Using Kalman Filter to Extract and Test for Common Stochastic Trends1
نویسندگان
چکیده
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 likelihood ratio test to determine the number of common stochastic trends in a system of integrated time series. The asymptotic distribution of the test statistic is also derived as standard chi-square. First Draft: Jan 13, 2006 This Version: October 4, 2007 JEL Classification: C22, C51
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