Real count data time series often show an excessive number of zeros, which can form quite different patterns. We develop four extensions of the binomial autoregressive model for autocorrelated counts with a bounded support, which can accommodate a broad variety of zero patterns. The stochastic properties of these models are derived, and ways of parameter estimation and model identification are discussed. The usefulness of the models is illustrated, among others, by an application to the monetary policy decisions of the National Bank of Poland.
Binomial distribution Count data time series Hidden Markov model Markov model Zero inflation
Mathematics Subject Classifications (2010)
62M10 91B70 60G10 60J10
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The authors thank the referee for carefully reading the article and for the comments, which greatly improved the article. H.-Y. Kim’s study is supported by the project “Small & Medium Business Administration” under Project S2312692 “Technological Innovation Development Business” for the innovative company in the year 2015. Main parts of this research were completed while H.-Y. Kim stayed as a guest professor at the Helmut Schmidt University in Hamburg.
Barreto-Souza W (2015) Zero-modified geometric INAR(1) process for modelling count time series with deflation or inflation of zeros. J Time Ser Anal 36(6):839–852MathSciNetCrossRefzbMATHGoogle Scholar
Billingsley P (1961) Statistical inference for Markov processes. Statistical research monographs, University of Chicago PressGoogle Scholar
Emiliano PC, Vivanco MJF, De Menezes FS (2014) Information criteria: how do they behave in different models? Comput Stat Data Anal 69:141–153MathSciNetCrossRefGoogle Scholar
Jung RC, Kukuk M, Liesenfeld R (2006) Time series of count data: modelling and estimation and diagnostics. Comput Stat Data Anal 51(4):2350–2364CrossRefzbMATHGoogle Scholar
McKenzie E (1985) Some simple models for discrete variate time series. Water Resour Bull 21(4):645–650CrossRefGoogle Scholar
Möller TA, Silva ME, Weiß CH, Scotto MG, Pereira I (2016) Self-exciting threshold binomial autoregressive processes. AStA Adv Stat Anal 100(4):369–400MathSciNetCrossRefGoogle Scholar
Nastić AS, Ristić MM, Miletić Ilić A (2017) A geometric time series model with an alternative dependent Bernoulli counting series. Commun Stat Theory Methods 46(2):770–785MathSciNetCrossRefzbMATHGoogle Scholar