Advertisement

Model-based INAR bootstrap for forecasting INAR(p) models

  • Luisa BisagliaEmail author
  • Margherita Gerolimetto
Original paper
  • 8 Downloads

Abstract

In this paper we analyse some bootstrap techniques to make inference in INAR(p) models. First of all, via Monte Carlo experiments we compare the performances of these methods when estimating the thinning parameters in INAR(p) models; we state the superiority of model-based INAR bootstrap approaches on block bootstrap in terms of low bias and Mean Square Error. Then we adopt the model-based bootstrap methods to obtain coherent predictions and confidence intervals in order to avoid difficulty in deriving the distributional properties. Finally, we present an empirical application.

Keywords

INAR(p) models Estimation Forecast Bootstrap 

Notes

References

  1. Al-Osh MA, Alzaid AA (1987) First order integer-valued autoregressive INAR(1) process. J Time Ser Anal 8(3):261–275MathSciNetCrossRefzbMATHGoogle Scholar
  2. Al-Osh MA, Alzaid AA (1988) Integer valued moving average (INMA) process. Stat Pap 29:281–300MathSciNetCrossRefzbMATHGoogle Scholar
  3. Alzaid AA, Al-Osh MA (1990) An integer-valued ph-order autoregressive structure INAR(p) process. J Appl Probab 27:314–323MathSciNetCrossRefzbMATHGoogle Scholar
  4. Awale M, Balakrishna N, Ramanathan T (2017) Testing the constancy of the thinning parameter in a random coefficient integer autoregressive model. Stat Pap.  https://doi.org/10.1007/s00362-017-0884-x Google Scholar
  5. Bouzar N, Jayakumar K (2008) Time series with discrete semi-stable marginals. Stat Pap 49:619–635CrossRefzbMATHGoogle Scholar
  6. Bu R, McCabe B (2008) Model selection, estimation and forecasting in INAR(p) models: a likelihood-based markov chain approach. Int J Forecast 24:151–162CrossRefGoogle Scholar
  7. Bu R, McCabe B, Hadri K (2008) Maximum likelihood estimation of higher-order integer-valued autoregressive process. J Time Ser Anal 29:973–994MathSciNetCrossRefzbMATHGoogle Scholar
  8. Cao R, Febrero-Bande M, Gonzalez-Manteiga W, Prada-Sanchez J, Garcfa-Jurado I (1997) Saving computer time in constructing consistent bootstrap prediction intervals for autoregressive processes. Commun Stat Simul Comput 26:961–978MathSciNetCrossRefGoogle Scholar
  9. Cardinal M, Roy R, Lambert J (1999) On the application of integer-valued time series models for the analysis of disease incidence. Stat Med 18:2025–2039CrossRefGoogle Scholar
  10. Chatfield C (2000) Time-series forecasting. Chapman & Hall, LondonCrossRefGoogle Scholar
  11. Clements M, Kim J (2007) Bootstrap prediction intervals for autoregressive time series. Comput Stat Data Anal 51:3580–3594MathSciNetCrossRefzbMATHGoogle Scholar
  12. Clements M, Taylor N (2001) Bootstrapping prediction intervals for autoregressive models. Int J Forecast 17:247–267CrossRefGoogle Scholar
  13. Drost F, van den Akker R, Werker BJM (2009) Efficient estimation of autoregression parameters and innovation distributions for semiparametric interger-valued AR(p) models. J R Stat Soc Ser B 71:467–485CrossRefzbMATHGoogle Scholar
  14. Du JG, Li Y (1991) The integer-valued autoregressive INAR(p) model. J Time Ser Anal 12:129–142MathSciNetCrossRefzbMATHGoogle Scholar
  15. Efron B (1979) Bootstrap methods: another look at the jackknife. Ann Stat 7:1–26MathSciNetCrossRefzbMATHGoogle Scholar
  16. Freedman D (1981) Bootstrapping regression models. Ann Stat 9:1218–1228MathSciNetCrossRefzbMATHGoogle Scholar
