Cover
Title Page
Copyright
Contents
Preface
About the Author
Chapter 1 Difference Equations
Introduction
1 Time-Series Models
2 Difference Equations and Their Solutions
3 Solution by Iteration
Iteration without an Initial Condition
Reconciling the Two Iterative Methods
Nonconvergent Sequences
4 An Alternative Solution Methodology
The Solution Methodology
Generalizing the Method
5 The Cobweb Model
6 Solving Homogeneous Difference Equations
Stability Conditions
Higher Order Systems
7 Particular Solutions for Deterministic Processes
8 The Method of Undetermined Coefficients
Higher Order Systems
A Solved Problem
9 Lag Operators
Lag Operators in Higher Order Systems
10 Summary
Questions and Exercises
Chapter 2 Stationary Time-Series Models
1 Stochastic Difference Equation Models
2 ARMA Models
3 Stationarity
Stationarity Restrictions for an AR(1) Process
4 Stationarity Restrictions for an ARMA (p, q) Model
Stationarity Restrictions for the Autoregressive Coefficients
5 The Autocorrelation Function
The Autocorrelation Function of an AR(2) Process
The Autocorrelation Function of an MA(1) Process
The Autocorrelation Function of an ARMA(1,1) Process
6 The Partial Autocorrelation Function
7 Sample Autocorrelations of Stationary Series
Model Selection Criteria
Estimation of an AR(1) Model
Estimation of an ARMA(1, 1) Model
Estimation of an AR(2) Model
8 Box-Jenkins Model Selection
Parsimony
Stationarity and Invertibility
Goodness of Fit
Postestimation Evaluation
9 Properties of Forecasts
Higher-Order Models
Forecast Evaluation
10 A Model of the Interest Rate Spread
Out-of-Sample Forecasts
11 Seasonality
Models of Seasonal Data
Seasonal Differencing
12 Parameter Instability and Structural Change
Testing for Structural Change
Endogenous Breaks
Parameter Instability
An Example of a Break
13 Combining Forecasts
Optimal Weights
Example Using the Spread
14 Summary and Conclusions
Questions and Exercises
Chapter 3 Modeling Volatility
1 Economic Time Series: The Stylized Facts
2 ARCH and GARCH Processes
ARCH Processes
The GARCH Model
3 ARCH and GARCH Estimates of Inflation
Engle’s Model of U.K. Inflation
Bollerslev’s Estimates of U.S. Inflation
4 Three Examples of GARCH Models
A GARCH Model of Oil Prices
Volatility Moderation
A GARCH Model of the Spread
Formal Tests for ARCH Errors
Alternative Estimates of the Model
5 A GARCH Model of Risk
6 The ARCH-M Model
Implementation
7 Additional Properties of GARCH Processes
Properties of GARCH(1, 1) Error Processes
Assessing the Fit
Diagnostic Checks for Model Adequacy
Forecasting the Conditional Variance
8 Maximum Likelihood Estimation of GARCH Models
9 Other Models of Conditional Variance
The IGARCH Model
Models with Explanatory Variables
Models with Asymmetry: TARCH and EGARCH
Testing for Leverage Effects
Nonnormal Errors
10 Estimating the NYSE U.S. 100 Index
The Model of the Mean
Testing for GARCH errors
Alternative Estimates of the Model
Diagnostic Checking
The Asymmetric Models
11 Multivariate GARCH
Updating the Study
12 Volatility Impulse Responses
An Example
13 Summary and Conclusions
Questions and Exercises
Chapter 4 Models with Trend
1 Deterministic and Stochastic Trends
The Random Walk Model
The Random Walk Plus Drift Model
Generalizations of the Stochastic Trend Model
2 Removing the Trend
Differencing
Detrending
Difference versus Trend Stationary Models
Are There Business Cycles?
