1 chapter 16 forecasting with nonlinear models: an introduction figure 16.1 time series of a setar...

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CHAPTER 16FORECASTING WITH NONLINEAR MODELS:

AN INTRODUCTION

Figure 16.1 Time Series of a SETAR Process with Two Regimes and Threshold Zero

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16.1 Nonlinear Dependence

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Figure 16.2 SETAR Process in a Regression Framework

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Figure 16.3 Unconditional Histogram of the SETAR Time Series

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Figure 16.4 Autocorrelograms of a SETAR Process

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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?

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Figure 16.6 3-Month Treasury Bill Rates

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

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Figure 16.8 Autocorrelations of a Bilinear Process

16.1.3 Nonlinearity, Correlation, and Dependence

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Figure 16.9 3-Month Treasury Bill Interest Rates (Monthly Data)

16.2.1 Threshold Autoregressive Models (TAR)

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Table 16.1 Augmented Dickey-Fuller Unit Root Test for 3-Month Treasury Bill Rates

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Table 16.2 OLS Estimation of a Two-Regime SETAR Model for 3-Month Treasury Bill

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Figure 16.10 Logistic and Exponential Transition Functions

16.2.2 Smooth Transition Models

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Figure 16.11 U.S. Industrial Production (Quarterly Growth Rates)

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Table 16.3 The Best Linear Model for U.S. Industrial Production Growth

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Table 16.4 Testing for Linearity

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Table 16.5 Testing for Linearity

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Figure 16.12 Logistic Transition Function for U.S. Industrial Production Growth

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Table 16.6 Estimation of Logistic Smooth Transition Autoregressive Model

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Figure 16.13 A Time Series of a 2-State Markov Switching Process

16.2.3 Markov Regime-Switching Models: A Descriptive Introduction

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Figure 16.14 Unconditional Density of a 2-State Markov Regime Switching Process and the Densities in Each State