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# ie_Slide10 - Introductory Econometrics ECON2206/ECON3209...

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Introductory Econometrics ECON2206/ECON3209 Slides10 Rachida Ouysse ie_Slides10 School of Economics, UNSW 1

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10. Regression Analysis with Time Series Data (Ch10) 10. Regression with Time Series Data • Lecture plan Having built a foundation for regression analysis, we look at how to analyse time series data. y – Nature of time series data ime series regression examples Time series regression examples – Properties of OLS for time series regressions rend and seasonality Assumptions of cross sectional regression Trend and seasonality MLR1: linear model; MLR2: random sample; MLR3: no colinearity; MLR4: zero conditional mean; MLR5: homoskedasticity; MLR6: normality. ie_Slides10 School of Economics, UNSW 2 Are they suitable for time series data/model?
10. Regression Analysis with Time Series Data (Ch10) • The nature of times series data – Features of time series data • Observations have temporal ordering (time-indexed). • The past and present may affect the future. Variables may have serial correlation or autocorrelation. eg. Next quarter’s inflation is likely correlated with inflation istory available today history available today. • Variables may have trends and seasonality. Seasonality depends on data frequency. – Time series viewed as stochastic process (SP) SP is a random variable indexed by time, aka, time series process . • An observed time series is one realisation of a SP. ie_Slides10 School of Economics, UNSW 3

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10. Regression Analysis with Time Series Data (Ch10) • The nature of times series data eg. US annual inflation and unemployment rate Time Series Plots 51 0 nflation I 9 5678 Unemploymen t 34 1950 1960 1970 1980 1990 2000 ie_Slides10 School of Economics, UNSW 4 Time
10. Regression Analysis with Time Series Data (Ch10) • Examples of time series regression – Static models • A static model describe the relationship among contemporaneous variables. eg. Static Phillips curve: inf t = β 0 + β 1 unem t + u t may be used to study the contemporaneous trade-off etween fl tion and nem loyment between infl ation and unem ployment. – Finite distributed lag (FDL) models • A FDL model allows the lags of one or more variables to affect the dependent variable: y t = α 0 + δ 0 z t + δ 1 z t- 1 +...+ δ q z t-q + u t which is called an FDL of order q . ie_Slides10 School of Economics, UNSW 5

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10. Regression Analysis with Time Series Data (Ch10) • Examples of time series regression – Finite distributed lag (FDL) models When t = 1, our convention is that the initial values •FDL ( q ) model: y t = α 0 + δ 0 z t + δ 1 z t- 1 +...+ δ q z t-q + u t . { z 0 , z -1 ,..., z 1-q } are in the sample. • The partial effect of z t-j on y t is δ j , j = 0, 1, . .., q (holding everything else fixed). • The lag distribution is (a plot of) δ j as a function of j , while δ 0 is called the impact propensity ( multiplier ). hen there is a permanent one nit shift in t • When there is a permanent one-unit shift in z at t , ie, Δ z s = 0 for s < t and Δ z s = 1 for s t , e eventual effect on ( + known as the eventual effect on y is ( δ 0 + δ 1 +...+ δ q ), known as the long-run propensity ( multiplier ).
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ie_Slide10 - Introductory Econometrics ECON2206/ECON3209...

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