Bootstrap Prediction in Unobserved Component Models

One advantage of state space models is that they deliver estimates of the unobserved components and predictions of future values of the observed series and their corresponding Prediction Mean Squared Errors (PMSE). However, these PMSE are obtained by running the Kalman filter with the true parameters substituted by consistent estimates and, consequently, they do not incorporate the uncertainty due to parameter estimation. This paper reviews new bootstrap procedures to estimate the PMSEs of the unobserved states and to construct prediction intervals of future observations that incorporate parameter uncertainty and do not rely on particular assumptions of the error distribution. The new bootstrap PMSEs of the unobserved states have smaller biases than those obtained with alternative procedures. Furthermore, the prediction intervals have better coverage properties. The results are illustrate by obtaining prediction intervals of the quarterly mortgages changes and of the unobserved output gap in USA.