1701.html
   My bibliography  Save this paper

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

    Download full text from publisher

    File URL: https://www.nuffield.ox.ac.uk/economics/papers/2017/CensorAus5d_Submit.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Creal, Drew & Koopman, Siem Jan & Lucas, André, 2011. "A Dynamic Multivariate Heavy-Tailed Model for Time-Varying Volatilities and Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(4), pages 552-563.
    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.
    3. Harvey, Andrew & Thiele, Stephen, 2016. "Testing against changing correlation," Journal of Empirical Finance, Elsevier, vol. 38(PB), pages 575-589.
    4. Harvey,Andrew C., 2013. "Dynamic Models for Volatility and Heavy Tails," Cambridge Books, Cambridge University Press, number 9781107630024, January.
    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. Blasques, Francisco & van Brummelen, Janneke & Koopman, Siem Jan & Lucas, André, 2022. "Maximum likelihood estimation for score-driven models," Journal of Econometrics, Elsevier, vol. 227(2), pages 325-346.
    7. 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.
    8. Nikolaus Hautsch & Peter Malec & Melanie Schienle, 2014. "Capturing the Zero: A New Class of Zero-Augmented Distributions and Multiplicative Error Processes," Journal of Financial Econometrics, Oxford University Press, vol. 12(1), pages 89-121.
    9. Tilmann Gneiting & Roopesh Ranjan, 2011. "Comparing Density Forecasts Using Threshold- and Quantile-Weighted Scoring Rules," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(3), pages 411-422, July.
    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. 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.
    12. 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.
    13. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Harvey, Andrew & Ito, Ryoko, 2020. "Modeling time series when some observations are zero," Journal of Econometrics, Elsevier, vol. 214(1), pages 33-45.
    2. Harvey, A., 2021. "Score-driven time series models," Cambridge Working Papers in Economics 2133, Faculty of Economics, University of Cambridge.
    3. Catania, Leopoldo & Grassi, Stefano, 2022. "Forecasting cryptocurrency volatility," International Journal of Forecasting, Elsevier, vol. 38(3), pages 878-894.
    4. Mauro Bernardi & Leopoldo Catania, 2015. "Switching-GAS Copula Models With Application to Systemic Risk," Papers 1504.03733, arXiv.org, revised Jan 2016.
    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. 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.
    7. Ayala Astrid & Blazsek Szabolcs & Escribano Alvaro, 2023. "Anticipating extreme losses using score-driven shape filters," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 27(4), pages 449-484, September.
    8. Buccheri, Giuseppe & Corsi, Fulvio & Flandoli, Franco & Livieri, Giulia, 2021. "The continuous-time limit of score-driven volatility models," Journal of Econometrics, Elsevier, vol. 221(2), pages 655-675.
    9. Harvey, Andrew & Palumbo, Dario, 2023. "Score-driven models for realized volatility," Journal of Econometrics, Elsevier, vol. 237(2).
    10. Delle Monache, Davide & Petrella, Ivan, 2017. "Adaptive models and heavy tails with an application to inflation forecasting," International Journal of Forecasting, Elsevier, vol. 33(2), pages 482-501.
    11. Blasques, Francisco & Koopman, Siem Jan & Lucas, Andre & Schaumburg, Julia, 2016. "Spillover dynamics for systemic risk measurement using spatial financial time series models," Journal of Econometrics, Elsevier, vol. 195(2), pages 211-223.
    12. Ito, Ryoko, 2013. "Modeling Dynamic Diurnal Patterns in High-Frequency Financial Data," Cambridge Working Papers in Economics 1315, Faculty of Economics, University of Cambridge.
    13. Leopoldo Catania & Alessandra Luati & Pierluigi Vallarino, 2021. "Economic vulnerability is state dependent," CREATES Research Papers 2021-09, Department of Economics and Business Economics, Aarhus University.
    14. Astrid Ayala & Szabolcs Blazsek, 2018. "Equity market neutral hedge funds and the stock market: an application of score-driven copula models," Applied Economics, Taylor & Francis Journals, vol. 50(37), pages 4005-4023, August.
    15. Pawel Janus & André Lucas & Anne Opschoor & Dick J.C. van Dijk, 2014. "New HEAVY Models for Fat-Tailed Returns and Realized Covariance Kernels," Tinbergen Institute Discussion Papers 14-073/IV, Tinbergen Institute, revised 19 Aug 2015.
    16. Rutger-Jan Lange & Bram van Os & Dick van Dijk, 2022. "Implicit score-driven filters for time-varying parameter models," Tinbergen Institute Discussion Papers 22-066/III, Tinbergen Institute, revised 21 Nov 2024.
    17. David Ardia & Kris Boudt & Leopoldo Catania, 2016. "Generalized Autoregressive Score Models in R: The GAS Package," Papers 1609.02354, arXiv.org.
    18. Marco Bazzi & Francisco Blasques & Siem Jan Koopman & Andre Lucas, 2017. "Time-Varying Transition Probabilities for Markov Regime Switching Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(3), pages 458-478, May.
    19. Francisco Blasques & Siem Jan Koopman & André Lucas, 2014. "Maximum Likelihood Estimation for correctly Specified Generalized Autoregressive Score Models: Feedback Effects, Contraction Conditions and Asymptotic Properties," Tinbergen Institute Discussion Papers 14-074/III, Tinbergen Institute.
    20. Francisco Blasques & Siem Jan Koopman & André Lucas, 2014. "Information Theoretic Optimality of Observation Driven Time Series Models," Tinbergen Institute Discussion Papers 14-046/III, Tinbergen Institute.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:nuf:econwp:1701. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Maxine Collett (email available below). General contact details of provider: https://www.nuffield.ox.ac.uk/economics/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.