Topics in Control. 1. State Variable Approach to Time Series Representation and Forecasting.
Abstract
The state variable approach to modelling discrete linear dynamic-stochastic systems is discussed and related to that using transfer function and autoregressive-integrated-moving-average (ARIMA) models. It is shown that the standard form of the state variable model using two independent Gaussian noise vectors which is used extensively in the literature is not a parsimonious representation (i.e., one that is efficient in its use of parameters) but that it can always be written in a more parsimonious form employing a single Gaussian noise vector. Several such parsimonious state representations are given for the general transfer function-ARIMA model. The Kalman filter for estimating the state vector is derived using a Bayesian argument and its use in time series forecasting and its relationship to recursive least squares are discussed. (Author Modified Abstract)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1972
- Accession Number
- AD0757573
Entities
People
- John F. Macgregor
Organizations
- University of Wisconsin–Madison