Random Products and Product Auto-Regression

Hassan S. Bakouch, Miroslav M. Ristić, E. Sandhya, S. Satheesh

The operation of taking random products of random variables and the notions of infinite divisibility (ID) and stability of distributions under this operation are discussed here. Based on this stationary product auto-regressive time series models are introduced. We investigate some properties of the models, like autocorrelation function, spectral density function, multi-step ahead conditional mean and parameter estimation.