Parameter estimation in a stationary autoregressive process with correlated multiple observations

Abstract

An autoregressive process is proposed to model time series data with multiple observations at each time point. The joint autocorrelation function for the model has a product form, the first factor being the autocorrelation function for a stationary AR( p) process and the second factor involving a constant intraclass correlation ρ. The least-squares and the Gaussian maximum likelihood estimators of the autoregression parameters θ=( θ 1,…, θ p ) T and the intraclass correlation ρ are presented and their limit distributions are derived.