IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v134y2019icp157-170.html
   My bibliography  Save this article

Exact Bayesian designs for count time series

Author

Listed:
  • Singh, Rakhi
  • Mukhopadhyay, Siuli

Abstract

Exact D-optimal Bayesian designs for time series experiments are discussed in this article. This work is motivated by an RNA sequencing experiment and two disease surveillance studies, where the response is count type and has a correlated structure over time points. The conditional distribution of the count responses given a weakly stationary latent process is assumed to follow a log-linear model. The latent process allows for both overdispersion and autocorrelation in the responses. Linear predictor with the trend and seasonal components are studied. An estimating approach based on only the first two moments of the responses is used for parameter estimation. The D-optimality criterion based on minimization of the log determinant of the variance–covariance matrix of the parameter estimates is used for choosing the exact designs. To address the dependency of the design selection criterion on the unknown parameter values, prior distributions are assumed on the parameters. From the numerical results, it is noted that for linear predictors with only trend component, the optimal design is very close to the equispaced design for high correlation values. However, when the linear predictor has both the trend and seasonal components, the two designs are similar for smaller correlations.

Suggested Citation

  • Singh, Rakhi & Mukhopadhyay, Siuli, 2019. "Exact Bayesian designs for count time series," Computational Statistics & Data Analysis, Elsevier, vol. 134(C), pages 157-170.
  • Handle: RePEc:eee:csdana:v:134:y:2019:i:c:p:157-170
    DOI: 10.1016/j.csda.2018.12.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947318302871
    Download Restriction: Full text for ScienceDirect subscribers only.

    File URL: https://libkey.io/10.1016/j.csda.2018.12.008?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Davutyan, Nurhan, 1989. "Bank failures as Poisson variates," Economics Letters, Elsevier, vol. 29(4), pages 333-338.
    2. J. Durbin & S. J. Koopman, 2000. "Time series analysis of non‐Gaussian observations based on state space models from both classical and Bayesian perspectives," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 3-56.
    3. Winkelmann, Rainer, 1995. "Duration Dependence and Dispersion in Count-Data Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(4), pages 467-474, October.
    4. Benjamin M.A. & Rigby R.A. & Stasinopoulos D.M., 2003. "Generalized Autoregressive Moving Average Models," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 214-223, January.
    5. Fahrmeir, Ludwig & Wagenpfeil, Stefan, 1997. "Penalized likelihood estimation and iterative Kalman smoothing for non-Gaussian dynamic regression models," Computational Statistics & Data Analysis, Elsevier, vol. 24(3), pages 295-320, May.
    6. Konstantinos Fokianos & Benjamin Kedem, 2004. "Partial Likelihood Inference For Time Series Following Generalized Linear Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(2), pages 173-197, March.
    7. Baran, S. & Stehlík, M., 2015. "Optimal designs for parameters of shifted Ornstein–Uhlenbeck sheets measured on monotonic sets," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 114-124.
    8. Singh, Satya Prakash & Mukhopadhyay, Siuli, 2016. "Bayesian crossover designs for generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 35-50.
    9. Ucinski Dariusz & Atkinson Anthony C., 2004. "Experimental Design for Time-Dependent Models with Correlated Observations," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(2), pages 1-16, May.
    10. Rose, Nancy L, 1990. "Profitability and Product Quality: Economic Determinants of Airline Safety Performance," Journal of Political Economy, University of Chicago Press, vol. 98(5), pages 944-964, October.
    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. Subhadra Dasgupta & Siuli Mukhopadhyay & Jonathan Keith, 2024. "G‐optimal grid designs for kriging models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 51(3), pages 1061-1085, September.

