Topics in Control. 1. State Variable Approach to Time Series Representation and Forecasting.
WISCONSIN UNIV MADISON DEPT OF STATISTICS
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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
- Statistics and Probability