Prediction of Noisy ARIMA Time Series via Butterworth Digital Filter

Abstract

The problem of predicting noisy time series, realization of processes of the type ARIMA (Auto Regressive Integrated Moving Average), is addressed in the framework of digital signal processing in conjunction with an iterative forecast procedure. Other than Gaussian random noise, deterministic shocks either superimposed to the signal at hand or embedded in the ARIMA excitation sequence, are considered. Standard ARIMA forecasting performances are enhanced by pre-filtering the observed time series according to a digital filter of the type Butterworth, whose cut-off frequency, iteratively determined, is the minimizer of a suitable loss function. An empirical study, involving computer generated time series with different noise levels, as well as real-life ones (macroeconomic and tourism data), will also be presented.