Using Kalman Filter to Extract and Test for Common Stochastic Trends∗

This paper considers a state space model with integrated latent variables. The model provides an effective framework to specify, identify and extract common stochastic trends for a set of integrated time series. The model can be readily estimated by the standard Kalman filter, whose asymptotics are fully developed in the paper. In particular, we establish the consistency and asymptotic mixed normality of the maximum likelihood estimator, which validates the use of conventional methods of inference for our model. Moreover, we show that the standard information criteria are consistent and can be used to determine the number of common stochastic trends in our model. Our simulation study clearly demonstrates the relevancy of our asymptotic theory in finite samples. For illustrations, we apply our methodology to analyze common stochastic trends in the fluctuations of macroeconomic aggregates across countries and in the prices of Dow Jones Industrial Average (DJIA) component stocks. This Version: March 14, 2013 JEL Classification: C22, C51