On an autoregressive model with time-dependent coefficients (Q1819515)

The authors treat non-stationary processes which can be described as first-order autoregressive processes whose coefficients depend on time, and discuss asymptotic properties of the least squares estimators of parameters included in the model. They assume that the autoregressive coefficient is expressed as a function of t (time parameter) and an unknown parameter vector \(\theta\), i.e., \(f_ t(\theta)\) such that \(f_ t(\theta)\) satisfies several smoothness and other conditions. After two preparing lemmas, they show that the least squares estimators of the unknown parameters (parameter vector \(\theta)\) are strongly consistent and asymptotically normal with mean vector 0 and a certain covariance matrix which is explicitly given. Finally, they give some simulation studies.