32_TimeSeriesB_handout

32_TimeSeriesB_handout - Time Series - II Wooldridge 11,18...

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Unformatted text preview: Time Series - II Wooldridge 11,18 73-261 Y. Kryukov CMU, Tepper School of Business November 17, 2010 Y. Kryukov (CMU) 73-261: Time Series Nov-17 1 / 14 Overview 3.2 Time series: residuals Stationary processes &MA, AR Non-stationary process &random walk: Testing: dickey fuller Fixing: di/erences Serially correlated residuals: Testing: Durbin-Watson Fixing: di/erences FGSL Y. Kryukov (CMU) 73-261: Time Series Nov-17 2 14 Stationary processes Stochastic process: x t , t = 1 , 2 , ... Process is stationary if "distribution of x t " does not depend on t . Take several points in time: t 1 , t 2 , ..., t m and a gap h & 1. Stationarity = joint distribution of ( x t 1 , x t 2 , ..., x t m ) is same that of ( x t 1 + h , x t 2 + h , ..., x t m + h ) . Covariance-stationary process: E ( x t ) = V ( x t ) = 2 Cov ( x t , x t + h ) = c h Weak dependence: c h ! 0 as h ! Y. Kryukov (CMU) 73-261: Time Series Nov-17 3 / 14 Moving Average (MA) process MA(1): x t is Moving Average of degree 1 if x t = e t + e t & 1 where e t &i.i.d. with E ( e t ) = , V ( e t ) = 2 e MA(1) is stationary: E ( x t ) = ( 1 + ) E ( e t ) = .... V ( x t ) = & 1 + 2 2 e cov ( x t , x t + 1 ) = .... cov ( x t , x t + h ) = .... if h 2 MA( M ) &Moving average of degree M : x t = e t + 1 e t & 1 + ... + M e t & M Stationary for any M Y. Kryukov (CMU) 73-261: Time Series Nov-17 4 / 14 Autoregressive (AR) process AR(1): y...
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This note was uploaded on 01/21/2011 for the course ECON 73261 taught by Professor Kyrkv during the Spring '10 term at Carnegie Mellon.

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32_TimeSeriesB_handout - Time Series - II Wooldridge 11,18...

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