Time Series Econometrics .pdf
大小:(11.36 MB)

只需: RMB 17元  马上下载

时间序列计量经济学资料，内容非常新2025，内容非常丰富，一共430多页的大型资料！
Part I Univariate Time Series Analysis
1 Introduction and Basic Theoretical Concepts ........................... 3
1.1 Some Examples ...................................................... 4
1.2 Stochastic Processes.................................................. 9
1.3 Stationarity ........................................................... 11
1.4 Construction of Stochastic Processes................................ 13
1.4.1 White Noise ................................................. 13
1.4.2 Construction of Stochastic Processes: Some Examples .. 14
1.4.3 Moving Average Process of Order One ................... 16
1.4.4 Random Walk ............................................... 17
1.4.5 Changing Expected Value .................................. 18
1.5 Properties of Autocovariance Functions ............................ 19
1.5.1 Characterization ............................................ 19
1.5.2 Autocovariance Function of MA(1) Processes............ 20
1.6 Exercises.............................................................. 21
2 Autoregressive Moving-Average Processes .............................. 23
2.1 The Lag Operator..................................................... 24
2.2 Two Important Special Cases ........................................ 25
2.2.1 Moving-Average Processes of Order q .................... 26
2.2.2 First-Order Autoregressive Process........................ 26
2.3 Causality and Invertibility ........................................... 29
2.4 Computation of the Autocovariance Function of Stationary
ARMA Processes..................................................... 36
2.4.1 First Procedure.............................................. 37
2.4.2 Second Procedure........................................... 39
2.5 Exercises.............................................................. 41
3 Forecasting Stationary Processes ......................................... 43
3.1 Linear Least-Squares Forecasts...................................... 43
3.1.1 Forecasting with an AR(p) Process ........................ 47
3.1.2 Forecasting with MA(q) Processes ........................ 48
3.1.3 Forecasting from the Infinite Past.......................... 51
3.2 Wold Decomposition Theorem ...................................... 52
3.3 The Partial Autocorrelation Function ............................... 56
3.3.1 Definition ................................................... 57
3.3.2 Interpretation of ACF and PACF........................... 59
3.4 Exponential Smoothing .............................................. 60
3.5 Exercises.............................................................. 62
4 Estimation of the Expected Value and the Autocorrelation
Function of a Stationary Stochastic Processes........................... 67
4.1 Estimation of the Expected Value ................................... 68
4.2 Estimation of Autocovariance and Autocorrelation Functions..... 73
4.3 Estimation of Partial Autocorrelation Functions.................... 78
4.4 Estimation of Long-Run Variance ................................... 80
4.4.1 An Example ................................................. 84
4.5 Exercises.............................................................. 85
5 Modeling Stationary ARMA Processes .................................. 87
5.1 The Yule-Walker Estimator .......................................... 88
5.2 The Ordinary Least-Squares (OLS) Estimator for AR Models .... 91
5.3 Maximum-Likelihood Estimation of ARMA Models .............. 93
5.4 Estimation of Orders p and q ........................................ 98
5.5 Modeling a Stochastic Process ...................................... 100
5.6 Modeling Swiss Real GDP .......................................... 102
6 Spectral Analysis and Linear Filters ..................................... 107
6.1 The Spectral Density ................................................. 108
6.2 Spectral Decomposition of a Time Series........................... 112
6.3 Periodogram and Estimation of Spectral Densities ................. 115
6.3.1 Nonparametric Estimation ................................. 115
6.3.2 Parametric Estimation ...................................... 119
6.4 Linear Time-Invariant Filters ........................................ 121
6.5 Some Important Filters............................................... 125
6.5.1 Construction of Low- and High-Pass Filters .............. 125
6.5.2 The Hodrick-Prescott Filter ................................ 127
6.5.3 Seasonal Filters ............................................. 129
6.5.4 Using Filtered Data ......................................... 130
6.6 Exercises.............................................................. 131
7 Integrated Processes........................................................ 133
7.1 Definition, Properties, and Interpretation ........................... 133
7.1.1 Long-Run Forecast ......................................... 135
7.1.2 Variance of Forecast Error ................................. 136
7.1.3 Impulse Response Function ................................ 137
7.1.4 The Beveridge-Nelson Decomposition .................... 138
7.2 OLS Estimator with Integrated Variables ........................... 141
7.3 Unit-Root Tests....................................................... 148
7.3.1 The Dickey-Fuller Test (DF-Test) ......................... 149
7.3.2 The Phillips-Perron Test (PP-Test)......................... 151
7.3.3 Unit Root Test: Testing Strategy ........................... 153
7.3.4 Examples for Unit Root Tests.............................. 155
7.4 Generalizations of Unit Root Tests .................................. 156
7.4.1 Structural Breaks in the Trend Function................... 156
7.4.2 Testing for Stationarity (KPSS Test)....................... 160
7.5 Regression with Integrated Variables................................ 161
7.5.1 The Spurious Regression Problem......................... 161
7.5.2 Cointegration ............................................... 164
7.6 Exercises.............................................................. 167
8 Models of Volatility ......................................................... 171
8.1 The GARCH(1,1) Model ............................................ 172
8.2 General Models of Volatility......................................... 179
8.3 Tests for Heteroskedasticity ......................................... 184
8.3.1 Autocorrelation of Quadratic Residuals ................... 184
8.3.2 Engle’s Lagrange-Multiplier Test .......................... 185
8.4 Estimation of GARCH(p,q) Models................................. 185
8.4.1 Maximum Likelihood Estimation.......................... 185
8.4.2 Method of Moment Estimation ............................ 188
8.5 Example: Swiss Market Index (SMI) ............................... 189
8.6 Exercises.............................................................. 195
