Time Series : A First Course with Bootstrap Starter /: A First Course with Bootstrap Starter. (2020)

• Record Type: Book
• Further Information: Note: Dimitris N. Politis, Tucker S. McElroy.
• Authors: Politis, Dimitris N; McElroy, Tucker S
• Contents: 1. Introduction ; Time Series Data; Cycles in Time Series Data; Spanning and Scaling Time Series; Time Series Regression and Autoregression; Overview; Exercises 2. The Probabilistic Structure of Time Series ; Random Vectors; Time Series and Stochastic Processes; Marginals and Strict Stationarity; Autocovariance and Weak Stationarity; Illustrations of Stochastic Processes; Three Examples of White Noise; Overview; Exercises 3. Trends, Seasonality, and Filtering ; Nonparametric Smoothing; Linear Filters and Linear Time Series; Some Common Types of Filters; Trends; Seasonality; Trend and Seasonality Together; Integrated Processes; Overview; Exercises 4. The Geometry of Random Variables ; Vector Space Geometry and Inner Products; L2(; P;F): The Space of Random Variables with Finite Second Moment; Hilbert Space Geometry; Projection in Hilbert Space; Prediction of Time Series; Linear Prediction of Time Series; Orthonormal Sets and Infinite Projection; Projection of Signals; Overview; Exercises 5. ARMA Models with White Noise Residuals ; Definition of the ARMA Recursion; Difference Equations; Stationarity and Causality of the AR(1); Causality of ARMA Processes; Invertibility of ARMA Processes; The Autocovariance Generating Function; Computing ARMA Autocovariances via the MA Representation; Recursive Computation of ARMA Autocovariances; Overview; Exercises 6. Time Series in the Frequency Domain ; The Spectral Density; Filtering in the Frequency Domain; Inverse Autocovariances; Spectral Representation of Toeplitz Covariance Matrices; Partial Autocorrelations; Application to Model Identification; Overview; Exercises 7. The Spectral Representation; The Herglotz Theorem; The Discrete Fourier Transform; The Spectral Representation; Optimal Filtering; Kolmogorov's Formula; The Wold Decomposition; Spectral Approximation and the Cepstrum; Overview; Exercises 8. Information and Entropy ; Introduction; Events and Information Sets; Maximum Entropy Distributions; Entropy in Time Series; Markov Time Series; Modeling Time Series via Entropy; Relative Entropy and Kullback-Leibler Discrepancy; Overview; Exercises 9. Statistical Estimation ; Weak Correlation and Weak Dependence; The Sample Mean; CLT for Weakly Dependent Time Series; Estimating Serial Correlation; The Sample Autocovariance; Spectral Means; Statistical Properties of the Periodogram; Spectral Density Estimation; Refinements of Spectral Analysis; Overview; Exercises 10. Fitting Time Series Models ; MA Model Identification; EXP Model Identification; AR Model Identification; Optimal Prediction Estimators; Relative Entropy Minimization; Computation of Optimal Predictors; Computation of the Gaussian Likelihood; Model Evaluation; Model Parsimony and Information Criteria; Model Comparisons; Iterative Forecasting; Applications to Imputation and Signal Extraction; Overview; Exercises 11. Nonlinear Time Series Analysis ; Types of Nonlinearity; The Generalized Linear Process; The ARCH Model; The GARCH Model; The Bi-spectral Density; Volatility Filtering; Overview; Exercises 12. The Bootstrap; Sampling Distributions of Statistics; Parameters as Functionals and Monte Carlo; The Plug-in Principle and the Bootstrap; Model-based Bootstrap and Residuals; Sieve Bootstraps; Time Frequency Toggle Bootstrap; Subsampling; Block Bootstrap Methods; Overview; Exercises A. Probability ; Probability Spaces; Random Variables; Expectation and Variance; Joint Distributions; The Normal Distribution; Exercises B. Mathematical Statistics ; Data; Sampling Distributions; Estimation; Inference; Con_dence Intervals; Hypothesis Testing; Exercises C. Asymptotics ; Convergence Topologies; Convergence Results for Random Variables; Asymptotic Distributions; Central Limit Theory for Time Series; Exercises D. Fourier Series; Complex Random Variables; Trigonometric Polynomials E. Stieltjes Integration ; Deterministic Integration; Stochastic Integration;
• Edition: 1st
• Publisher Details: Chapman and Hall/CRC
• Publication Date: 2020
• Extent: 1 online resource (300 pages)
• Languages: English
• ISBNs: 9780429527227; 0429527225
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.