On a periodic negative binomial SETINAR model. Issue 3 (4th March 2023)

• Record Type: Journal Article
• Authors: Manaa, Abderrahmen; Bentarzi, Mohamed
• Is Part Of: Communications in statistics. Volume 52:Issue 3(2023)
• Page Start: 569
• Page End: 595
• Publication Date: 2023-03-04
• Subjects: Periodically correlated integer-valued process -- Periodic NBSETINAR model -- Strictly periodically stationary model; 62F12 -- 62M10; Mathematical statistics -- Periodicals; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5
• DOI: 10.1080/03610918.2021.1873372
• Languages: English
• ISSNs: 0361-0918

Abstract

Abstract: In this paper, we introduce a class of periodic negative binomial self-exciting threshold integer-valued autoregressive model. The basic probabilistic and statistical properties of this class are studied. Furthermore, the existence of a high moment and the strict periodic stationarity as well as the ergodicity, are established. The periodic autocovariance structure is also considered. The Conditional Least Squares ( CLS ) and the Conditional Maximum Likelihood ( CML ) methods are applied to estimate the underlying parameters, while using the periodic adaptation of the Nested Sub-Sample Search (NeSS) algorithm, to estimate the periodic threshold parameter. The asymptotic properties of the estimators are obtained. The performance of the CLS and the CML are compared through an intensive simulation study. An application on a real data set is provided.