Using Kalman Filter to Extract and Test for Common Stochastic Trends 1 Yoosoon Chang 2 , Bibo Jiang 3 and Joon Y. Park 4 Abstract This paper considers a state space model with integrated latent variables. The model provides an effective framework to specify, test 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, and therefore, validate the use of conventional methods of inference for our model. Moreover, we construct a trace statistic, which can be used to determine the number of common stochastic trends in a system of integrated time series. It is shown that the limit distribu- tion of the statistic is standard normal. The test is very simple to implement in practical applications. Our simulation study shows that it behaves quite well in finite samples. For an illustration, we apply our methodology to analyze the common stochastic trend in various default-free interest rates with different maturities. First Draft: Jan 13, 2006 This Version: September 24, 2008 JEL Classification: C22, C51 Key words and phrases : state space model, Kalman filter, common stochastic trends, max- imum likelihood estimation, asymptotic theory. 1 This version is prepared for the presentation at the Midwest Econometrics Conference, October 12-13, St. Louis. Chang and Park gratefully acknowledge the financial supports from the NSF under Grant No. SES-0453069/0730152 and SES-0518619, respectively. 2 Department of Economics, Texas A&M University 3 Department of Economics, Rice University 4 Department of Economics, Texas A&M University and Sungkyunkwan University