Econometrics-I-24

Econometrics-I-24 - Applied Econometrics William Greene...

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Applied Econometrics William Greene Department of Economics Stern School of Business
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Applied Econometrics 24. Time Series Data
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Modeling an Economic Time Series Observed y 0 , y 1 , …, y t ,… What is the “sample” Random sampling? The “observation window”
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Estimators Functions of sums of observations Law of large numbers? Nonindependent observations What does “increasing sample size” mean? Asymptotic properties? (There are no finite sample properties.)
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Interpreting a Time Series Time domain: A “process” y(t) = ax(t) + by(t-1) + … Regression like approach/interpretation Frequency domain: A sum of terms y(t) = Contribution of different frequencies to the observed series. (“High frequency data and financial econometrics – “frequency” is used slightly differently here.) ( ) ( ) j j j Cos t t β α + ε
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For example,… Index of Hourly Traffic Flow on L.I. Distressway HOUR 2 4 6 0 34 67 101 134 168 0 FLOW
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In parts… Index of Hourly Traffic Flow on L.I. Distressway HOUR -.63 -.21 .21 .63 1.05 -1.05 34 67 101 134 168 0 SEASON WEEK DAY U Variable
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Studying the Frequency Domain Cannot identify the number of terms Cannot identify frequencies from the time series Deconstructing the variance, autocovariances and autocorrelations Contributions at different frequencies Apparent large weights at different frequencies Using Fourier transforms of the data Does this provide “new” information about the series?
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Autocorrelation in Regression Y t = b’x t + ε t Cov(ε t , ε t-1 ) ≠ 0 Ex. RealCons t = a +
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