Chapter 14 - Time series regression and forecasting

Chapter 14 - Time series regression and forecasting -...

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12-1 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 capital for a state
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12-2 Example #1 of time series data: US rate of inflation
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12-3 Example #2: US rate of unemployment
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12-4 Why use time series data? To develop forecasting models o What will the rate of inflation be next year? To estimate dynamic causal effects o 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? o What is the effect over time on cigarette consumption of a hike in the cigarette tax Plus, sometimes you don’t have any choice… o Rates of inflation and unemployment in the US can be observed only over time.
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12-5 Time series data raises new technical issues Time lags Correlation over time ( serial correlation or autocorrelation ) Forecasting models that have no causal interpretation (specialized tools for forecasting): o autoregressive (AR) models o autoregressive distributed lag (ADL) models Conditions under which dynamic effects can be estimated, and how to estimate them Calculation of standard errors when the errors are serially correlated
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12-6 Using Regression Models for Forecasting (SW Section 14.1) Forecasting and estimation of causal effects are quite different objectives. For forecasting, o 2 R matters (a lot!) o Omitted variable bias isn’t a problem! o We will not worry about interpreting coefficients in forecasting models o External validity is paramount: the model estimated using historical data must hold into the (near) future
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12-7 Introduction to Time Series Data and Serial Correlation (SW Section 14.2) First we must introduce 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, evenly-spaced observations (for example, monthly, 1960 to 1999, no missing months) (else yet more complications. ..)
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12-8 We will transform time series variables using lags, first differences, logarithms, & growth rates
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12-9 Example : Quarterly rate of inflation at an annual rate CPI in the first quarter of 1999 (1999:I) = 164.87 CPI in the second quarter of 1999 (1999:II) = 166.03 Percentage change in CPI, 1999:I to 1999:II = 166.03 164.87 100 164.87 × = 1.16 100 164.87 × = 0.703% Percentage change in CPI, 1999:I to 1999:II, at an annual rate = 4 × 0.703 = 2.81 % (percent per year) Like interest rates, inflation rates are (as a matter of convention) reported at an annual rate.
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Chapter 14 - Time series regression and forecasting -...

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