A p-Order signed integer-valued autoregressive (SINAR(p)) model

Abstract

International audienceIn this article, we propose an extension of integer-valued autoregressive INAR models. Using a signed version of the thinning operator, we define a larger class of -valued processes, called SINAR, which can have positive as well as negative correlations. Using a Markov chain method, conditions for stationarity and the existence of moments are investigated. In particular, it is shown that the autocorrelation function of any real-valued AR process can be recovered with a SINAR process, which improves INAR modeling

On some distributions arising from a generalized trivariate reduction scheme

“…It is understood that the counting sequences associated to each operator are mutually independent. Note that the above operator is none other than a particular case of the signed thinning operator, for details please see Latour and Truquet (2008) and Kachour and Truquet (2011). On the other hand, one can see the operator as a generalization of the random walk on Z, where the number of steps is also an non-negative integer-valued random variable.…”

Thinning-based models in the analysis of integer-valued time series: a review

“…The signed binomial thinning operator of Kim and Park (2008) has been generalized in many ways. Kachour and Truquet (2011), e.g., define the generalized signed thinning operator as…”

Intraday Stochastic Volatility in Discrete Price Changes: The Dynamic Skellam Model

“…A very different approach to observations in Z is related to integer autoregressive (INAR) models. Barreto-Souza and Bourguignon (2015), Zhang, Wang, andZhu (2009), Freeland (2010), Kachour and Truquet (2010), Alzaid and Omair (2014), and Andersson and Karlis (2014) all proposed extensions to the INAR model to enable the treatment of variables in Z. These models are relatively simple to analyze as closed-form expressions for the likelihood are available.…”