Rates of convergence to steady state for the linear growth version of a dynamic linear model (DLM)

The use of dynamic linear models and structural models for time series analysis and forecasting requires some form of initial conditions to commence the Kalman filter recursions. It is known that eventually a steady state is reached which is independent of prior knowledge. This paper is concerned with the rate of approach to steady state for the practically important ‘linear growth model’. Aspects of forecasting in the transient period are also included. Numerical results suggest that there is significant influence of the start on rates of convergence to steady state particularly for (i)high signal-to-noise variance ratios of the trend component, and (ii)the presence of initial covariance between the level and trend components.