A BAYESIAN APPROACH TO ESTIMATING AND FORECASTING ADDITIVE NONPARAMETRIC AUTOREGRESSIVE MODELS

Abstract

Abstract. We present a Bayesian approach for estimating nonparametrically an additive autoregressive model with the regression curve estimates cubic smoothing splines. Our approach is robust to innovation outliers; it can handle missing observations and produce multistep ahead forecasts. The computation is carried out using Markov chain Monte Carlo and requires O( nM ) operations where n is the sample size and M is the number of Markov chain iterations. This makes it the first exact algorithm for spline smoothing of an additive autoregressive model which can handle large data sets. The properties of the estimates and forecasts are studied empirically using simulated and real data sets.