AISM 52, 108-122

## Time-varying parameters prediction

### Carlo Grillenzoni

IUAV : University Institute of Architecture of Venice,
St. Croce 1957, 30135 Venezia, Italy

(Received February 12, 1997; revised August 31, 1998)

Abstract.
This paper develops a method of adaptive modeling that may be applied to
forecast non-stationary time series. The starting point are time-varying
coefficients models introduced in statistics, econometrics and engineering.
The basic step of modeling is represented by the
implementation of adaptive recursive estimators for tracking parameters.
This is achieved by unifying basic algorithms — such as recursive
least squares (RLS) and extended Kalman filter (EKF) — into a
general scheme and next by selecting its coefficients with the minimization
of the sum of squared prediction errors. This defines a non-linear
estimation problem that may be analyzed in the context of
the conditional least squares (CLS) theory. A numerical application on the
IBM stock price series of Box-Jenkins illustrates the method and shows its good forecasting ability.

Key words and phrases:
Conditional least squares, extended Kalman filter, IBM stock price
series, recursive least squares, time-varying parameter models.

**Source**
( TeX , DVI )