Ch. 1 Difference Equations 1
1 Time-Series Models 2
2 Difference Equations and Their Solutions 7
3 Solution by Iteration 10
4 An Alternative Solution Methodology 16
5 The Cobweb Model 20
6 Solving Homogeneous Difference Equations 25
7 Finding Particular Solutions for Determimstic Processes 35
8 The Method of Undetermined Coefficients 38
9 Lag Operators 45
10 Forward-Versus Backward-Looking Solutions 48
Ch. 2 Stationary Time-Series Models 63
1 Stochastic Difference Equation Models 63
2 ARMA Models 67
3 Stationarity 68
4 Stationarity Restrictions for an ARMA(p, q) Model 72
5 The Autocorrelation Function 78
6 The Partial Autocorrelation Function 82
7 Sample Autocorrelations of Stationary Series 86
8 Box-Jenkins Model Selection 95
9 The Forecast Function 99
10 A Model of the WPI 106
11 Seasonality 111
Ch. 3 Modeling Economic Time Series: Trends and Volatility 135
1 Economic Time Series: The Stylized Facts 135
2 ARCH Processes 139
3 ARCH and GARCH Estimates of Inflation 149
4 Estimating a GARCH Model of the WPI: An Example 152
5 A GARCH Model of Risk 156
6 The ARCH-M Model 158
7 Maximum Likelihood Estimation of GARCH and ARCH-M Models 162
8 Deterministic and Stochastic Trends 166
9 Removing the Trend 176
10 Are There Business Cycles? 181
11 Stochastic Trends and Univariate Decompositions 185
Ch. 4 Testing for Trends and Unit Roots 211
1 Unit Root Processes 212
2 Dickey-Fuller Tests 221
3 Extensions of the Dickey-Fuller Tests 225
4 Examples of the Augmented Dickey-Fuller Test 233
5 Phillips-Perron Tests 239
6 Structural Change 243
7 Problems in Testing for Unit Roots 251
Ch. 5 Multiequation Time-Series Models 269
1 Intervention Analysis 270
2 Transfer Function Models 277
3 Estimating a Transfer Function 286
4 Limits to Structural Multivariate Estimation 291
5 Introduction to VAR Analysis 294
6 Estimation and Identification 300
7 The Impulse Response Function 305
8 Hypothesis Testing 312
9 Example of a Simple VAR: Terrorism and Tourism in Spain 316
10 Structural VARs 320
11 Examples of Structural Decompositions 324
12 The Blanchard and Quah Decomposition 331
13 Decomposing Real and Nominal Exchange Rate Movements: An Example 338
Ch. 6 Cointegration and Error-Correction Models 355
1 Linear Combinations of Integrated Variables 356
2 Cointegration and Common Trends 363
3 Cointegration and Error Correction 365
4 Testing for Cointegration: The Engle-Granger Methodology 373
5 Illustrating the Engle-Granger Methodology 377
6 Cointegration and Purchasing-Power Parity 381
7 Characteristic Roots, Rank, and Cointegration 385
8 Hypothesis Testing in a Cointegration Framework 393
9 Illustrating the Johansen Methodology 396
10 Generalized Purchasing-Power Parity 400
Statistical tables A. Empirical Distributions of the [tau] Statistics 419
Statistical tables B. Empirical Distributions of the [phi] Statistics 420
Statistical tables C. Empirical Distributions of the [lambda[subscript max]] and [lambda[subscript trace]] Statistics 421
References 423
Author Index 427
Subject Index 429