1 CHAPTER 7 FORECASTING WITH AUTOREGRESSIVE (AR) MODELS Figure 7.1 A Variety of Time Series Cycles González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc.

2 Figure 7.2 Deterministic Cycle González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 7.1 Cycles

3 González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. Figure 7.3 Unemployed Persons, (Seasonally Adjusted) A B C D

4 González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. Figure 7.4 Autoregressive Processes AR(1) The AR(1) Process

González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 5 Figure 7.5 Autocorrelation Functions of Covariance-Stationary AR(1) Processes

6 Figure 7.6 Time Series Plot and Autocorrelation Functions of AR(1) with Negative Parameter González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc.

7 Figure 7.7 Per Capita Income Growth (California, )

González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 8 Figure 7.8 Autoregressive Processes AR(2) AR(2) Process

González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 9 Figure 7.9 Nonstationary AR(2)

González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 10 Figure 7.10 Autocorrelation Functions of Covariance-Stationary AR(2) Processes

González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 11 Figure 7.11 U.S. Inflation Rate

González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 12 Table 7.1 Estimation Results, U.S. Inflation Rate, AR(2) Model

González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 13 Table 7.2 Multistep Forecast of U.S. Inflation Rate

González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 14 Figure 7.12 U.S. Inflation Rate, Multistep Forecast

González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 15 Figure 7.13 Number of Unemployed People Looking for Part-Time Work AR(p) Process

González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 16 Figure 7.14 Deterministic Seasonality Deterministic and Stochastic Seasonal Cycles

González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 17 Figure 7.15 Stochastic Seasonality

González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 18 Figure 7.16 Seasonal AR(1) and AR(2), Time Series Plots and Autocorrelograms Seasonal ARMA Models

González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 19 Figure 7.17 Monthly Clothing Sales in the United States. Time Series Plot and Autocorrelation Functions

González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 20 Figure 7.18 Seasonal MA(1) and MA(2), Time Series Plots and Autocorrelograms

González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 21 Figure 7.19 Monthly Changes of Private Residential Construction in U.S. (Millions of Dollars), Time Series Plot and Autocorrelograms Combining ARMA and Seasonal ARMA Models

González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 22 Table 7.3 Monthly Changes in Residential Construction. Estimation Results of AR(1) and S-AR(1) Model

González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 23 Figure 7.20 Monthly Changes in Residential Construction, Multistep Forecast