Empirical Economic and Financial Research (eBook)

Jan Beran is a Professor of Statistics at the University of Konstanz (Department of Mathematics and Statistics). After completing his PhD in Mathematics at the ETH Zurich, he worked at several U.S. universities and the University of Zurich. He has a broad range of interests, from long-memory processes and asymptotic theory to applications in finance, biology and musicology.Yuanhua Feng is a Professor of Econometrics at the University of Paderborn’s Department of Economics. He previously worked at the Heriot-Watt University, UK, after completing his PhD and postdoctoral studies at the University of Konstanz. His research interests include financial econometrics, time series and semiparametric modeling.Hartmut Hebbel is a Professor (emeritus) of Empirical Economic Research at the University of the Federal Armed Forces in Hamburg, Germany. He studied Mathematics at the Technische Universität Berlin and previously worked at different German universities after receiving his PhD and German PD in Statistics from the University of Dortmund. His research interests include space and time series analysis and applications of statistical methods in the natural and environmental sciences.

Foreword 8
Editorial 10
Contents 12
List of Contributors 16
Introduction 20
References 23
[Part 1:] Common References 23
[Part 2:] Selected Publications of Prof. Heiler Cited in this Chapter 23
Part I Empirical Economic Research 26
Decomposition of Time Series Using the Generalised Berlin Method (VBV) 27
1 Introduction 27
2 Components and Base Model 29
2.1 Components of an Econometric Time Series 30
2.2 Components of the Decomposition Model 31
2.2.1 Trend-Cycle (Short: Trend) 31
2.2.2 Season-Calendar (Short: Season) 31
2.2.3 Rest- and Extreme Values (Short: Rest) 32
2.3 Base Model 32
3 Estimation Principle and Solutions 33
3.1 Construction of the Estimation Principle 33
3.2 Representation of Solutions 38
3.3 Properties of Solutions 43
3.3.1 Properties of Linearity 43
3.3.2 Spline Properties 43
3.3.3 Weight Properties 44
3.3.4 Property of Interpolation 46
3.3.5 Values of Smoothness of Solutions 47
3.3.6 Empirical Coefficient of Determination 47
3.3.7 Properties of Monotonicity 48
3.3.8 Limiting Cases 49
3.3.9 Property of Iteration 51
3.4 Choice of Smoothing Parameters 52
4 Local, Moving Version 52
5 Examples for Decompositions with VBV 54
5.1 Algorithm 54
5.1.1 Parameter Settings 54
5.1.2 Truncated Functions 55
5.1.3 Vector Functions and Matrices 55
5.1.4 Intermediate Calculations 56
5.1.5 Weight Functions and Weight Matrices 56
5.1.6 Solutions for Data-Vector 56
5.2 Decomposition of Unemployment Numbers in Germany 56
5.3 Decomposition of the DAX Closings 58
References 59
Time Series Segmentation Procedures to Detect, Locate and Estimate Change-Points 62
1 Introduction 62
2 The Change-Point Problem 63
3 Segmentation Procedures to Detect, Locate, and Estimate Change-Points 64
3.1 Cusum Methods 65
3.2 Automatic Procedure Based on Parametric Autoregressive Model (Auto-PARM) 65
3.3 Automatic Procedure Based on Smooth Localized Complex EXponentials (Auto-SLEX) Functions 66
3.4 Informational Approach 67
3.5 A Proposed Procedure to Detect Changes in Mean, Variance, and Autoregressive Coefficients in AR Models 68
4 Multiple Change-Point Problem 69
5 Monte Carlo Simulation Experiments 70
5.1 Empirical Size 71
5.2 Power for Piecewise Stationary Processes 71
6 Application to a Speech Recognition Dataset 73
Conclusions 75
References 75
Regularization Methods in Economic Forecasting 77
1 Introduction 77
2 Data and Model 78
3 Regularization Methods 79
