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A seasonal binomial autoregressive process with applications to monthly rainy-days counts

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Abstract

Count time series exhibiting seasonal patterns are frequently encountered in practical scenarios. For example, the number of hospital emergency service arrivals may show seasonal behavior (Moriña et al. 2011 Stat Med 30:3125–3136). Numerous models have been proposed for the analysis of seasonal count time series with an unbounded support, yet seasonal patterns in bounded count time series, which are sometimes suffered in environmental science such as the number of monthly rainy-days and air quality level data, have not received formal attention. The contribution of this article lies in coping with the modeling challenges associated with seasonal count time series with a bounded support, which is beneficial for enhancing the applicability of environmental science data. This is achieved by introducing a seasonal structure and seasonally varying model parameters into the first-order binomial autoregressive (BAR(1)) model (McKenzie 1985 J Am Water Resour Assoc 21:645–650). The probabilistic and statistical properties, marginal distribution and some special cases of the proposed model are studied. Estimation of model parameters is conducted using the Yule-Walker, conditional least squares and maximum likelihood methods. The asymptotic normality of the estimators is also presented. To demonstrate the utility of our model in environmental data, applications are carried out on the monthly number of rainy-days in two Russian cities.

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Data will be made available on request.

References

  • Al-Osh MA, Alzaid AA (1987) First-order integer-valued autoregressive (INAR(1)) process. J Time Ser Anal 8:261–275

    Article  Google Scholar 

  • Bentarzi M, Souakri R (2023) On periodic generalized Poisson INAR(1) model. Commun Stat-Simul Comput, Forthcom. https://doi.org/10.1080/03610918.2023.2205613

    Article  Google Scholar 

  • Freeland RK, McCabe BPM (2004) Analysis of low count time series data by Poisson autoregression. J Time Ser Anal 25:701–722

    Article  Google Scholar 

  • Góuveia S, Möller TA, Weiß CH, Scotto MG (2018) A full ARMA model for counts with bounded support and its application to rainy-days time series. Stoch Env Res Risk A 32:2495–2514

    Article  Google Scholar 

  • Jahn M, Weiß CH (2024) Nonlinear GARCH-type models for ordinal time series. Stoch Env Res Risk A 38:637–649

    Article  Google Scholar 

  • Kang Y, Wang D, Yang K (2020) Extended binomial AR(1) processes with generalized binomial thinning operator. Commun Stat-Theor Methods 49:3498–3520

    Article  Google Scholar 

  • Kang Y, Wang D, Yang K (2021) A new INAR(1) process with bounded support for counts showing equidispersion, underdispersion and overdispersion. Stat Papers 62:745–767

    Article  Google Scholar 

  • Kang Y, Wang S, Wang D, Zhu F (2023) Analysis of zero-and-one inflated bounded count time series with applications to climate and crime data. TEST 32:34–73

    Article  Google Scholar 

  • Kang Y, Lu F, Wang S (2024) Bayesian analysis for an improved mixture binomial autoregressive model with applications to rainy-days and air quality level data. Stoch Env Res Risk A 38:1313–1333

  • Latour A (1997) The multivariate GINAR(\(p\)) process. Adv Appl Probab 29:228–248

    Article  Google Scholar 

  • Li H, Liu Z, Yang K, Dong X, Wang W (2023) A \(p\)th-order random coefficients mixed binomial autoregressive process with explanatory variables. Comput Stat, Forthcom. https://doi.org/10.1007/s00180-023-01396-8

    Article  Google Scholar 

  • Liu M, Li Q, Zhu F (2022a) Modeling air quality level with a flexible categorical autoregression. Stoch Env Res Risk A 36:2835–2845

  • Liu M, Zhu F, Zhu K (2022b) Modeling normalcy-dominant ordinal time series: an application to air quality level. J Time Ser Anal 43:460–478

  • Marcelo B, Klaus LPV, Valdério AR, Márton I (2016) A Poisson INAR(1) process with a seasonal structure. J Stat Comput Simul 86:373–387

    Article  Google Scholar 

  • McKenzie E (1985) Some simple models for discrete variate time series. J Am Water Resour Assoc 21:645–650

    Article  Google Scholar 

  • Möller TA, Silva ME, Weiß CH, Scotto MG, Pereira I (2016) Self-exciting threshold binomial autoregressive processes. AStA Adv Stat Anal 100:369–400

    Article  Google Scholar 

  • Möller TA, Weiß CH, Kim HY, Sirchenko A (2018) Modeling zero inflation in count data time series with bounded support. Methodol Comput Appl Probab 20:589–609

    Article  Google Scholar 

  • Monteiro M, Scotto MG, Pereira I (2010) Integer-valued autoregressive processes with periodic structure. J Stat Plann Infer 140:1529–1541

