Introduction to Time Series Regression and Forecasting (SW Chapter 14)

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Introduction to Time Series Regression and Forecasting(SW Chapter 14)

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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

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Example #2: US rate of unemployment

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Why use time series data?

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Time series data raises new technical issues

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Using Regression for Forecasting

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Time Series data & Serial Correlation

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Example: Quarterly rate of inflation at an annual rate (U.S.)

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Example: U.S. CPI inflation

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Autocorrelation

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Sample autocorrelations

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Example

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Other economic time series:

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Other economic time series, ctd:

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Stationarity: a key requirement for external validity of time series regression

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First Order Autoregressive Model

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Example: AR(1) model of the change in inflation

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Example: AR(1) model of inflation – STATA

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Example: AR(1) model of inflation

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Example: AR(1) model of inflation

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Forecasts: terminology and notation

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Forecast errors

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Example: forecasting inflation using an AR(1)

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The AR(p) model

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Example: AR(4) model of inflation

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Example: AR(4) model of inflation

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Example: AR(4) model of inflation

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Digression: we used Inf, not Inf, in the AR’s. Why?

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So why use Inft, not Inft?

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Autoregressive Distributed Lag (ADL) Model

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Example: inflation and unemployment

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The empirical U.S. “Phillips Curve,” 1962 – 2004 (annual)

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The empirical (backwards-looking) Phillips Curve, ctd.

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Example: dinf and unem

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Example: ADL(4,4) model of inflation & Granger causality test