Article
Full entry | Fulltext not available
(moving wall
24 months)
Feedback
Keywords:
$\mathbb {Z}$-valued time series; signed thinning operator; statistical distribution on $\mathbb {Z}$; simulation; SVR-RBINAR-DDL(1); standardized Pearson residual; bootstrap; forecasting
$\mathbb {Z}$-valued time series; signed thinning operator; statistical distribution on $\mathbb {Z}$; simulation; SVR-RBINAR-DDL(1); standardized Pearson residual; bootstrap; forecasting
Summary:
The motivation for implementing this model arises from the need to analyze dependent count data that can take both positive and negative values, exhibit fluctuations around a zero mean, and demonstrate unimodal-bimodal aspects. To capture these features commonly observed in real-world applications, we propose a first-order integer-valued autoregressive process, INAR(1), with discrete double Lindley innovations. The model is constructed using a signed thinning mechanism, referred to as the relative binomial thinning operator, which extends the classical binomial thinning operator. The proposed model is appropriate for $\mathbb {Z}$-valued time series with both positive and negative dependence. The main statistical properties of the process are derived. Parameter estimation is addressed using modified conditional least squares, Yule-Walker, and conditional maximum likelihood methods, whose performance is evaluated through simulation studies. The practical relevance of the model is demonstrated using data from the Saudi stock market. Model adequacy is assessed via standardized residuals and the cumulative periodogram, and predictive performance is evaluated using a hybrid framework combining Support Vector Regression (SVR) with the proposed model, in comparison with bootstrap and classical approaches.
References:
[1] Ali, N. S. M., Mohammed, F. A.: The use of ARIMA, ANN and SVR models in time series hybridization with practical application. Int. J. Nonlinear Anal. Appl. 14 (2023), 87-102. DOI 10.22075/ijnaa.2022.7168
[2] Al-Osh, M. A., Alzaid, A. A.: First-order integer-valued autoregressive (INAR(1)) process. J. Time Ser. Anal. 8 (1987), 261-275. DOI 10.1111/j.1467-9892.1987.tb00438.x | MR 0903755 | Zbl 0617.62096
[3] Alzaid, A. A., Omair, M. A.: Poisson difference integer valued autoregressive model of order one. Bull. Malays. Math. Sci. Soc. (2) 37 (2014), 465-485. MR 3188051 | Zbl 1291.62159
[4] Barreto-Souza, W., Bourguignon, M.: A skew INAR(1) process on $\Bbb{Z}$. AStA, Adv. Stat. Anal. 99 (2015), 189-208. DOI 10.1007/s10182-014-0236-2 | MR 3328160 | Zbl 1443.62242
[5] Bourguignon, M., Vasconcellos, K. L. P.: A new skew integer valued time series process. Stat. Methodol. 31 (2016), 8-19. DOI 10.1016/j.stamet.2016.01.002 | MR 3477725 | Zbl 1487.62105
[6] Bu, R., McCabe, B.: Model selection, estimation and forecasting in INAR$(p)$ models: A likelihood-based Markov Chain approach. Int. J. Forecast. 24 (2008), 151-162. DOI 10.1016/j.ijforecast.2007.11.002
[7] Chen, H., Zhang, J., Zhu, F.: A trinomial difference autoregressive model and its applications. Stat 12 (2023), Article ID e596, 16 pages. DOI 10.1002/sta4.596 | MR 4641217 | Zbl 07858720
[8] Chesneau, C., Bakouch, H. S., Tomy, L., Veena, G.: A new discrete distribution on integers: Analytical and applied study on stock exchange and flood data. J. Stat. Manag. Syst. 25 (2022), 1899-1917. DOI 10.1080/09720510.2021.1995199
[9] Chesneau, C., Kachour, M.: A parametric study for the first-order signed integer-valued autoregressive process. J. Stat. Theory Pract. 6 (2012), 760-782. DOI 10.1080/15598608.2012.719816 | MR 3196577 | Zbl 1425.62124
[10] Cunha, E. T. da, Vasconcellos, K. L. P., Bourguignon, M.: A skew integer-valued time-series process with generalized Poisson difference marginal distribution. J. Stat. Theory Pract. 12 (2018), 718-743. DOI 10.1080/15598608.2018.1470046 | MR 3878055
[11] Davis, R. A., Fokianos, K., Holan, S. H., Joe, H., Livsey, J., Lund, R., Pipiras, V., Ravishanker, N.: Count time series: A methodological review. J. Am. Stat. Assoc. 116 (2021), 1533-1547. DOI 10.1080/01621459.2021.1904957 | MR 4309291 | Zbl 1510.62356
[12] Guerrero, M. B., Barreto-Souza, W., Ombao, H.: Integer-valued autoregressive processes with prespecified marginal and innovation distributions: A novel perspective. Stoch. Models 38 (2022), 70-90. DOI 10.1080/15326349.2021.1977141 | MR 4359301 | Zbl 1493.62525
[13] Hu, X.: Support Vector Machine and Its Application to Regression and Classification: Master's Thesis. Missouri State University, Springfield (2017).
