Prediction of continuous time processes by \(C_{[0,1]}\)-valued autoregressive process. (English) Zbl 0944.62087
Summary: In order to predict a continuous time process on an entire-time interval, we introduce the \(C_{[0,1]}\)-valued autoregressive process of first order. We show, under mild regularity conditions, the convergence almost sure of the predictor. We propose an estimator of the dimension of the projecting space of observations and illustrate the results by a numerical example.
MSC:
| 62M20 | Inference from stochastic processes and prediction |
| 60B11 | Probability theory on linear topological spaces |
| 46N30 | Applications of functional analysis in probability theory and statistics |
