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Unformatted text preview: Time Series Regression I (Fall 2010) Lecture 22 Seyhan Erden Arkonac, PhD Problem Set 9 is (last one ) is posted. It is due on Tuesday, Dec. 7 th . 1 2 Introduction to Time Series Regression and Forecasting (SW Chapter 14) Time series data are data collected on the same observational unit at multiple time periods • Aggregate consumption and GDP for a country (for example, 20 years of quarterly observations = 80 observations) • Yen/$, pound/$ and Euro/$ exchange rates (daily data for 1 year = 365 observations) • Cigarette consumption per capita in a state, by year 3 Example #1 of time series data: US rate of price inflation, as measured by the quarterly percentage change in the Consumer Price Index (CPI), at an annual rate 4 Example #2: US rate of unemployment 5 Why use time series data? • To develop forecasting models • What will the rate of inflation be next year? • To estimate dynamic causal effects • If the Fed increases the Federal Funds rate now, what will be the effect on the rates of inflation and unemployment in 3 months? in 12 months? • What is the effect over time on cigarette consumption of a hike in the cigarette tax? • Or, because that is your only option … • Rates of inflation and unemployment in the US can be observed only over time! 6 Time series data raises new technical issues • Time lags • Correlation over time ( serial correlation , a.k.a. autocorrelation ) • Forecasting models built on regression methods: • autoregressive (AR) models • autoregressive distributed lag (ADL) models • need not (typically do not) have a causal interpretation • Conditions under which dynamic effects can be estimated, and how to estimate them • Calculation of standard errors when the errors are serially correlated 7 Using Regression Models for Forecasting (SW Section 14.1) • Forecasting and estimation of causal effects are quite different objectives. • For forecasting, • 2 R matters (a lot!) • Omitted variable bias isn’t a problem! • We will not worry about interpreting coefficients in forecasting models • External validity is paramount: the model estimated using historical data must hold into the (near) future 8 Introduction to Time Series Data and Serial Correlation (SW Section 14.2) First, some notation and terminology. Notation for time series data • Y t = value of Y in period t . • Data set: Y 1 ,…, Y T = T observations on the time series random variable Y • We consider only consecutive, evenlyspaced observations (for example, monthly, 1960 to 1999, no missing months) (missing and nonevenly spaced data introduce technical complications) 9 We will transform time series variables using lags, first differences, logarithms, & growth rates 10 Example : Quarterly rate of inflation at an annual rate (U.S.) CPI = Consumer Price Index (Bureau of Labor Statistics) • CPI in the first quarter of 2004 (2004:I) = 186.57 • CPI in the second quarter of 2004 (2004:II) = 188.60 • Percentage change in CPI, 2004:I to 2004:II...
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This note was uploaded on 11/10/2011 for the course ECON 3142 taught by Professor Arkonac during the Spring '11 term at Columbia.
 Spring '11
 Arkonac
 Econometrics

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