[14] Hyndman, R. J., Koehler, A. B.: Another look at measures of forecast accuracy. Int. J. Forecast. 22 (2006), 679-688. DOI 10.1016/j.ijforecast.2006.03.001
[15] Inusah, S., Kozubowski, T. J.: A discrete analogue of the Laplace distribution. J. Stat. Plann. Inference 136 (2006), 1090-1102. DOI 10.1016/j.jspi.2004.08.014 | MR 2181990 | Zbl 1081.60011
[16] Jung, R. C., Tremayne, A. R.: Coherent forecasting in integer time series models. Int. J. Forecast. 22 (2006), 223-238. DOI 10.1016/j.ijforecast.2005.07.001
[17] Jung, R. C., Tremayne, A. R.: Convolution-closed models for count time series with applications. J. Time Ser. Anal. 32 (2011), 268-280. DOI 10.1111/j.1467-9892.2010.00697.x | MR 2808254 | Zbl 1290.62078
[18] Kachour, M.: On the rounded integer-valued autoregressive process. Commun. Stat., Theory Methods 43 (2014), 355-376. DOI 10.1080/03610926.2012.661506 | MR 3171042 | Zbl 1462.62537
[19] Kachour, M., Bakouch, H. S., Mohammadi, Z.: A new INAR(1) model for $\Bbb{Z}$-valued time series using the relative binomial thinning operator. Jahrb. Nationalökon. Stat. 243 (2023), 125-152. DOI 10.1515/jbnst-2022-0059
[20] Kachour, M., Truquet, L.: A $p$-order signed integer-valued autoregressive (SINAR$(p)$) model. J. Time Ser. Anal. 32 (2011), 223-236. DOI 10.1111/j.1467-9892.2010.00694.x | MR 2808251 | Zbl 1290.62079
[21] Kachour, M., Yao, J. F.: First-order rounded integer-valued autoregressive (RINAR(1)) process. J. Time Ser. Anal. 30 (2009), 417-448. DOI 10.1111/j.1467-9892.2009.00620.x | MR 2536061 | Zbl 1224.62060
[22] Karlsen, H., Tjøstheim, D.: Consistent estimates for the NEAR(2) and NLAR(2) times series models. J. R. Stat. Soc., Ser. B 50 (1988), 313-320. DOI 10.1111/j.2517-6161.1988.tb01730.x | MR 0964184
[23] Khoo, W. C., Ong, S. H., Atanu, B.: Coherent forecasting for a mixed integer-valued time series model. Mathematics 10 (2022), Article ID 2961, 15 pages. DOI 10.3390/math10162961
[24] Kim, H.-Y., Park, Y.: A non-stationary integer-valued autoregressive model. Stat. Pap. 49 (2008), 485-502. DOI 10.1007/s00362-006-0028-1 | MR 2399216 | Zbl 1148.62074
[25] Kiwon, F.: Frequentist Model Averaging for $\varepsilon$-Support Vector Regression: Ph.D. Thesis. McMaster University, Hamilton (2019).
[26] Lee, S., Lee, S.: Change point test for the conditional mean of time series of counts based on support vector regression. Entropy 23 (2021), Article ID 433, 17 pages. DOI 10.3390/e23040433 | MR 4252529
[27] McCabe, B. P. M., Martin, G. M.: Bayesian predictions of low count time series. Int. J. Forecast. 21 (2005), 315-330. DOI 10.1016/j.ijforecast.2004.11.001
[28] McKenzie, E.: Some simple models for discrete variate time series. JAWRA, J. Am. Water Resour. Assoc. 21 (1985), 645-650. DOI 10.1111/j.1752-1688.1985.tb05379.x
[29] Pascual, L., Romo, J., Ruiz, E.: Bootstrap predictive inference for ARIMA processes. J. Time Ser. Anal. 25 (2004), 449-465. DOI 10.1111/j.1467-9892.2004.01713.x | MR 2073232 | Zbl 1062.62199
[30] Scotto, M. G., WeiÃ, C. H., Gouveia, S.: Thinning-based models in the analysis of integer-valued time series: A review. Stat. Model. 15 (2015), 590-618. DOI 10.1177/1471082X15584701 | MR 3441230 | Zbl 07259004
[31] Steutel, F. W., Harn, K. van: Discrete analogues of self-decomposability and stability. Ann. Probab. 7 (1979), 893-899. DOI 10.1214/aop/1176994950 | MR 0542141 | Zbl 0418.60020
[32] Weiß, C. H.: Thinning operations for modeling time series of counts: A survey. AStA, Adv. Stat. Anal. 92 (2008), 319-341. DOI 10.1007/s10182-008-0072-3 | MR 2426093 | Zbl 1477.62256
[33] Yan, H., Wang, D.: Random environment $\Bbb{Z}$-valued AR(1) process with Poisson difference marginal distributions. (to appear) in Commun. Stat., Simul. Comput. DOI 10.1080/03610918.2026.2613953
[34] Zhang, H., Wang, D., Zhu, F.: Inference for INAR$(p)$ processes with signed generalized power series thinning operator. J. Stat. Plan. Inference 140 (2010), 667-683. DOI 10.1016/j.jspi.2009.08.012 | MR 2558396 | Zbl 1177.62110
[35] Zhang, H., Wang, D., Zhu, F.: Generalized RCINAR(1) process with signed thinning operator. Commun. Stat., Theory Methods 41 (2012), 1750-1770. DOI 10.1080/03610926.2010.551452 | MR 2913009 | Zbl 1270.62125
Search
Partner of
