Forecasting with the damped trend model using the structural approach

The damped trend model is a strong benchmark for time series forecasting. This model is usually estimated by adopting the innovations approach rather than the structural one, since the latter is more complex, requiring the use of the Kalman filter. In this paper, we introduce a simple method for estimating the damped trend using the structural approach. The proposed method relies on the analytical solution to the algebraic Riccati equation for the covariance matrix of the state vector’s estimation error. The solution fully simplifies both the Kalman filter recursions and the likelihood evaluation. The likelihood evaluation using the proposed method actually becomes very similar to that of the innovations approach. Moreover, the solution facilitates the smoothing of the state vector, which is crucial for signal extraction. A Monte Carlo simulation shows that both innovations and structural approaches have a similar out-of-sample forecasting performance. This is also confirmed empirically by working with the annual time series from the M3-competition database and with quarterly time series on total credit to the non-financial sector relative to GDP published by the Bank for International Settlements.