Time‐variable parameter and trend estimation in non‐stationary economic time series

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Abstract
The paper describes a general approach to the modelling of nonlinear and nonstationary economic systems from time‐series data. This method exploits recursive state space filtering and fixed interval smoothing algorithms to decompose the time‐series into long term trend and short term ‘small perturbational’ components, each of which are then modelled by linear stochastic models which may be characterised by time variable parameters. The approach is illustrated by an example which explores the relationship between the variations in quarterly GNP and Unemployment in the USA over the period 1948 to 1988 and questions previous claims about the changes in the slope of the long term trend in loge(GNP) over this same period. The paper also points out that the recursive approach to estimation facilitates the use of these methods in the development of adaptive forecasting and control systems.

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