forecasting_lecture_06

forecasting_lecture_06 - 1 Lecture Notes 6 1....

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Unformatted text preview: 1 Lecture Notes 6 1. Autocorrelation (or Serial Correlation) 1. Definition A problem usually for time series data The error terms, u t , are supposed to be random However, they are related by time The error terms are correlated Using the covariance term, then j i for u u Cov j i The correlation between u t and u t-r is called an autocorrelation of order r. Usually econometricians use k, but then it is confusing Could result from the impact of a missing x variable Parameters estimates are unbiased, but estimated standard errors are biased. F and t-statistics are invalid t kt k t t t u X X X Y 3 3 2 2 1 If you plot the residuals, then 2 Autocorrelation of degree 1 is very common Denoted AR(1) t kt k t t t u X X X Y 3 3 2 2 1 Where t t t v u u 1 Rho, , is between -1 and 1 v is error term Covariance function shows how two variables vary together Correlation comes from this function Y E Y X E X E Y X Cov , (i) If X = Y, then this becomes the variance for X X Var X E X E X E X X E X E X X Cov 2 , (ii) Remember, E(X) is the expected value and average (iii) Remember, E(u t ) = E(u t-1 ) = 0 Autocorrelated error terms are still equal to zero on average 1 1 1 1 , t t t t t t t t u u E u E u u E u E u u Cov 3 I can pull out (i.e. factor) the rho from the expression and t t t v u u...
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forecasting_lecture_06 - 1 Lecture Notes 6 1....

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