A heuristic method for estimating time-series models for forecasting. I

The aim is to develop a heuristic method for estimating time-series models for forecasting. The study consists of two parts. This one presents the analytical framework of the proposed procedure; the second will present the actual algorithm and numerical evaluations of the process. Our approach makes use of the frequency-domain theory of second-order stochastic processes to remedy several of the problems that we encounter in fitting ARIMA-type models for forecasting. Within this framework some of the problems that the present study addresses are: sample size of time series, initial estimates of the coefficients, convergence of difficult data to stable estimates, and computing time.