Egész értékű idősorok alkalmazásai
Applications of integer-valued time series
Kulcsszavak:
integer-valued autoregression, binomial thinning, periodicity, seasonality, Pickup data, /, egész értékű autoregresszió, binomiális ritkítás, periodikusság, szezonalitás, Pickup adatokAbsztrakt
Periodically correlated and seasonal non-negative integer-valued autoregressive processes are investigated. A spectral criterion involving the model parameters is given for the existence and uniqueness. The structure of the mean and covariance functions of the periodically stationary distribution of the model is derived. Two infinite series representations for the process, the moving average, and the immigrant generation, are established. A real data application is presented for Pickup data.
Kivonat
Periodikusan korrelált és szezonális, nem negatív egészértékű autoregressziós folyamatokat vizsgálunk. A folyamat létezésére és egyértelműségére vonatkozóan megadunk egy, a modell paramétereit figyelembe vevő spektrális kritériumot. Levezetjük a modell periodikusan stacionárius eloszlása átlag- és kovariancia-függvényeinek szerkezetét. Meghatározzuk a folyamat két végtelen sorral való előállítását: a mozgóátlagot és a bevándorlók generációin alapulót. Bemutatunk egy valós adatalkalmazást az átvételi (Pickup) adatokra vonatkozóan.
Hivatkozások
[1] Al-Osh MA, Alzaid AA. First-order integer-valued autoregressive (INAR(1)) process. Journal of Time Series Analysis, 1987 8(3):261–275.
[2] Baek C, Davis RA, Pipiras V. Sparse seasonal and periodic vector autoregressive modeling. Computational Statistics and Data Analysis, 2017 106:103–126.
[3] Basawa IV, Lund R. Large sample properties of parameter estimates for periodic ARMA models. Journal of Time Series Analysis, 2001 22(6):651–663.
[4] Basawa IV, Lund R, Shao Q. First-order seasonal autoregressive processes with periodically varying parameters. Statistics & Probability Letters, 2004 67:299–306.
[5] Chatfield C, Prothero DL. Box-Jenkins seasonal forecasting: problems in a case-study. Journal of the Royal Statistical Society: Series A, 1973 136(3):295–315.
[6] Davis RA, Fokianos K, Holan SH, Joe H, Livsey J, Lund R. 2021. Count time series: a methodological review. Journal of the American Statistical Association 116(535):1533–1547.
[7] Filho PRP, Reisen VA, Bondon P, Ispány M, Melo MM, Serpa FS. A periodic and seasonal statistical model for non-negative integer-valued time series with an application to dispensed medications in respiratory diseases. Applied Mathematical Modelling, 2021 96:545–558.
[8] Gardner WA, Napolitano A, Paura L. Cyclostationarity: half a century of research. Signal Processing, 2006. 86(4):639-697.
[9] Hindrayanto I, Koopman SJ, Ooms M. Exact maximum likelihood estimation for non-stationary periodic time series models. Computational Statistics and Data Analysis, 2010 54:2641–2654.
[10] Hurd HL, Miamee A. Periodically Correlated Random Sequences: Spectral Theory and Practice, Vol. 355 John Wiley & Sons, Hoboken, NJ, 2007.
[11] Ispány M, Bondon P, Reisen VA, Filho PRP. Existence of a periodic and seasonal INAR process. Journal of Time Series Analysis, 2024 45:980–1005.
[12] Koopman SJ, Ooms M, Hindrayanto I. Periodic unobserved cycles in seasonal time series with an application to US unemployment. Discussion Paper No. 06-101/4. Amsterdam and Rotterdam: Tinbergen Institute, 2006. https://www.econstor.eu/handle/10419/86347.
[13] Lund R. Choosing seasonal autocovariance structures: PARMA or SARMA. In Economic Time Series: Modelling and Seasonality, Bell WR, Holan SH, McElroy TS (eds.). CRC Press, Boca Raton, 2012 63–80.
[14] Lund R, Basawa IV. Recursive prediction and likelihood evaluation for periodic ARMA models. Journal of Time Series Analysis, 2000 21(1):75–93.
[15] McKenzie E. Some simple models for discrete variate time series. Journal of the American Water Resources Association, 1985 21(4):645–650.
[16] Nguyen T-T-T, Cabani A, Cabani I, De Turck K, Kieffer M. Load prediction of parcel pick-up points: model-driven vs data-driven approaches. International Journal of Production Research, 2023 62(11):4046–4075.
[17] Pagano M. On periodic and multiple autoregressions. The Annals of Statistics, 1978 6(6):1310–1317.
[18] Shumway RH, Stoffer DS. Time Series Analysis and Its Applications With R Examples. Springer Texts in Statistics, 4th ed. Springer International Publishing, Cham, Switzerland, 2017.
[19] Vecchia AV. Periodic autoregressive-moving average (PARMA) modeling with applications to water resources. Journal of the American Water Resources Association, 1985 21(5):721–730.
[20] Weiss CH. An Introduction to Discrete-Valued Time Series. Wiley, Hoboken, NJ, 2018.
