# TAMU ECMT 475 - note-7 (20 pages)

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# note-7

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## note-7

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20
School:
Texas A&M University
Course:
Ecmt 475 - Economic Forecasting
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Lecture Notes 7 Model with More Components ECMT 475 Economic Forecasting Spring 2011 Guangyi Ma Regression Models Textbook Chapter 11 So far we have studied modelling and forecasting techniques for a univariate time series Multivariate model might be more useful a variable can be explained and forecast on the history of other variables as well as their own history In the trend and seasonal components one or more variables other than the lagged y are used but they are deterministic Consider regression models yt 0 1xt et where et Correlation VS causation Endogenous VS exogenous variables Bivariate data yt xt Multivariate data yt x1t x2t xkt W N 0 2e Forecasting in Regression Models Forecast for y at h period ahead conditional on x is yT h T jxT h 0 1xT h This forecast of yT h requires knowledge of xT h This is not typically feasible We might use a forecast of x Suppose x follows an AR 1 process W N 0 2u xt xt 1 ut where ut Then we can combine the models 1xt et where et yt 0 xt xt 1 ut where ut W N 0 2e W N 0 2u to have yt 0 xt 1 t where t Here W N 0 2 1 t 1ut et If et and ut are independent then 2 Distributed Lags If instead we assume an AR q model for x then yt 1 xt 1 2 xt 2 q xt q t W N 0 2 0 A L xt 1 t where t 0 This is called a distributed lags model The coe cients can be interpretted as the e ect of x on y 1 is the immediate impact 1 q is the long run impact Distributed Lags with Lagged Dependent Variables We can also include past dynamics of y to explain itself yt yt 1 yt 1 p y t p 1 xt 1 0 B L yt 1 A L xt 1 t 0 Can use arima or regress command Forecast procedures as before q xt q t Distributed Lags with ARMA Disturbances We can further include ARMA disturbances yt t A L xt 1 t L W N 0 2 t where t L 0 Distributed lags with AR 1 disturbances is equivalent to Example yt 0 1xt 1 t t t 1 t where t W N 0 2 Most General Framework This is the so called transfer function yt C L A L xt t where t B L D L W N 0 2 All previous models can be viewed as special cases of this

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