Time Series Analysis (Chapman & Hall/CRC Texts in Statistical Science)
By: Henrik Madsen (author)Hardback
1 - 2 weeks availability
With a focus on analyzing and modeling linear dynamic systems using statistical methods, Time Series Analysis formulates various linear models, discusses their theoretical characteristics, and explores the connections among stochastic dynamic models. Emphasizing the time domain description, the author presents theorems to highlight the most important results, proofs to clarify some results, and problems to illustrate the use of the results for modeling real-life phenomena. The book first provides the formulas and methods needed to adapt a second-order approach for characterizing random variables as well as introduces regression methods and models, including the general linear model. It subsequently covers linear dynamic deterministic systems, stochastic processes, time domain methods where the autocorrelation function is key to identification, spectral analysis, transfer-function models, and the multivariate linear process. The text also describes state space models and recursive and adaptivemethods.
The final chapter examines a host of practical problems, including the predictions of wind power production and the consumption of medicine, a scheduling system for oil delivery, and the adaptive modeling of interest rates. Concentrating on the linear aspect of this subject, Time Series Analysis provides an accessible yet thorough introduction to the methods for modeling linear stochastic systems. It will help you understand the relationship between linear dynamic systems and linear stochastic processes.
Technical University Denmark, Lyngby, Denmark
Preface Introduction Examples of time series A first crash course Contents and scope of the book Multivariate random variables Joint and marginal densities Conditional distributions Expectations and moments Moments of multivariate random variables Conditional expectation The multivariate normal distribution Distributions derived from the normal distribution Linear projections Problems Regression-based methods The regression model The general linear model (GLM) Prediction Regression and exponential smoothing Time series with seasonal variations Global and local trend model-an example Problems Linear dynamic systems Linear systems in the time domain Linear systems in the frequency domain Sampling The z transform Frequently used operators The Laplace transform A comparison between transformations Problems Stochastic processes Introduction Stochastic processes and their moments Linear processes Stationary processes in the frequency domain Commonly used linear processes Non-stationary models Optimal prediction of stochastic processes Problems Identification, estimation, and model checking Introduction Estimation of covariance and correlation functions Identification Estimation of parameters in standard models Selection of the model order Model checking Case study: Electricity consumption Problems Spectral analysis The periodogram Consistent estimates of the spectrum The cross-spectrum Estimation of the cross-spectrum Problems Linear systems and stochastic processes Relationship between input and output processes Systems with measurement noise Input-output models Identification of transfer-function models Multiple-input models Estimation Model checking Prediction in transfer-function models Intervention models Problems Multivariate time series Stationary stochastic processes and their moments Linear processes The multivariate ARMA process Non-stationary models Prediction Identification of multivariate models Estimation of parameters Model checking Problems State space models of dynamic systems The linear stochastic state space model Transfer function and state space formulations Interpolation, reconstruction, and prediction Some common models in state space form Time series with missing observations ML estimates of state space models Problems Recursive estimation Recursive LS Recursive pseudo-linear regression (RPLR) Recursive prediction error methods (RPEM) Model-based adaptive estimation Models with time varying parameters Real life inspired problems Prediction of wind power production Prediction of the consumption of medicine Effect of chewing gum Prediction of stock prices Wastewater treatment: Using root zone plants Scheduling system for oil delivery Warning system for slippery roads Statistical quality control Modeling and control Sales numbers Modeling and prediction of stock prices Adaptive modeling of interest rates appendix A: The solution to difference equations appendix B: Partial autocorrelations appendix C: Some results from trigonometry appendix D: List of Acronyms appendix E: List of symbols Bibliography Index
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