DOI QR코드

DOI QR Code

Bootstrap Confidence Intervals for the INAR(p) Process

Kim, Hee-Young;Park, You-Sung

  • 발행 : 2006.08.31

초록

The distributional properties of forecasts in an integer-valued time series model have not been discovered yet mainly because of the complexity arising from the binomial thinning operator. We propose two bootstrap methods to obtain nonparametric prediction intervals for an integer-valued autoregressive model : one accommodates the variation of estimating parameters and the other does not. Contrary to the results of the continuous ARMA model, we show that the latter is better than the former in forecasting the future values of the integer-valued autoregressive model.

키워드

Stationary process;Integer valued time series;Prediction interval;Sieve Bootstrap

참고문헌

  1. Alzaid, A.A. and Al-Osh, M. (1990). An integer-valued pth-order autoregressive structure (INAR(p))process. Journal of Applied Probability, Vol. 27, 314-324
  2. Alonso, A.M., Pena, D. and Romo, J (2002). Forecasting time series with sieve bootstrap. Journal of Statistical Planning and Inference, Vol. 100, 1-11 https://doi.org/10.1016/S0378-3758(01)00092-1
  3. Al-Osh, M.A. and Alzaid, A.A. (1987). First-order integer-valued autoregressive (INAR(l)) process. Journal of Time Series Analysis, Vol. 8, 261-275
  4. Cheng, Q.S. (1999). On time reversibility of linear processes. Biometrika, Vol. 86, 483-486
  5. Cox, D.R. (1981). Statistical analysis of time series: Some recent developments. Scandinavian Journal of Statistics, Vol. 8, 93-115
  6. Du, J.-Guan and Li, Y. (1991), The integer-valued autoregressive (INAR(p)) model. Journal of Time Series Analysis, Vol. 12, 129-142 https://doi.org/10.1111/j.1467-9892.1991.tb00073.x
  7. Findley, D.F. (1986). The uniqueness of moving average representations with independent and identically distributed random variables for non -Gaussian stationary time series. Biometrika, Vol. 73, 520-521 https://doi.org/10.1093/biomet/73.2.520
  8. Freeland, R.K. and McCabe, B.P.M. (2004). Forecasting discrete valued low count time series. International Journal of Forecasting, Vol. 20, 427-434 https://doi.org/10.1016/S0169-2070(03)00014-1
  9. Garcia-Jurado, I., Gonzalez-Manteiga W., Prada-Sanchez, J.M., Febrero-Bande, N., Febrero-Bande, M. and Cao, R. (1995). Predicting using Box-Jenjins, nonparametric bootstrap techniques. Technometrics, Vol. 37, 303-310 https://doi.org/10.2307/1269914
  10. Grigoletto, M. (1998). Bootstrap prediction intervals for autoregression: some alternative. International Journal of Forecasting, Vol. 14, 447-456 https://doi.org/10.1016/S0169-2070(98)00004-1
  11. Grunwald, G.K., Hyndman, R.J., Tedeso, L. and Tweedie, R. L. (2000). Non-Gaussian conditional linear AR(1) models. Australian & New Zealand Journal of Statistics, Vol. 42, 479-495 https://doi.org/10.1111/1467-842X.00143
  12. Hallin, M., Lefevre, C. and Puri, M.L. (1988). On time-reversibility and the uniqueness of moving average representation for non-Gaussian stationary time series. Biometrika, Vol. 75, 170-171 https://doi.org/10.1093/biomet/75.1.170
  13. Jung, R.C. and Tremayne, A.R. (2006). Coherent forecasting m integer time series models. International Journal of Forecasting, To appear
  14. Kashiwagi, N., and Yanagimoto, T. (1992). Smoothing serial count data through a state-space model. Biometrics, Vol. 48, 1187-1194 https://doi.org/10.2307/2532709
  15. McCabe, B.P.M. and Martin, G.M. (2005). Bayesian predictions of low count time series. International Journal of Forecasting, Vol. 21, 315-330 https://doi.org/10.1016/j.ijforecast.2004.11.001
  16. McKenzie, E. (1985). Some simple models for discrete variate time series. Water Resources Bulletin, Vol. 21, 645-650 https://doi.org/10.1111/j.1752-1688.1985.tb05379.x
  17. McKenzie, E. (1988). Some ARMA models for dependent sequence of Poisson counts. Advances in Applied Probability, Vol. 20, 822-835 https://doi.org/10.2307/1427362
  18. Park, Y.S., Choi, J.W. and Kim, H.Y. (2006). Forecasting Cause-Age specific mortality using two random processes. Journal of American Statistical Association, Vol. 101, 472-483
  19. Park, Y.S. and Kim, H.Y. (2000). On the autocovariance function of INAR(l) process with a negative binomial or a poisson marginal. Journal of the Korean Statistical Society, Vol. 29, 269-284
  20. Silva, M.E. and Oliveira, V.L. (2005). Difference equations for the higher order moments and cumulants of the INAR(p) model. Journal of Time Series Analysis, Vol. 26, 17-36 https://doi.org/10.1111/j.1467-9892.2005.00388.x
  21. Stine, R.A. (1987). Estimating properties of autoregressive forecasts. Journal of American Statistical Association. Vol. 82, 1072-1078 https://doi.org/10.2307/2289383
  22. Sueutel, F.W. and Van Ham, K. (1979). Discrete analogues of self-decomposability and stability. The Annals of Probability, Vol. 7, 893-899 https://doi.org/10.1214/aop/1176994950
  23. Thombs, L.A. and Schucany, W.R. (1990). Bootstrap prediction intervals for autoregression. Journal of the American Statistical Association, Vol. 85, 486-492 https://doi.org/10.2307/2289788
  24. Latour, A. (1998). Existence and stochastic structure of non-negative inter-valued autoregressiive processes. Journal of Time Series Analysis, Vol. 19, 439-455
  25. Pacual, L., Romo, J. and Ruiz, E. (2004). Bootstrap predictive inference for ARIMA processes. Journal of Time Series Analysis, Vol. 25, 449-465
  26. Kim, H.Y. and Park, Y.S. (2006). Prediction mean sqaured error of the Poisson INAR(1) process with estimated parameters. Journal of the Korean Statistical Society. Vol. 35, 37-47

피인용 문헌

  1. Coherent Forecasting in Binomial AR(p) Model vol.17, pp.1, 2010, https://doi.org/10.5351/CKSS.2010.17.1.027