Part II Multivariate Time Series Analysis
9 Synopsis on Empirical Macroeconomic Research ...................... 199
10 Definitions and Stationarity ............................................... 203
11 Estimation of Mean and Covariance Function .......................... 209
11.1 Estimators and Their Asymptotic Distributions .................... 209
11.2 Testing Bivariate Cross-Correlations ................................ 211
11.3 Examples for Independence Tests ................................... 213
11.4 Exercises.............................................................. 217
12 Vector Autoregressive Moving-Average Processes ...................... 219
12.1 VAR(1) Processes .................................................... 220
12.2 Representation in Companion Form................................. 222
12.3 Causal Representation................................................ 223
12.4 Computation of the Covariance Function of Causal VAR
Processes.............................................................. 225
12.5 Exercises.............................................................. 228
13 Estimation of Vector Autoregressive Models ............................ 231
13.1 Ordinary Least Squares Estimation.................................. 232
13.2 Yule-Walker Estimator ............................................... 237
13.3 Maximum Likelihood Estimation ................................... 239
13.4 Proof of the Asymptotic Normality of OLS Estimators ............ 239
13.5 Exercises.............................................................. 247
14 Forecasting with VAR Models............................................. 249
14.1 Forecasting with Known Parameters ................................ 249
14.2 Wold’s Decomposition Theorem .................................... 253
14.3 Forecasting with Estimated Parameters ............................. 253
14.4 Modeling VAR Processes ............................................ 255
14.5 Wiener-Granger Causality ........................................... 256
14.5.1 The VAR Approach......................................... 258
14.5.2 Wiener-Granger Causality and Causal Representation ... 260
14.5.3 The Cross-Correlation Approach .......................... 260
14.6 A VAR Model for the US Economy ................................. 261
15 Structural VAR (SVAR) Models .......................................... 269
15.1 Structural and Reduced Form........................................ 269
15.1.1 A Prototypical Example .................................... 269
15.1.2 Identification: The General Case........................... 272
15.1.3 Identification in the Case n = 2............................ 276
15.2 Identification via Short-Run Restrictions ........................... 277
15.3 Interpretation of VAR Models ....................................... 279
15.3.1 Impulse Response Functions............................... 279
15.3.2 Forecast Error Variance Decomposition ................... 280
15.3.3 Confidence Intervals........................................ 282
15.3.4 Example: Advertisement and Sales........................ 284
15.3.5 Example: IS-LM Model with Phillips Curve .............. 286
15.4 Identification via Long-Run Restrictions............................ 289
15.4.1 A Prototypical Example .................................... 289
15.4.2 The General Approach ..................................... 295
15.4.3 Example: Identifying Aggregate Demand and
Supply Shocks .............................................. 297
15.5 Sign Restrictions ..................................................... 299
15.6 Non-Gaussian Identification ......................................... 303
16 Cointegration................................................................ 307
16.1 A Theoretical Example............................................... 308
16.2 Cointegrated Processes............................................... 314
16.2.1 Definition ................................................... 314
16.2.2 Vector Autoregressive (VAR) and Vector Error
Correction Models (VECM) ............................... 318
16.2.3 The Beveridge-Nelson Decomposition .................... 320
16.2.4 Common Trend and Triangular Representation ........... 322
16.3 Johansen’s Test for Cointegration ................................... 324
16.3.1 Specification of Deterministic Components............... 329
16.3.2 Testing Hypotheses on Cointegrating Vectors............. 330
16.4 An Example .......................................................... 331
17 State-Space Models and the Kalman Filter .............................. 335
17.1 The State Space Model............................................... 336
17.2 Examples of State Space Models .................................... 338
17.2.1 VAR(p) Process............................................. 339
17.2.2 ARMA(1,1) Process ........................................ 339
17.2.3 ARMA(p,q) Process ........................................ 340
17.2.4 Missing Observations ...................................... 341
17.2.5 Time-Varying Coefficients ................................. 341
17.2.6 Structural Time Series Analysis ........................... 342
17.2.7 Dynamic Factor models .................................... 344
17.2.8 Real Business Cycle Model (RBC Model) ................ 346
17.3 Filtering and Smoothing ............................................. 347
17.3.1 The Kalman Filter .......................................... 349
17.3.2 The Kalman Smoother ..................................... 351
17.4 Estimation of State Space Models................................... 354
17.4.1 The Likelihood Function ................................... 354
17.4.2 Identification ................................................ 356
17.5 Examples ............................................................. 356
17.5.1 Computing Quarterly GDP from Yearly Data ............. 356
17.5.2 Structural Time Series Analysis ........................... 359
17.6 Exercises.............................................................. 360
18 Advanced Time Series Models ............................................ 363
18.1 Bayesian Time Series Models ....................................... 363
18.1.1 Preliminaries ................................................ 364
18.1.2 Bayesian Parameter Estimation ............................ 366
18.2 Structural Breaks ..................................................... 371
18.2.1 Test Methodology .......................................... 372
18.2.2 An Example ................................................. 374
18.3 Time-Varying Parameters ............................................ 375
18.4 Regime Switching Models........................................... 379
18.5 Smooth Transition and Threshold VAR Models .................... 383
Bibliography ...................................................................... 409
Index ............................................................................... 423