A simple integer-valued bilinear time series model

Abstract

In this paper, we extend the integer-valued model class to give a nonnegative integervalued bilinear process, denoted by INBL(p, q, m, n), similar to the real-valued bilinear model. We demonstrate the existence of this strictly stationary process and give an existence condition for it. The estimation problem is discussed in the context of a particular simple case. The method of moments is applied and the asymptotic joint distribution of the estimators is given: it turns out to be a normal distribution. We present numerical examples and applications of the model to real time series data on meningitis and Escherichia coli infections.

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

“…sequence of non-negative, integer-valued r.v's having finite mean and variance. Doukhan et al (2006) analyzed the special INBL(1, 0, 1, 1) model…”

“…Doukhan et al (2006) and Drost et al (2008) assume that the distinct binomial thinning operators involved in (2.6) and (2.7) are independent and also independent when applied to the different random variables. Figure …”

“…As expected, when the bilinear parameter 1,1 tends to 1, bursts of large values become more obvious. Drost et al (2008) derived a condition guaranteeing the existence of a unique strictly stationary process satisfying (2.6) with finite first moment, andDoukhan et al (2006) obtained conditions to ensure that the INBL(1, 0, 1, 1) process is second-order stationary. For the bilinear model in (2.7),Drost et al (2008) also provided sufficient conditions for the Simulated sample paths from bilinear model…”

Stability analysis of the first-order periodic autoregressive diagonal bilinear model

“…Several generalizations of the original bilinear formulation have been proposed in the literature to re ect various time series features such as multivariate dependence (Stensholt and Tjøstheim [29]), change in regime (Ferrante, Fonseca and Vidoni [14], Aknouche and Rabehi [3]), spatial interaction (Dai and Billard [11]) and value discreetness (Doukhan, Latour and Oraichi [12]). A particular important extension dealing with periodic phenomena is the so-called periodic bilinear (PBL) formulation in which the parameters vary periodically over time.…”

Rejoinder on: Subsampling weakly dependent time series and application to extremes

“…Conferences now develop such preoccupations: for example, the Second international workshop on integervalued time series was organized in Protaras, Cyprus, 19-21 June 2011. Many papers also appeared, and we only cite some few of them: Ferland et al (2006), Doukhan et al (2006), Fokianos and Tjostheim (2011), Fokianos (2011), Doukhan et al (2011.…”