Applied time series analysis. (2011)

• Record Type: Book
• Further Information: Note: Wayne A Woodward, Henry L. Gray, and Alan C. Elliott.
• Other Names: Woodward, Wayne A; Gray, Henry L; Elliott, Alan C, 1952-
• Contents: Stationary Time Series; Time Series; Stationary Time Series; Autocovariance and Autocorrelation Functions for Stationary Time Series; Estimation of the Mean, Autocovariance, and Autocorrelation for Stationary Time Series; Power Spectrum; Estimating the Power Spectrum and Spectral Density for Discrete Time Series; Time Series Examples; ; Linear Filters; Introduction to Linear Filters; Stationary General Linear Processes; Wold Decomposition Theorem; Filtering Applications; ; ARMA Time Series Models; Moving Average Processes; Autoregressive Processes; Autoregressive–Moving Average Processes; Visualizing Autoregressive Components; Seasonal ARMA(p, q )x (Ps, Qs )s Models; Generating Realizations from ARMA(p, q ) Processes; Transformations; ; Other Stationary Time Series Models; Stationary Harmonic Models; ARCH and GARCH Models; ; Nonstationary Time Series Models; Deterministic Signal-Plus-Noise Models; ARIMA(p, d, q) and ARUMA(p, d, q ) Models; Multiplicative Seasonal ARUMA(p, d, q ) x (Ps, Ds, Qs )s Model; Random Walk Models; G-Stationary Models for Data with Time-Varying Frequencies; ; Forecasting; Mean Square Prediction Background; Box–Jenkins Forecasting for ARMA(p, q ) Models; Properties of the Best Forecast Xto (l ); pi-Weight Form of the Forecast Function; Forecasting Based on the Difference Equation; Eventual Forecast Function; Probability Limits for Forecasts; Forecasts Using ARUMA(p, d, q ) Models; Forecasts Using Multiplicative Seasonal ARUMA Models; Forecasts Based on Signal-plus-Noise Models; ; Parameter Estimation; Introduction; Preliminary Estimates; Maximum Likelihood Estimation of ARMA( p, q ) Parameters; Backcasting and Estimating σ 2 a ; Asymptotic Properties of Estimators; Estimation Examples Using Data; ARMA Spectral Estimation; ARUMA Spectral Estimation; ; Model Identification; Preliminary Check for White Noise; Model Identification for Stationary ARMA Models; Model Identification for Nonstationary ARUMA(p, d, q ) Models; Model Identification Based on Pattern Recognition; ; Model Building; Residual Analysis; Stationarity versus Nonstationarity; Signal-plus-Noise versus Purely Autocorrelation-Driven Models; Checking Realization Characteristics; Comprehensive Analysis of Time Series Data: A Summary; ; Vector-Valued (Multivariate) Time Series; Multivariate Time Series Basics; Stationary Multivariate Time Series; Multivariate (Vector) ARMA Processes; Nonstationary VARMA Processes; Testing for Association between Time Series; State-Space Models; Proof of Kalman Recursion for Prediction and Filtering; ; Long-Memory Processes; Long Memory; Fractional Difference and FARMA Models; Gegenbauer and GARMA Processes; k -Factor Gegenbauer and GARMA Models; Parameter Estimation and Model Identification; Forecasting Based on the k -Factor GARMA Model; Modeling Atmospheric CO2 Data Using Long-Memory Models; ; Wavelets; Shortcomings of Traditional Spectral Analysis for TVF Data; Methods That Localize the ‘‘Spectrum’’ in Time; Wavelet Analysis; Wavelet Packets; Concluding Remarks on Wavelets; Appendix: Mathematical Preliminaries for This Chapter; ; G-Stationary Processes; Generalized-Stationary Processes; M-Stationary Processes; G(λ)-Stationary Processes; Linear Chirp Processes; Concluding Remarks; ; Index
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2011
• Extent: 1 online resource (xxiii, 540 pages), illustrations
• Subjects: 519.55; Time-series analysis; Time-series analysis; Electronic books
• Languages: English
• ISBNs: 9781439897690; 1439897697
• Notes: Note: Includes bibliographical references and index.
• 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.