Useful in the theoretical and empirical analysis of nonlinear time series data, semiparametric methods have received extensive attention in the economics and statistics communities over the past twenty years. Recent studies show that semiparametric methods and models may be applied to solve dimensionality reduction problems arising from using fully nonparametric models and methods. Answering the call for an up-to-date overview of the latest developments in the field, Nonlinear Time Series: Semiparametric and Nonparametric Methods focuses on various semiparametric methods in model estimation, specification testing, and selection of time series data. After a brief introduction, the book examines semiparametric estimation and specification methods and then applies these approaches to a class of nonlinear continuous-time models with real-world data. It also assesses some newly proposed semiparametric estimation procedures for time series data with long-range dependence. Even though the book only deals with climatological and financial data, the estimation and specifications methods discussed can be applied to models with real-world data in many disciplines. This resource covers key methods in time series analysis and provides the necessary theoretical details. The latest applied finance and financial econometrics results and applications presented in the book enable researchers and graduate students to keep abreast of developments in the field.
Author(s): Jiti Gao
Series: Chapman & Hall/CRC Monographs on Statistics & Applied Probability
Edition: 1
Publisher: Chapman and Hall/CRC
Year: 2007
Language: English
Pages: 243
Nonlinear Time Series, Semiparametric and Nonparametric Methods......Page 5
Table of Contents......Page 7
MONOGRAPHS ON STATISTICS AND APPLIED PROBABILITY......Page 2
Preface......Page 9
1.2 Examples and models......Page 12
1.3 Bibliographical notes......Page 25
2.1.1 Partially linear time series models......Page 26
2.1.2 Semiparametric additive time series models......Page 27
2.1.3 Semiparametric single–index models......Page 28
2.2 Semiparametric series estimation......Page 29
2.3 Semiparametric kernel estimation......Page 37
2.4 Semiparametric single–index estimation......Page 46
2.5.1 Assumptions......Page 50
2.5.2 Proofs of Theorems......Page 54
2.6 Bibliographical notes......Page 58
3.1 Introduction......Page 60
3.2 Testing for parametric mean models......Page 61
3.2.1 Existing test statistics......Page 63
3.2.2 Asymptotic distributions and expansions......Page 68
3.2.3 Size and power functions......Page 71
3.2.4 An example of implementation......Page 72
3.3 Testing for semiparametric variance models......Page 76
3.4.1 Testing for subset regression......Page 79
3.4.3 Testing for single–index regression......Page 80
3.4.4 Testing for partially linear single–index regression......Page 81
3.4.5 Testing for additive regression......Page 82
3.5.1 Assumptions......Page 83
3.5.2 Technical lemmas......Page 85
3.5.3 Proof of Theorem 3.1......Page 89
3.5.4 Proof of Theorem 3.2......Page 90
3.6 Bibliographical notes......Page 91
4.1 Introduction......Page 93
4.2 Semiparametric cross–validation method......Page 96
4.3 Semiparametric penalty function method......Page 102
4.4 Examples and applications......Page 105
4.5.1 Assumptions......Page 115
4.5.3 Proofs of Theorems 4.1 and 4.2......Page 117
4.6 Bibliographical notes......Page 120
5.1.1 Parametric models......Page 121
5.1.2 Nonparametric models......Page 123
5.1.3 Semiparametric models......Page 124
5.2 Nonparametric and semiparametric estimation......Page 126
5.2.1 Method 1......Page 127
5.2.2 Method 2......Page 128
5.2.3 Method 3......Page 130
5.3 Semiparametric specification......Page 133
5.3.1 Specification of diffusion function......Page 134
5.3.2 Specification of drift function......Page 135
5.3.3 Testing for linearity in the drift......Page 136
5.4.1 The data......Page 140
5.4.3 Results and comparisons for the Fed data......Page 142
5.4.4 Results and comparisons for the Euro data......Page 150
5.4.5 Conclusions and discussion......Page 155
5.5.1 Assumptions......Page 156
5.5.2 Proof of Equation (5.11)......Page 157
5.5.3 Proofs of Theorems 5.2–5.5......Page 159
5.5.4 Technical lemmas......Page 161
5.6 Bibliographical notes......Page 166
6.1 Introductory results......Page 167
6.2 Gaussian semiparametric estimation......Page 169
6.3 Simultaneous semiparametric estimation......Page 171
6.3.1 Gaussian models with LRD and intermittency......Page 172
6.3.2 Semiparametric spectral density estimation......Page 174
6.4.1 Introduction......Page 179
6.4.2 Simultaneous semiparametric estimation......Page 182
6.4.3 Simulation results......Page 186
6.4.4 Applications to market indexes......Page 193
Real data......Page 194
Empirical results......Page 197
6.5.1 Proof of Theorem 6.6......Page 199
6.6 Bibliographical notes......Page 201
7.1 Technical lemmas......Page 203
7.2 Asymptotic normality and expansions......Page 208
References......Page 218
Author Index......Page 239
