SpringerLink Springer Engineering eBooks 2017 English+International

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.

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.

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.

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.

This book gathers contributions presented at the 9th Workshop on Cyclostationary Systems and Their Applications, held in Gródek nad Dunajcem, Poland in February 2016. It includes both theory-oriented and practice-oriented chapters. The former focus on heavy-tailed time series and processes, PAR models, rational spectra for PARMA processes, covariance invariant analysis, change point problems, and subsampling for time series, as well as the fraction-of-time approach, GARMA models and weak dependence. In turn, the latter report on case studies of various mechanical systems, and on stochastic and statistical methods, especially in the context of damage detection. The book provides students, researchers and professionals with a timely guide to cyclostationary systems, nonstationary processes and relevant engineering applications.