Time Series: A First Course with Bootstrap Starter (Hardcover)

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