1. 1 CHAPTER 16 FORECASTING WITH NONLINEAR MODELS: AN INTRODUCTION Figure 16.1 Time Series of a SETAR Process with Two Regimes and Threshold Zero González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 16.1 Nonlinear Dependence

2. 2 Figure 16.2 SETAR Process in a Regression Framework González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc.

3. 3 González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. Figure 16.3 Unconditional Histogram of the SETAR Time Series

4. 4 González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. Figure 16.4 Autocorrelograms of a SETAR Process

5. González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 5 Figure 16.5 U.S. Industrial Production Index (Year-to-Year Changes) 16.1.2 Is There Any Evidence of Nonlinear Dynamics in the Data?

6. 6 Figure 16.6 3-Month Treasury Bill Rates González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc.

7. 7 Figure 16.7 U.S. GNP Business Cycle with Four Regimes (Stylized Business Cycle)

8. González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 8 Figure 16.8 Autocorrelations of a Bilinear Process 16.1.3 Nonlinearity, Correlation, and Dependence

9. González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 9 Figure 16.9 3-Month Treasury Bill Interest Rates (Monthly Data) 16.2.1 Threshold Autoregressive Models (TAR)

10. González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 10 Table 16.1 Augmented Dickey-Fuller Unit Root Test for 3-Month Treasury Bill Rates

11. González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 11 Table 16.2 OLS Estimation of a Two-Regime SETAR Model for 3-Month Treasury Bill

12. González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 12 Figure 16.10 Logistic and Exponential Transition Functions 16.2.2 Smooth Transition Models

13. González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 13 Figure 16.11 U.S. Industrial Production (Quarterly Growth Rates)

14. González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 14 Table 16.3 The Best Linear Model for U.S. Industrial Production Growth

15. González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 15 Table 16.4 Testing for Linearity

16. González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 16 Table 16.5 Testing for Linearity

17. González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 17 Figure 16.12 Logistic Transition Function for U.S. Industrial Production Growth

18. González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 18 Table 16.6 Estimation of Logistic Smooth Transition Autoregressive Model

19. González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 19 Figure 16.13 A Time Series of a 2-State Markov Switching Process 16.2.3 Markov Regime-Switching Models: A Descriptive Introduction

20. González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 20 Figure 16.14 Unconditional Density of a 2-State Markov Regime Switching Process and the Densities in Each State