Lecture_10

# Lecture_10 - T ime Series Course Summary Quantitative...

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Time Series Course Summary Quantitative Economics and Econometrics Sorawoot Srisuma Lecture 10

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Time Series Course Summary Relaxing (Losing) i.i.d. assumptions Under independence and identical distribution we can readily apply LLN and CLT With a time series, say f Y t g T t = 1 , we argued that iid is not an appropriate assumption We focus on the (distinct!) concepts of stationarity and weak dependence
Time Series Course Summary Stationarity There are several notions of stationarity 1. Strictly stationary The joint distribution of ( Y t 1 , . . . , Y t k ) is identical to the distribution of ( Y t 1 + m , . . . , Y t k + m ) for all m 2. Covariance (aka Second Order ) stationary Constant mean and variance across time. And, the autocovariance(or correlation) function does not depend on time, only time lag matters, i.e. γ ( j ) = Cov ( Y t , Y t j ) for all t ρ ( j ) = Corr ( Y t , Y t j ) for all t

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Time Series Course Summary Weak Dependence One way to think of this is asymptotic uncorrelatedness (or stronger - independence) In other words (for a stationary process) lim j ! Corr ( Y t , Y t j ) = 0
Time Series Course Summary Example with an AR(1) Model Recall: Y t = β 0 + β 1 Y t 1 + u

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## This note was uploaded on 01/27/2011 for the course ECON 2007 taught by Professor Srisuma during the Spring '10 term at University of London.

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Lecture_10 - T ime Series Course Summary Quantitative...

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