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Unformatted text preview: 10. Basic Regressions with Times Series Data 10.1 The Nature of Time Series Data 10.2 Examples of Time Series Regression Models 10.3 Finite Sample Properties of OLS Under Classical Assumptions 10.4 Functional Form, Dummy Variables, and Index Numbers 10.5 Trends and Seasonality 10.1 Nature of Time Series Time series data is any data that follows one observation (location, person, etc) over timetemporal ordering is very important for time series data (higher observations correspond to more recent data)this is due to the fact that the past can affect the future but not the other way aroundrecall that for crosssectional data ordering was of little importancea sequence of random variables indexed by time is call a STOCHASTIC (random) PROCESS or TIME SERIES PROCESS 10.1 Random Time Series How is time series data considered to be random? 1) We dont know the future. 2) There are a variety of variables that impact the future. 3) Future outcomes are thus random variables.Each data point is one possible outcome, or realizationIf certain conditions were different, the realization could have been differentbut we dont have a time machine to go back in time and obtain this realization 10.2 Time Series RegressionsThe simplest time series model, closest to cross sectional models, is a STATIC MODEL relating two variables y and z: (10.1) ..., 2 , 1 , 1 n t u z y t t t = + + = this equation models a contemporaneous relationship between y and zhere a change in z has an IMMEDIATE effect on yfor example, if eating chocolate each day made one (un)happy: t t t u chocolate U + + = 1 10.2 Time Series RegressionsIf one or more variables affect our y variable in time periods after the current period, we have a FINITE DISTRIBUTED LAG (FDL) MODEL: t t t t t u z z z y + + + + + = ......
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 Spring '09
 Priemaza
 Econometrics

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