Linked e-resources
Details
Table of Contents
Introduction; Weak Dependence: An Introduction Through Asymmetric ARCH Models; 1 Introduction; 2 Weak Dependence; 3 Models with Infinite Memory; 3.1 Assumptions; 3.2 Properties of the Stationary Solution; 3.3 Asymptotic Results; 4 Asymmetric ARCH(1)-model; 4.1 Existence of a Stationary Solution; 5 Moment Estimators; 5.1 Explicit Moments; 5.2 Moment Based Estimation; 5.3 Asymptotic Considerations; 6 Estimating the Density of the Residuals; 6.1 Fitted Residuals; 6.2 Density Estimation; References.
Subsampling for Non-stationary Time Series with Long Memory and Heavy Tails Using Weak Dependence Condition1 Introduction; 2 Basic Concepts and Definitions; 3 The Model and Its Properties; 4 Central Limit Theorems in the GED Case; 5 Consistency of the Subsampling Method for the Mean; 6 Conclusions; References; Change-Point Problem in the Fraction-Of-Time Approach; 1 Introduction; 2 Change-Point Problem in the FOT Approach; 2.1 The Nonstochastic Idea of FOT; 2.2 Change-Point Detection Methodology; 3 Simulation Study; 3.1 Data Sets Description; 3.2 Change-Point Detection
Simulations Results.
4 Final ConclusionsReferences; 4 Seismic Signal Enhancement via AR Filtering and Spatial Time-Frequency Denoising; Abstract; 1 Introduction; 2 Methodology; 2.1 Autoregressive Filter; 2.2 Algorithm of Enhancement via AR Filtering; 2.3 Algorithm of Spatial Time-Frequency Denoising; 2.4 AR Order and Reference Noise Length Selection Based on AIC; 3 Simulation Results; 4 Real Data Results; 5 Conclusions; References; Transformed GARMA Model with the Inverse Gaussian Distribution; 1 Introduction; 2 Transformations; 3 TGARMA Model Fitting; 3.1 Model Definition; 3.2 Inverse Gaussian TGARMA Model.
3.3 Model Fitting4 Simulation Study; 5 Real Data Analysis; 6 Conclusion; References; GARCH Process with GED Distribution; 1 Introduction; 2 Theory; 3 Testing and Estimation; 3.1 Correlation Testing; 4 Prediction; 5 Applications; 6 Conclusions; References; A Residual Based Method for Fitting PAR Models Using Fourier Representation of Periodic Coefficients; 1 Introduction; 2 Determination of PAR Coefficients by Yule Walker Method; 3 OLS Fit for Periodic Function with Additive Noise; 4 OLS fit of a Fourier Series Parametrization of a PAR Model; 5 Conclusions; References.
8 Vectorial Periodically Correlated Random Processes and Their Covariance Invariant AnalysisAbstract; 1 Introduction; 2 The First and the Second Order Moment Functions; 2.1 The Vector of a Mean Function; 2.2 The Covariance Tensor-Function; 3 The Linear Invariants of the Covariance Tensor-Function; 4 The Quadratic Invariant Properties; 5 The Harmonic Analysis of the Covariance Tensor-Functions and Their Invariants; 6 Invariant Covariance Analysis of Modulated Signals; 7 The Examples of Using the Covariance Invariants for Vibration Analysis; 8 Conclusions; References.
Subsampling for Non-stationary Time Series with Long Memory and Heavy Tails Using Weak Dependence Condition1 Introduction; 2 Basic Concepts and Definitions; 3 The Model and Its Properties; 4 Central Limit Theorems in the GED Case; 5 Consistency of the Subsampling Method for the Mean; 6 Conclusions; References; Change-Point Problem in the Fraction-Of-Time Approach; 1 Introduction; 2 Change-Point Problem in the FOT Approach; 2.1 The Nonstochastic Idea of FOT; 2.2 Change-Point Detection Methodology; 3 Simulation Study; 3.1 Data Sets Description; 3.2 Change-Point Detection
Simulations Results.
4 Final ConclusionsReferences; 4 Seismic Signal Enhancement via AR Filtering and Spatial Time-Frequency Denoising; Abstract; 1 Introduction; 2 Methodology; 2.1 Autoregressive Filter; 2.2 Algorithm of Enhancement via AR Filtering; 2.3 Algorithm of Spatial Time-Frequency Denoising; 2.4 AR Order and Reference Noise Length Selection Based on AIC; 3 Simulation Results; 4 Real Data Results; 5 Conclusions; References; Transformed GARMA Model with the Inverse Gaussian Distribution; 1 Introduction; 2 Transformations; 3 TGARMA Model Fitting; 3.1 Model Definition; 3.2 Inverse Gaussian TGARMA Model.
3.3 Model Fitting4 Simulation Study; 5 Real Data Analysis; 6 Conclusion; References; GARCH Process with GED Distribution; 1 Introduction; 2 Theory; 3 Testing and Estimation; 3.1 Correlation Testing; 4 Prediction; 5 Applications; 6 Conclusions; References; A Residual Based Method for Fitting PAR Models Using Fourier Representation of Periodic Coefficients; 1 Introduction; 2 Determination of PAR Coefficients by Yule Walker Method; 3 OLS Fit for Periodic Function with Additive Noise; 4 OLS fit of a Fourier Series Parametrization of a PAR Model; 5 Conclusions; References.
8 Vectorial Periodically Correlated Random Processes and Their Covariance Invariant AnalysisAbstract; 1 Introduction; 2 The First and the Second Order Moment Functions; 2.1 The Vector of a Mean Function; 2.2 The Covariance Tensor-Function; 3 The Linear Invariants of the Covariance Tensor-Function; 4 The Quadratic Invariant Properties; 5 The Harmonic Analysis of the Covariance Tensor-Functions and Their Invariants; 6 Invariant Covariance Analysis of Modulated Signals; 7 The Examples of Using the Covariance Invariants for Vibration Analysis; 8 Conclusions; References.