    Article  Google Scholar 

  • Moriña D, Puig P, Ríos J, Vilella A, Trilla A (2011) A statistical model for hospital admissions caused by seasonal diseases. Stat Med 30:3125–3136

    Article  Google Scholar 

  • Prezotti Filho PR, Reisen VA, Bondon P, Ispány M, Melo MM, Serpa FS (2021) A periodic and seasonal statistical model for non-negative integer-valued time series with an application to dispensed medications in respiratory diseases. Appl Math Model 96:545–558

    Article  Google Scholar 

  • Ristić MM, Popović B (2019) A new bivariate binomial time series model. Markov Processes Relat Fields 25:1–26

    Google Scholar 

  • Ristić MM, Bakouch HS, Nastić AS (2009) A new geometric first-order integer-valued autoregressive (NGINAR(1)) process. J Stat Plan Infer 139:2218–2226

    Article  Google Scholar 

  • Ristić MM, Weiß CH, Janjić AD (2016) A binomial integer-valued ARCH model. The Int J Biostat 12:20150051

    Google Scholar 

  • Scotto MG, Weiß CH, Silva ME, Pereira I (2014) Bivariate binomial autoregressive models. J Multivar Anal 125:233–251

    Article  Google Scholar 

  • Steutel FW, Van Harn K (1979) Discrete analogues of self-decomposability and stability. The Annals Probab 7:893–899

    Article  Google Scholar 

  • Tian S, Wang D, Cui S (2020) A seasonal geometric INAR process based on negative binomial thinning operator. Stat Papers 61:2561–2581

    Article  Google Scholar 

  • Weiß CH (2009) A new class of autoregressive models for time series of binomial counts. Commun Stat-Theor Methods 38:447–460

    Article  Google Scholar 

  • Weiß CH, Kim HY (2013) Binomial AR(1) processes: moments, cumulants, and estimation. Stat 47:494–510

    Article  Google Scholar 

  • Weiß CH, Kim HY (2013) Parameter estimation for binomial AR(1) models with applications in finance and industry. Stat Papers 54:563–590

    Article  Google Scholar 

  • Weiß CH, Kim HY (2014) Diagnosing and modeling extra-binomial variation for time-dependent counts. Appl Stoch Model Bus Ind 30:588–608

    Article  Google Scholar 

  • Weiß CH, Pollett PK (2012) Chain binomial models and binomial autoregressive processes. Biom 68:815–824

    Article  Google Scholar 

  • Weiß CH, Pollett PK (2014) Binomial autoregressive processes with density-dependent thinning. J Time Ser Anal 35:115–132

    Article  Google Scholar 

  • Yang K, Zhao X, Dong X, Weiß CH (2023) Self-exciting hysteretic binomial autoregressive processes. Stat Papers, Forthcom. https://doi.org/10.1007/s00362-023-01444-x

    Article  Google Scholar 

  • Zhang J, Shao S, Yang K, Dong X (2023a) A statistical study for some classes of first-order mixed generalized binomial autoregressive models. Commun Stat-Theor Methods, Forthcom. https://doi.org/10.1080/03610926.2023.2205046

  • Zhang J, Wang J, Tai Z, Dong X (2023b) A study of binomial AR(1) process with an alternative generalized binomial thinning operator. J Korean Stat Soc 52:110–129

  • Zheng H, Basawa IV, Datta S (2006) Inference for \(p\)th-order random coefficient integer-valued autoregressive processes. J Time Ser Anal 27:411–440

    Article  Google Scholar 

  • Zhu R, Joe H (2006) Modelling count data time series with Markov processes based on binomial thinning. J Time Ser Anal 27:725–738

    Article  Google Scholar 

Download references

Funding

This article is supported by National Natural Science Foundation of China (No. 12101485), China Postdoctoral Science Foundation (No. 2021M702624), Fundamental Research Funds for the Central Universities (No. xzy012024037).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, China

    Yao Kang

  2. School of Science, University of Science and Technology Liaoning, Anshan, China

    Feilong Lu

  3. School of Mathematics and Statistics, Liaoning University, Shenyang, China

    Danshu Sheng & Shuhui Wang

Authors
  1. Yao Kang
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  2. Feilong Lu
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  3. Danshu Sheng
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  4. Shuhui Wang
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Contributions

Yao Kang: main manuscript text and methodology. Feilong Lu: data curation. Danshu Sheng: software. Shuhui Wang: software and formal analysis. All authors reviewed the manuscript.

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Correspondence to Shuhui Wang.

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Kang, Y., Lu, F., Sheng, D. et al. A seasonal binomial autoregressive process with applications to monthly rainy-days counts. Stoch Environ Res Risk Assess (2024). https://doi.org/10.1007/s00477-024-02718-y

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  • DOI: https://doi.org/10.1007/s00477-024-02718-y

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