3.1 L2-Boosting 79
3.2 Lasso 80
3.3 Elastic Net 81
3.4 Generalized Path Seeking 82
3.5 Group Lasso 83
3.6 Principal Components Regression 84
3.7 Partial Least Squares Regression 85
4 Comparison of Forecasts 85
5 Results 86
6 Ensemble Methods 89
6.1 Methods 89
6.1.1 Weighted Means 90
6.1.2 Ridge-Weights 90
6.1.3 Shrinkage-Forecast 90
6.1.4 MSFE and MAFE 91
6.1.5 HLN-Test 91
6.2 Results 92
Concluding Remarks 94
References 94
Investigating Bavarian Beer Consumption 97
1 Introduction 97
2 Data 98
3 Considered Models 100
4 Results 100
5 Summary 103
References 103
The Algebraic Structure of Transformed Time Series 105
1 Introduction 105
2 Statistical Background 106
3 Algebraic Structure of the Parent Space 108
Example 1: Logarithm 109
Example 2: Box–Cox 109
Example 3: Logistic 109
Example 4: Hyperbolic Sine 110
Example 5: Distributional Transforms 110
4 Numerical Illustrations 110
5 Empirical Illustrations 113
5.1 Example 1: Square Root Transform 113
5.2 Example 2: Logistic Transform 115
6 Discussion 118
Disclaimer 119
References 119
Reliability of the Automatic Identification of ARIMA Models in Program TRAMO 121
1 Introduction 121
2 Summary of the Automatic Identification Procedure 123
2.1 The Regression-ARIMA Model 123
2.2 AMI in the Presence of Outliers 124
2.2.1 Identification of the Nonstationary Polynomial ?(B) 125
2.2.2 Identification of the Stationary ARMA Polynomials 125
3 Performance of AMI on Simulated Series 125
3.1 Simulation of the Series 125
3.2 AMI Results 127
3.2.1 Preadjustment 127
3.2.2 Model Diagnostics 133
Summary and Conclusions 135
References 136
Panel Model with Multiplicative Measurement Errors 139
1 Introduction 139
2 The Model 141
3 Estimating Equations for ? 142
4 Estimating ?2 145
5 Remarks 146
5.1 Additive Measurement Errors 146
5.2 The Within Least Squares Estimator 147
6 Simulation Study 148
7 An Empirical Example 153
Conclusion and Discussion 155
Appendix: Equivalence of GMM and LS in the Error Free Panel Model 156
References 158
A Modified Gauss Test for Correlated Samples with Application to Combining Dependent Tests or P-Values 160
1 Introduction 160
2 A Modified Gauss Test 161
3 Combining Tests or p-Values 165
4 Simulation Results 167
5 An Example 170
References 171
Panel Research on the Demand of Organic Food in Germany: Challenges and Practical Solutions 173
1 Introduction 173
2 Commercial FMCG Panels in Germany 174
3 Building Up an Information System for Organic Food and Beverages 175
4 Challenges and Solutions 177
4.1 How Can Organic Products with Bar Codes be Identified? 177
4.2 How Can Organic Products Without Bar Codes be Identified by Panel Households? 178
4.3 How Can Sales Data be Projected in Case of Missing Information on the Universe? 181
4.4 How Can Projections Based on the Different Sources be Combined to Total Market Estimates? 182
5 Applications of Panel Data for Organic Food and Beverages 184
6 Further Research Requirements 185
References 186
The Elasticity of Demand for Gasoline: A Semi-parametric Analysis 187
1 Introduction 187
2 Theory and Data 189
3 Models and Estimation Techniques 194
3.1 The Semi-parametric Model 194
3.2 Quantile Smoothing B-Splines 194
3.3 Choice of the Smoothing Parameter 195
3.4 Confidence Set 196
3.5 A Parametric Conditional Mean Model 197
4 Estimation Results 197
Conclusion 206
References 206
The Pitfalls of Ignoring Outliers in Instrumental Variables Estimations: An Application to the Deep Determinantsof Development 208
1 Introduction 208
2 Classical IV Estimator 209
3 Robust IV Estimator 211
4 Alternative Robust IV Estimators and Monte Carlo Simulations 213
4.1 Alternative Robust IV Estimators 213
