An integer-valued threshold autoregressive process based on negative binomial thinning

2016 ◽  
Vol 59 (3) ◽  
pp. 1131-1160 ◽  
Author(s):  
Kai Yang ◽  
Dehui Wang ◽  
Boting Jia ◽  
Han Li
Keyword(s):  
Negative Binomial ◽  
Autoregressive Process ◽  
Binomial Thinning ◽  
Threshold Autoregressive ◽  
Threshold Autoregressive Process

scholarly journals Bayesian Analysis of Multiplicative Seasonal Threshold Autoregressive Processes

2020 ◽  
Vol 43 (2) ◽  
pp. 251-284
Author(s):  
Joaquín González Borja ◽  
Fabio Humberto Nieto Sánchez
Keyword(s):  
Time Series ◽  
Autoregressive Process ◽  
Autoregressive Processes ◽  
Model Estimate ◽  
Threshold Autoregressive ◽  
Proposed Model ◽  
Threshold Autoregressive Process ◽  
Identification Stage ◽  
The Relationship ◽  
Special Case

Seasonal fluctuations are  often  found  in many  time  series.   In addition, non-linearity  and  the  relationship  with  other   time series   are  prominent behaviors  of  several,  of  such   series. In this   paper,    we  consider   the modeling  of multiplicative seasonal threshold autoregressive processes with exogenous input (TSARX), which explicitly and simultaneously incorporate multiplicative seasonality and threshold nonlinearity. Seasonality is modeled to  be  stochastic and  regime  dependent.  The  proposed model  is  a  special case  of a  threshold autoregressive process with  exogenous input  (TARX). We  develop   a   procedure  based  on  Bayesian  methods   to   identify  the model,   estimate parameters,  validate  the  model  and  calculate  forecasts. In  the identification stage   of  the  model,   we  present a  statistical test   of regime  dependent multiplicative seasonality.  The proposed methodology is illustrated with a simulated example and applied  to economic empirical data. 

scholarly journals A mixed thinning based geometric INAR(1) model

Filomat ◽  
2017 ◽  
Vol 31 (13) ◽  
pp. 4009-4022 ◽  
Author(s):  
Aleksandar Nastic ◽  
Miroslav Ristic ◽  
Ana Janjic
Keyword(s):  
Parameter Estimation ◽  
Method Of Moments ◽  
Negative Binomial ◽  
Real Life ◽  
Binomial Thinning ◽  
Conditional Least Squares ◽  
Counting Data ◽  
Parameter Estimators ◽  
Thinning Operator

In this article a geometrically distributed integer-valued autoregressive model of order one based on the mixed thinning operator is introduced. This new thinning operator is defined as a probability mixture of two well known thinning operators, binomial and negative binomial thinning. Some model properties are discussed. Method of moments and the conditional least squares are considered as possible approaches in model parameter estimation. Asymptotic characterization of the obtained parameter estimators is presented. The adequacy of the introduced model is verified by its application on a certain kind of real-life counting data, while its performance is evaluated by comparison with two other INAR(1) models that can be also used over the observed data.

A negative binomial thinning‐based bivariate INAR(1) process

2020 ◽  
Vol 74 (4) ◽  
pp. 517-537
Author(s):  
Qingchun Zhang ◽  
Dehui Wang ◽  
Xiaodong Fan
Keyword(s):  
Negative Binomial ◽  
Binomial Thinning

Estimation in an Integer-Valued Autoregressive Process with Negative Binomial Marginals (NBINAR(1))

2012 ◽  
Vol 41 (4) ◽  
pp. 606-618 ◽  
Author(s):  
Miroslav M. Ristić ◽  
Aleksandar S. Nastić ◽  
Hassan S. Bakouch
Keyword(s):  
Negative Binomial ◽  
Autoregressive Process

Negative Binomial Autoregressive Process with Stochastic Intensity

2018 ◽  
Vol 40 (2) ◽  
pp. 225-247 ◽  
Author(s):  
Christian Gouriéroux ◽  
Yang Lu
Keyword(s):  
Negative Binomial ◽  
Autoregressive Process ◽  
Stochastic Intensity

scholarly journals Estimation for random coefficient integer-valued autoregressive model under random environment

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yan Cui ◽  
Yun Y. Wang
Keyword(s):  
Random Environment ◽  
Autoregressive Model ◽  
Strong Consistency ◽  
Negative Binomial ◽  
Random Coefficient ◽  
Model Parameters ◽  
Binomial Thinning ◽  
First Order ◽  
Proposed Model ◽  
Thinning Operator

AbstractA first-order random coefficient integer-valued autoregressive model based on the negative binomial thinning operator under r states random environment is introduced. This paper derives numerical characteristics of the proposed model, establishes Yule–Walker estimators of model parameters, and discusses the strong consistency of the obtained estimators. Finally, a simulation is carried out to verify the feasibility of parameter estimation.

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