Measuring the Uncertainty of Misspecified Unobserved Components

• Activity Number: 477
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Andrew Harvey and Alejandro Federico Rodriguez*+ and Esther Ruiz
• Companies: University of Cambridge and Universidad de Concepción and Universidad Carlos III de Madrid
• Keywords: Bootstrap ; Conditional heterocedasticity ; Iintegrated random walk ; Kalman filter ; State space models ; Stationary and wild bootstrap

Abstract

In the context of time series analysis, the Kalman filter (KF) is a very powerful tool to estimate underlying components as common factors, trends, time-varying parameters etc. However, the KF requires knowledge of the true specification and parameters. This is unrealistic situation as both the specification and the parameters are often unknown. Consequently, the Prediction Mean Squared Errors (PMSE) associated with the estimated unobserved components is biased. This paper has two contributions. First, we measure the biases attributed to model misspecification in two different contexts. First, we consider the biases when measuring the uncertainty associated with the underlying trend estimated by running the Integrated Random Walk when the true model is a Random Walk plus drift model. Secondly, we consider the biases incurred when the underlying level of the Local Level Model is estimated by assuming homoscedasticity when the true model is conditionally heteroscedastic. The second contribution of this paper is to show that traditional bootstrap procedures designed to obtain the PMSE in the presence of parameter uncertainty are not able to cope with model misspecification.