4.2 Monte Carlo Simulations 215
5 Empirical Example: The Deep Determinants of Development 220
Conclusion 225
References 225
Evaluation of Job Centre Schemes: Ideal Types Versus Statistical Twins 227
1 Problem 227
2 Determination of Twins by Propensity Score Matching 228
3 Cox Regression and Ideal Types 230
4 Application of the Two Methods 232
References 233
The Precision of Binary Measurement Methods 235
1 Introduction 235
2 The Model 236
3 The Determination of the Precision of a Binary Measurement Method 239
4 The Interlaboratory Variation of the PODs 241
5 An Example 245
6 Summary 246
References 247
Part II Empirical Financial Research 248
On EFARIMA and ESEMIFAR Models 249
1 Introduction 249
2 The Exponential FARIMA Model 250
3 Properties and Estimation of the EFARIMA Model 252
3.1 Relationship Between EFARIMA and EACD1 252
3.2 Moments, acf and Persistence of the EFARIMA Model 253
3.3 Estimation of the Model 255
4 The Exponential SEMIFAR Model 255
5 Data Examples 257
5.1 Daily Average Trade Durations 258
5.2 Average Sunshine Durations 258
6 Final Remarks 261
References 261
Prediction Intervals in Linear and Nonlinear Time Series with Sieve Bootstrap Methodology 264
1 Stochastic Processes 265
2 Time Series 266
2.1 Linear Models in Time Series 266
3 Parametric Time Series Models 267
3.1 ARMA Model 267
3.2 ARIMA and ARFIMA Models 268
3.3 GARCH Model 269
4 Bootstrap in Time Series 270
5 Bootstrap 271
5.1 Bootstrap Confidence Intervals 272
6 Bootstrap Methods in Time Series 273
6.1 Block Bootstrap 273
6.2 Sieve Bootstrap 273
7 Sieve Bootstrap Confidence Intervals 274
7.1 Winsorized Sieve Bootstrap 275
7.2 Winsorized AR-Sieve Bootstrap 275
7.3 Winsorized GARCH-Sieve Bootstrap 276
7.4 Simulations 278
8 Closing Remark 281
References 282
Do Industrial Metals Prices Exhibit Bubble Behavior? 283
1 Introduction 283
2 Testing Approach 285
3 Behavioral Motivation 287
4 Data and Empirical Results 289
4.1 The Data 289
4.2 Empirical Results 290
Conclusion 292
References 293
Forecasting Unpredictable Variables 295
1 Introduction 295
2 Minimum MSE Forecasts Based on Nonlinear Transformations 297
3 Univariate Forecasts of Stock Indexes 299
3.1 Unit Root Analysis 299
3.2 Box–Cox Transformation 300
3.3 Estimating the Optimal Predictor Based on Logs 301
4 Multivariate Forecasts of Stock Indexes 305
4.1 Cointegration Analysis 305
4.2 Forecast Comparison 307
Conclusions 310
References 311
Dynamic Modeling of the Correlation Smile 313
1 Introduction 313
2 Credit Derivatives and Correlation Smile 315
2.1 Credit Derivatives 315
2.1.1 CDS Indices 315
2.1.2 Index Tranches 316
2.2 Correlation Smiles 317
2.2.1 Volatility Smile 317
2.2.2 Correlation Smile 317
3 Asset Value Dynamics 318
3.1 General Model Features 318
3.2 First Passage Time Distribution 319
3.3 Integration of Market Risk 320
3.3.1 Modeling Equity Dynamics 320
3.3.2 Coupling Equity and Asset Dynamics 321
4 Model Changes and Correlation Smiles 322
4.1 Data Description 322
4.2 Basic Model 322
4.3 Market Dynamics 324
4.4 Idiosyncratic Jumps 326
4.5 Term Structure of Tranche Losses 328
4.6 Portfolio Heterogeneity 330
Conclusion 332
References 333
Findings of the Signal Approach: A Case Study for Kazakhstan 334
1 Introduction 334
2 The Signal Approach 335
2.1 Defining Currency Turbulences 335
2.2 Selecting Indicators 337
2.3 Composite Indicators 339
2.4 Calculating Crisis Probabilities 339
3 Results for Kazakhstan 340
3.1 Observed Currency Crises 340
3.2 Identifying Individual Indicators for Kazakhstan 341
4 Conduct of Composite Indicators 342
4.1 Signal Approach 342
4.2 Mixed Approach: Principal Components and Single Indicators 344
