Some advances in non‐linear and adaptive modelling in time‐series

Abstract This paper considers some recent developments in non‐linear and linear time series analysis. It consists of two main components. The first emphasizes the advances in non‐linear modelling and in Bayesian inference via the Gibbs sampler. Advantages and the usefulness of these advances are illustrated by real examples. The second component is concerned with adaptive forecasting. This shows that linear models can provide accurate forecasts provided that the parameters involved are estimated adaptively. In particular, we focus on forecasting long‐memory time series. Again, a real example is used to illustrate the results.