The Trend in Real GDP
3 Unit Roots and Regression Residuals
4 The Monte Carlo Method
Monte Carlo Experiments
Example of the Monte Carlo Method
Generating the Dickey–Fuller Distribution
5 Dickey-Fuller Tests
An Example
6 Examples of the Dickey-Fuller Test
Quarterly Real U.S. GDP
Unit Roots and Purchasing Power Parity
7 Extensions of the Dickey-Fuller Test
Selection of the Lag Length
The Test with MA Components
Multiple Roots
Seasonal Unit Roots
8 Structural Change
Perron’s Test for Structural Change
Perron’s Test and Real Output
Tests with Simulated Data
9 Power and the Deterministic Regressors
Power
Determination of the Deterministic Regressors
10 Tests with More Power
An Example
11 Panel Unit Root Tests
Limitations of the Panel Unit Root Test
12 Trends and Univariate Decompositions
The General ARIMA(p, 1,q) Model
The Hodrick–Prescott Decomposition
13 Summary and Conclusions
Questions and Exercises
Chapter 5 Multiequation Time-Series Models
1 Intervention Analysis
Estimating the Effect of Metal Detectors on Skyjackings
Estimating the Effect of the Libyan Bombing
2 ADLs and Transfer Functions
ADL Models
The Cross-Covariances of a Second-Order Process
Higher-Order Input Processes
Identification and Estimation
3 An ADL of Terrorism in Italy
4 Limits to Structural Multivariate Estimation
Multivariate Macroeconometric Models: Some Historical Background
5 Introduction to VAR Analysis
Stability and Stationarity
Dynamics of a VAR Model
6 Estimation and Identification
Forecasting
Identification
7 The Impulse Response Function
Confidence Intervals and Impulse Responses
Variance Decomposition
8 Testing Hypotheses
Granger Causality
Granger Causality and Money Supply Changes
9 Example of a Simple VAR: Domestic and Transnational Terrorism
Empirical Methodology
Empirical Results
10 Structural VARs
Structural Decompositions
11 Examples of Structural Decompositions
12 Overidentified Systems
Two Examples
13 The Blanchard-Quah Decomposition
The Blanchard and Quah Results
14 Decomposing Real and Nominal Exchange Rates: An Example
Limitations of the Technique
15 Summary and Conclusions
Questions and Exercises
Chapter 6 Cointegration and Error-Correction Models
1 Linear Combinations of Integrated Variables
2 Cointegration and Common Trends
3 Cointegration and Error Correction
The n-Variable Case
4 Testing for Cointegration: The Engle-Granger Methodology
5 Illustrating the Engle-Granger Methodology
The Engle–Granger Procedure with I(2) Variables
6 Cointegration and Purchasing Power Parity
7 Characteristic Roots, Rank, and Cointegration
8 Hypothesis Testing
Lag Length and Causality Tests
To Difference or Not to Difference
Tests on Multiple Cointegrating Vectors
The Test in the Presence of I(2) Variables
9 Illustrating the Johansen Methodology
10 Error-Correction and ADL Tests
Cointegration with Weak Exogeneity
Inference on the Cointegrating Vector
11 Comparing the Three Methods
The Engle–Granger Methodology
The Johansen Methodology
The Error-Correction Methodology
12 Summary and Conclusions
Questions and Exercises
Chapter 7 Nonlinear Models and Breaks
1 Linear Versus Nonlinear Adjustment
2 Simple Extensions of the ARMA Model
The GAR Model
The Bilinear Model
An Example
3 Testing for Nonlinearity
The ACF and the McLeod–Li Test
The RESET
Other Portmanteau Tests
Lagrange Multiplier Tests
Two Examples
Inference with Unidentified Nuisance Parameters
4 Threshold Autoregressive Models
The Basic Threshold Model
Estimation
Unknown Threshold
5 Extensions of the TAR Model
Selecting the Delay Parameter
Multiple Regimes
More on Estimating the Threshold
Threshold Regression Models
Pretesting for a TAR Model
TAR Models and Endogenous Breaks
6 Three Threshold Models
The Unemployment Rate
Asymmetric Monetary Policy
Capital Stock Adjustment with Multiple Thresholds
7 Smooth Transition Models
Pretests for STAR Models
8 Other Regime Switching Models
The Artificial Neural Network
The Markov Switching Model
9 Estimates of STAR Models
An LSTAR Model
The Real Exchange Rate as an ESTAR Process
10 Generalized Impulse Responses and Forecasting
Nonlinear Estimates of GNP Growth
Impulse Responses
Terrorist Incidents with Casualties
11 Unit Roots and Nonlinearity
An Example
12 More on Endogenous Structural Breaks
Two Examples
Nonlinear Breaks
Estimates of a Logistic Break
13 Summary and Conclusions
Questions and Exercises
Index
EULA