Parametric Poisson Bifurcated Autoregressive Process: Application to Worldwide, Regional, and Peculiar Countries’ of Automobile Production

Abstract

This article introduces Bifurcated Autoregressive (BAR) process with two apart marginal distribution error terms of  w2 and w2+1 of Poisson white noises to make it Poisson Bifurcated Autoregressive (PBAR) in a parametric setting. The statistical definition of PBAR (1) process with parameters B1 and B2 that must be |B1 | and |B2 |<1 for stationary process was spelt-out. Weighted Least Squares (WLS) parameter estimation technique was adopted and the process limiting distribution was carried-out via the combination methods of martingale process and Lindeberg’s condition. Monthly automobile production in Japan, Outside Japan, America, USA, Europe, Asia, and China that approximately tantamount to worldwide, regional, and peculiar countries’ of automobile production was subjected to the PBAR process. In conclusion, Japan automobile production possessed the highest and largest error correlation (w2 , w2+1 ) of 0.6582 (65%) with first order PBAR, with B1Y(t/2) , such that B1=0.2228 of degenerated two major divisions of automobile production of Registrations and Mini-Vehicles with descendant of different brands (models).