ABSTRACT
The term “signal extraction” refers to the definition and estimation of meaningful signals that are buried in a vector of time series. In the time series literature, it often refers to the decomposition of a single time series into the sum of “structural components” named as “trend”, “cycle”, “seasonal” and “irregular”. This chapter describes a signal extraction method for a vector of time series. It explains the calculation of the deterministic component of the time series. Estimating the deterministic component is useful in many situations. For example, if the inputs are control variables, their effect on the output provides a measure of the influence of past controls. If the inputs are leading indicators, their individual influence shows how each one affects the forecasts for the time series. The initial conditions for the deterministic subsystem can be determined by assuming that they are diffuse or by computing the Generalized Least Squares estimate of a non-zero initial state, with a null covariance.
