lec17 - MIT OpenCourseWare http://ocw.mit.edu 14.384 Time...

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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 14.384 Time Series Analysis Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . Estimating Cointegration Relationships 1 14.384 Time Series Analysis, Fall 2007 Professor Anna Mikusheva Paul Schrimpf, scribe Novemeber 6, 2007 Lecture 17 Cointegration Estimating Cointegration Relationships Suppose y 1 t and y 2 t are cointegrated, i.e. y 2 t- y 1 t = u 2 t y 1 t = u 1 t Case 1 u 1 t u 2 t iid with zero mean and uncorrelated, V = 1 1 . We went over this case last R W dW time. We saw that estimated by OLS of y on y 1 is super consistent with T ( - ) 1 2 2 and R W 2 1 dt t R W 1 dW 2 W 2 = N (0 , 1), where W = 1 is a standard two dimensional Brownian motion (that is, W R W 1 dt W 1 2 and W 2 are independent). u 1 t 1 Case 2 iid u 2 t N (0 , 1 ). Then we can write u 2 t = u 1 t + p 1- 2 e t where e t and u 1 t are iid 1 1 . The functional central limit theorem implies: 1 [ T ] T X e =1 u 1 t t t W = W 1 W 2 Now consider the OLS estimate of . We have 1 T ( - ) = t T y 1 u 2 t 1 2 T 2 y 2 t 1 = 1 t T...
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lec17 - MIT OpenCourseWare http://ocw.mit.edu 14.384 Time...

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