Some Solutions to the Time Series Modeling and Prediction Problem.

Given a sample Yt, t 1,2,...,T of a zero mean stationary time series, can one speak of the modeling problem. Using prediction k-steps ahead for k 1,...,h, a specified horizon, as the aim, the time series modeling problem will be defined as determining the infinite autoregressive filter transforming the data to white noise. A finite parameter scheme is then an approximate model rather than a true model. A procedure will be described for optimally estimating the frequency transfer function ARTF of this filter by means of the frequency transfer function ARTFACT of an autogressive scheme of suitable order m. The author calls the estimator an ARTFACT since it is an Autogressive Transfer Function Approximator Converging to the Truth. In effect, a solution is offered to the problem of determining the order of finite parameter ARMA models to be fitted to stationary time series data. Author