Lecture 15

Lecture 15 - Regression using time series data stationary...

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1 Regression using time series data - stationary I(0) series Procedures to be adopted depend on whether time series are stationary or nonstationary Hence we need to ‘pretest’ data using DF and ADF tests • Modelling I(0) series - ie all the series are stationary Then estimate y t = α + β x t +u t OLS estimators are unbiased and efficient It is important to distinguish between static and dynamic regression equations Dynamic equations include lagged or differenced values y t = α + β 1 x t + β 2 z t + β 3 z t-1 +u t a distributed lag y t = α + β 1 x t + β 2 z t + β 3 z t-1 + γ y t-1 +u t includes lagged value of y Equations with lagged y are known as Autoregressive Distributed Lag (ADL) equations OLS has good ‘large-sample’ properties for these Modelling nonstationary I(1) series The regression model y t = α + β x t +u t where y t is I(1), but x t is stationary, is not sensible because for trended y t E(u t ) = E(y t ) - α - β E(x t ) 0 Var(u t ) = Var(y t ) - β 2 Var(x t ) = If x t is also I(1) the trend in y t and x t can give high R 2 , and significant β , with no conceivable interpretation (eg price level and cumulated rainfall) These regressions are called ‘spurious’ regressions
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2 An example of OLS with I(1) data Relating unemployment to the deviation of GDP from
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This note was uploaded on 03/07/2012 for the course ECON 201 taught by Professor Cowell during the Spring '10 term at LSE.

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Lecture 15 - Regression using time series data stationary...

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