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
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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
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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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Lecture_10 - T ime Series Course Summary Quantitative...

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