1

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

2

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

3

Example #2: US rate of unemployment

4

Why use time series data?

5

Time series data raises new technical issues

6

Using Regression for Forecasting

7

Time Series data & Serial Correlation

8

9

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

10

Example: U.S. CPI inflation

11

Autocorrelation

12

13

Sample autocorrelations

14

Example

15

16

Other economic time series:

17

Other economic time series, ctd:

18

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

19

First Order Autoregressive Model

20

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

21

Example: AR(1) model of inflation – STATA

22

Example: AR(1) model of inflation

23

Example: AR(1) model of inflation

24

Forecasts: terminology and notation

25

Forecast errors

26

Example: forecasting inflation using an AR(1)

27

The AR(p) model

28

Example: AR(4) model of inflation

29

Example: AR(4) model of inflation

30

Example: AR(4) model of inflation

31

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

32

So why use Inft, not Inft?

33

Autoregressive Distributed Lag (ADL) Model

34

Example: inflation and unemployment

35

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

36

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

37

Example: dinf and unem

38

39

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