MATRIX FORMULAS FOR NONSTATIONARY ARIMA SIGNAL EXTRACTION

The paper provides general matrix formulas for minimum mean squared error signal extraction for a finitely sampled time series whose signal and noise components are nonstationary autoregressive integrated moving average processes+ These formulas are quite practical; in addition to being simple to implement on a computer, they make it possible to easily derive important general properties of the signal extraction filters+ We also extend these formulas to estimates of future values of the unobserved signal, and we show how this result combines signal extraction and forecasting+