Conclusions 346
References 347
Double Conditional Smoothing of High-Frequency Volatility Surface Under a Spatial Model 348
1 Introduction 348
2 The Model 349
3 Econometric Issues 351
3.1 Estimation of m 351
3.2 Estimation of ?2 353
4 Practical Implementation and Empirical Results 354
4.1 Data 354
4.2 The Results 354
Conclusion 358
Appendix: Some Technical Details 359
References 362
Zillmer's Population Model: Theory and Application 364
1 Introduction 364
2 Zillmer's Demographic Model 365
3 Population Forecasting with the Zillmer Model 371
Conclusion 373
Appendix 374
References 375
Part III New Econometric Approaches 377
Adaptive Estimation of Regression Parameters for the Gaussian Scale Mixture Model 378
1 Introduction 378
2 Empirical Bayes and the Kiefer–Wolfowitz MLE 379
3 Some Simulation Evidence 381
3.1 Some Implementation Details 381
3.2 Simulation Results 382
Conclusions 382
References 383
The Structure of Generalized Linear Dynamic Factor Models 384
1 Introduction 384
2 GDFMs: The Model Class 386
3 Denoising 388
3.1 Estimation of the Static Factors zt 388
3.2 Estimation of the Dynamic Factors 393
4 Structure Theory for the Latent Process 395
4.1 The Spectral Factorization and the Wold Representation of the Latent Process 395
4.2 Minimal Static Factor 396
4.3 State Space Realizations for the Latent Process and the Minimal Static Factors 397
5 Zeroless Transfer Functions and Singular AR Systems 399
6 The Yule–Walker Equations 402
7 Estimation and Model Selection 403
8 Summary 404
References 404
Forecasting Under Structural Change 406
1 Introduction 406
2 Adaptive Forecast Strategy 409
3 Theoretical Results 411
3.1 Forecasting a Stationary Process yt 412
3.2 Forecasting a Trend Stationary Process 414
4 Practical Performance 415
4.1 Forecast Methods 415
4.1.1 The Benchmark and Other Competitors 417
4.2 Illustrative Examples, Monte Carlo Experiments 417
4.2.1 General Patterns, Observations, Conclusions 418
4.2.2 Monte Carlo Results 420
References 423
Distribution of the Durbin–Watson Statistic in NearIntegrated Processes 425
1 Introduction 425
2 Notation and Assumptions 426
3 Fredholm Approach 428
4 Characteristic Functions 429
5 Power Calculation 432
6 Summary 433
Appendix 434
Proof of Proposition 1 434
Proof of Proposition 2 436
References 440
Testing for Cointegration in a Double-LSTR Framework 441
1 Introduction 441
2 Model Setup 443
2.1 Double Logistic STR 444
2.2 Testing Problem 445
3 Cointegration Tests 446
4 Finite-Sample Properties 448
4.1 Power Results 449
Conclusion 452
References 453
Fitting Constrained Vector Autoregression Models 455
1 Introduction 455
2 Theoretical Results 457
2.1 General Theory of QMLE 457
2.2 Constrained Versus Unconstrained VAR Models 462
2.2.1 Properties of the Unconstrained Case: Full Optimization 462
2.2.2 Properties of Optimization for Constrained Models 463
3 Numerical Illustrations 466
3.1 Finite-Sample Results 466
3.2 Gauging Forecast MSE 467
References 473
Minimax Versions of the Two-Step Two-Sample-Gauß- and t-Test 475
1 Introduction 475
2 Minimax Versions of the Two-Step TS-t-test 476
3 Minimax Versions of the Two-Step TS-Gaußtests 484
4 Numerical Examples 486
Concluding Remark 490
References 490
Dimensionality Reduction Models in Density Estimation and Classification 491
1 Introduction 491
2 Nonparametric Independent Component Analysis 492
3 Multi-Index Departure from Normality Model 494
4 IFA Model 495
5 Application to Nonparametric Classification 497
References 499
On a Craig–Sakamoto Theorem for Orthogonal Projectors 500
References 504
A Note of Appreciation: High Standards with Heart 506