Forecasting evaluation via parametric bootstrap for threshold-INARCH models

  • Received : 2019.07.08
  • Accepted : 2020.01.03
  • Published : 2020.03.31


This article is concerned with the issue of forecasting and evaluation of threshold-asymmetric volatility models for time series of count data. In particular, threshold integer-valued models with conditional Poisson and conditional negative binomial distributions are highlighted. Based on the parametric bootstrap method, some evaluation measures are discussed in terms of one-step ahead forecasting. A parametric bootstrap procedure is explained from which directional measure, magnitude measure and expected cost of misclassification are discussed to evaluate competing models. The cholera data in Bangladesh from 1988 to 2016 is analyzed as a real application.


  1. Ali M, Debes AK, Luquero FJ, Kim DR, Park JY, and Digilio L (2016). Potential for controlling cholera using a ring vaccination strategy: re-analysis of data from a cluster-randomized clinical trial, PLOS Medicine, 13, e1002120.
  2. Ali M, Kim DR, Yunus M, and Emch M(2013). Time series analysis of cholera in Matlab, Bangladesh, during 1988-2001, Journal of Health, Population, and Nutrition, 31, 11-19.
  3. Andre FE, Booy R, Bock HL, Clemens J, Datta SK, John TJ, and Schmitt HJ (2008). Vaccination greatly reduces disease, disability, death and inequity worldwide, Bulletin of the World Health Organization, 86, 140-146.
  4. Azman AS, Rudolph KE, Cummings DAT, and Lessler J (2013). The incubation period of cholera: a systematic review, Journal of Infection, 66, 432-438.
  5. Bourguignon M, Rodrigues J, and Santos-Neto M (2019). Extended Poisson INAR(1) processes with equidispersion, underdispersion and overdispersion, Journal of Applied Statistics, 46, 101-118.
  6. Cardinal M, Roy R, and Lambert J (1999). On the application of integer-valued time series models for the analysis of disease incidence, Statistics in Medicine, 18, 2025-2039.<2025::AID-SIM163>3.0.CO;2-D
  7. Ferland R, Latour A, and Oraichi D (2006). Integer-valued GARCH process, Journal of Time Series Analysis, 27, 923-942.
  8. Hyndman RJ and Koehler AB (2006). Another look at measures of forecast accuracy, International Journal of Forecasting, 22, 679-688.
  9. Kim DR, Yoon JE, and Hwang SY (2019). Threshold-asymmetric volatility models for integer-valued time series, Communications for Statistical Applications and Methods, 26, 295-304.
  10. AB and Terasvirta T (2010). Forecasting with nonlinear time series models (CREATES Research Papers), Department of Economics and Business Economics, Aarhus University, 2010-01.
  11. Liu M, Li Q, and Zhu F (2019). Threshold negative binomial autoregressive model, Statistics, 53, 1-25.
  12. Saha A and Dong D (1997). Estimating nested count data models, Oxford Bulletin of Economics and Statistics, 59, 423-430.
  13. Taieb SB, Bontempi G, Atiya AF, and Sorjamaa A (2012). A review and comparison of strategies for multi-step ahead time series forecasting based on the NN5 forecasting competition, Expert Systems with Applications, 39, 7067-7083.
  14. Timm NH (2002). Applied Multivariate Analysis (2nd ed), Springer, New York.
  15. Tsay RS (2010). Analysis of Financial Time Series (3rd Ed), John Wiley & Sons, Hoboken.
  16. Wang C, Liu H, Yao JF, Davis RA, and Li WK (2014). Self-excited threshold Poisson autoregression, Journal of the American Statistical Association, 109, 777-787.
  17. Weib CH (2010). The INARCH(1) model for overdispersed time series of counts, Communications in Statistics: Simulation and Computation, 39, 1269-1291.
  18. Yoon JE and Hwang SY (2015). Integer-valued GARCH models for count time series: case study, Korean Journal of Applied Statistics, 28, 115-122.
  19. Zhang X, Liu Y, Yang M, et al. (2013). Comparative study of four time series methods in forecasting typhoid fever incidence in China, PLoS ONE, 8, e63116.
  20. Zhu F (2011). A negative binomial integer-valued GARCH model, Journal of Time Series Analysis, 32, 54-67.
  21. Zhu F (2012). Modeling overdispersed or underdispersed count data with generalized Poisson integer-valued GARCH models, Journal of Mathematical Analysis and Applications, 389, 58-71.