    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. Vurukonda Sathish & Siuli Mukhopadhyay & Rashmi Tiwari, 2022. "Autoregressive and moving average models for zero‐inflated count time series," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 76(2), pages 190-218, May.
    2. Klingenberg, Bernhard, 2008. "Regression models for binary time series with gaps," Computational Statistics & Data Analysis, Elsevier, vol. 52(8), pages 4076-4090, April.
    3. Fokianos, Konstantinos & Rahbek, Anders & Tjøstheim, Dag, 2009. "Poisson Autoregression," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1430-1439.
    4. Yasuhiro Omori & Toshiaki Watanabe, 2003. "Block Sampler and Posterior Mode Estimation for a Nonlinear and Non-Gaussian State-Space Model with Correlated Errors," CIRJE F-Series CIRJE-F-221, CIRJE, Faculty of Economics, University of Tokyo.
    5. Guilherme Pumi & Taiane Schaedler Prass & Rafael Rigão Souza, 2021. "A dynamic model for double‐bounded time series with chaotic‐driven conditional averages," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 68-86, March.
    6. Andréa Rocha & Francisco Cribari-Neto, 2009. "Beta autoregressive moving average models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(3), pages 529-545, November.
    7. Kostas Triantafyllopoulos, 2009. "Inference of Dynamic Generalized Linear Models: On‐Line Computation and Appraisal," International Statistical Review, International Statistical Institute, vol. 77(3), pages 430-450, December.
    8. Yao Rao & David Harris & Brendan McCabe, 2022. "A semi‐parametric integer‐valued autoregressive model with covariates," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(3), pages 495-516, June.
    9. Moizes Melo & Airlane Alencar, 2020. "Conway–Maxwell–Poisson Autoregressive Moving Average Model for Equidispersed, Underdispersed, and Overdispersed Count Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(6), pages 830-857, November.
    10. Ella R Rothermel & Matthew T Balazik & Jessica E Best & Matthew W Breece & Dewayne A Fox & Benjamin I Gahagan & Danielle E Haulsee & Amanda L Higgs & Michael H P O’Brien & Matthew J Oliver & Ian A Par, 2020. "Comparative migration ecology of striped bass and Atlantic sturgeon in the US Southern mid-Atlantic bight flyway," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-24, June.
    11. Verdier Valentin, 2018. "Local Semi-Parametric Efficiency of the Poisson Fixed Effects Estimator," Journal of Econometric Methods, De Gruyter, vol. 7(1), pages 1-10, January.
    12. Mariano Amo-Salas & Jesús López-Fidalgo & Emilio Porcu, 2013. "Optimal designs for some stochastic processes whose covariance is a function of the mean," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 159-181, March.
    13. Junji Shimada & Yoshihiko Tsukuda, 2004. "Estimation of Stochastic Volatility Models : An Approximation to the Nonlinear State Space," Econometric Society 2004 Far Eastern Meetings 611, Econometric Society.
    14. Tianqing Liu & Xiaohui Yuan, 2013. "Random rounded integer-valued autoregressive conditional heteroskedastic process," Statistical Papers, Springer, vol. 54(3), pages 645-683, August.
    15. Talley, Wayne K., 1999. "Determinants of injuries in barge accidents," Transportation Research Forum Proceedings 1990s 312001, Transportation Research Forum.
    16. Fokianos, Konstantinos, 2024. "Multivariate Count Time Series Modelling," Econometrics and Statistics, Elsevier, vol. 31(C), pages 100-116.
    17. Motta, Anderson C. O. & Hotta, Luiz K., 2003. "Exact Maximum Likelihood and Bayesian Estimation of the Stochastic Volatility Model," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 23(2), November.
    18. Aknouche, Abdelhakim & Scotto, Manuel, 2022. "A multiplicative thinning-based integer-valued GARCH model," MPRA Paper 112475, University Library of Munich, Germany.
    19. Maravall, A. & del Rio, A., 2007. "Temporal aggregation, systematic sampling, and the Hodrick-Prescott filter," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 975-998, October.
    20. Breitung, Jörg & Hafner, Christian M., 2016. "A simple model for now-casting volatility series," International Journal of Forecasting, Elsevier, vol. 32(4), pages 1247-1255.

    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:eee:csdana:v:134:y:2019:i:c:p:157-170. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.