  17. Freeland RK, McCabe BPM (2004a) Analysis of low count time series data by poisson autoregression. J Time Ser Anal 25:701–722MathSciNetCrossRefzbMATHGoogle Scholar
  18. Freeland RK, McCabe BPM (2004b) Forecasting discrete valued low count time series. Int J Forecast 20:427–434CrossRefGoogle Scholar
  19. Gelman A, Hwang J, Vehtari A (2014) Understanding predictive information criteria for bayesian models. Stat Comput 24:997–1016MathSciNetCrossRefzbMATHGoogle Scholar
  20. Jentsch C, Weiß C (2018) Bootstrapping INAR models. Bernoulli (to appear)Google Scholar
  21. Jung RC, Tremayne AR (2006) Coherent forecasting in integer time series models. Int J Forecast 22:223–238CrossRefGoogle Scholar
  22. Khoo W, Ong S, Biswas A (2017) Modeling time series of counts with a new class of inar(1) model. Stat Pap 58:393–416MathSciNetCrossRefzbMATHGoogle Scholar
  23. Kim HY, Park Y (2008) A non-stationary integer-valued autoregressive model. Stat Pap 49:485–502MathSciNetCrossRefzbMATHGoogle Scholar
  24. Kim HY, Park Y (2010) Coherent forecasting in binomial AR(p) model. Commun Stat Appl Methods 17:27–37Google Scholar
  25. Kreiss JP, Lahiri SN (2012) Bootstrap methods for time series. Time Ser Anal Methods Appl 30:3–26Google Scholar
  26. Künsch H (1989) The jackknife and the bootstrap for general stationary observations. Ann Stat 17:1217–1241MathSciNetCrossRefzbMATHGoogle Scholar
  27. Lahiri S (2003) Model-based bootstrap. Springer New York, New York, pp 199–220zbMATHGoogle Scholar
  28. Liu RY, Singh K (1992) Moving blocks jackknife and bootstrap capture weak dependence. In: LePage R, Billard L (eds) Exploring the limits of bootstrap. Wiley, New YorkGoogle Scholar
  29. Liu T, Yuan X (2013) Random rounded integer-valued autoregressive conditional heteroskedastic process. Stat Pap 54:645–683MathSciNetCrossRefzbMATHGoogle Scholar
  30. MacKinnon J, Smith A (1998) Approximate bias correction in econometrics. J Econom 85:205–230MathSciNetCrossRefzbMATHGoogle Scholar
  31. McCabe BPM, Martin GM, Harris D (2011) Efficient probabilistic forecasts for counts. J R Stat Soc 73:253–272MathSciNetCrossRefzbMATHGoogle Scholar
  32. McKenzie E (1985) Some simple models for discrete variate time series. Water Resour Bull 21:645–650CrossRefGoogle Scholar
  33. Politis DN, Romano JP, Wolf M (1999) Subsampling. Springer, New YorkCrossRefzbMATHGoogle Scholar
  34. R Core Team (2015) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, AustriaGoogle Scholar
  35. Scotto M, Weiß C, Gouveia S (2015) Thinning based models in the analysis of integer-valued time series: a review. Stat Model 15:590–618MathSciNetCrossRefGoogle Scholar
  36. Sun J, McCabe B (2013) Score statistics for testing serial dependence in count data. J Time Ser Anal 34:315–329MathSciNetCrossRefzbMATHGoogle Scholar
  37. Weiß C (2008) Thinning operations for modeling time series of counts: a survey. AStA Adv Stat Anal 92:319–341MathSciNetCrossRefGoogle Scholar
  38. Weiß C (2013) Integer-valued autoregressive models for counts showing underdispersion. J Appl Stat 40(9):1931–1948MathSciNetCrossRefGoogle Scholar
  39. Weiß C, Homburg A, Puig P (2016) Testing for zero inflation and overdispersion in INAR(1) models. Stat Pap.  https://doi.org/10.1007/s00362-016-0851-y Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of PadovaPaduaItaly
  2. 2.Department of EconomicsCa’ Foscari University VeniceVeniceItaly

Personalised recommendations