Introductory Time Series with R

Media type: E-Book

Title: Introductory Time Series with R

Contains: Preface; CONTENTS; 1 Time Series Data; 1.1 Purpose; 1.2 Time series; 1.3 R language; 1.4 Plots, trends, and seasonal variation; 1.5 Decomposition of series; 1.6 Summary of commands used in examples; 1.7 Exercises; 2 Correlation; 2.1 Purpose; 2.2 Expectation and the ensemble; 2.3 The correlogram; 2.4 Covariance of sums of random variables; 2.5 Summary of commands used in examples; 2.6 Exercises; 3 Forecasting Strategies; 3.1 Purpose; 3.2 Leading variables and associated variables; 3.3 Bass model; 3.4 Exponential smoothing and the Holt-Winters method; 3.5 Summary of commands used in examples
3.6 Exercises4 Basic Stochastic Models; 4.1 Purpose; 4.2 White noise; 4.3 Random walks; 4.4 Fitted models and diagnostic plots; 4.5 Autoregressive models; 4.6 Fitted models; 4.7 Summary of R commands; 4.8 Exercises; 5 Regression; 5.1 Purpose; 5.2 Linear models; 5.3 Fitted models; 5.4 Generalised least squares; 5.5 Linear models with seasonal variables; 5.6 Harmonic seasonal models; 5.7 Logarithmic transformations; 5.8 Non-linear models; 5.9 Forecasting from regression; 5.10 Inverse transform and bias correction; 5.11 Summary of R commands; 5.12 Exercises; 6 Stationary Models; 6.1 Purpose
6.2 Strictly stationary series6.3 Moving average models; 6.4 Fitted MA models; 6.5 Mixed models: The ARMA process; 6.6 ARMA models: Empirical analysis; 6.7 Summary of R commands; 6.8 Exercises; 7 Non-stationary Models; 7.1 Purpose; 7.2 Non-seasonal ARIMA models; 7.3 Seasonal ARIMA models; 7.4 ARCH models; 7.5 Summary of R commands; 7.6 Exercises; 8 Long-Memory Processes; 8.1 Purpose; 8.2 Fractional differencing; 8.3 Fitting to simulated data; 8.4 Assessing evidence of long-term dependence; 8.5 Simulation; 8.6 Summary of additional commands used; 8.7 Exercises; 9 Spectral Analysis; 9.1 Purpose
9.2 Periodic signals9.3 Spectrum; 9.4 Spectra of simulated series; 9.5 Sampling interval and record length; 9.6 Applications; 9.7 Discrete Fourier transform (DFT); 9.8 The spectrum of a random process; 9.9 Autoregressive spectrum estimation; 9.10 Finer details; 9.11 Summary of additional commands used; 9.12 Exercises; 10 System Identification; 10.1 Purpose; 10.2 Identifying the gain of a linear system; 10.3 Spectrum of an AR(p) process; 10.4 Simulated single mode of vibration system; 10.5 Ocean-going tugboat; 10.6 Non-linearity; 10.7 Exercises; 11 Multivariate Models; 11.1 Purpose
11.2 Spurious regression11.3 Tests for unit roots; 11.4 Cointegration; 11.5 Bivariate and multivariate white noise; 11.6 Vector autoregressive models; 11.7 Summary of R commands; 11.8 Exercises; 12 State Space Models; 12.1 Purpose; 12.2 Linear state space models; 12.3 Fitting to simulated univariate time series; 12.4 Fitting to univariate time series; 12.5 Bivariate time series - river salinity; 12.6 Estimating the variance matrices; 12.7 Discussion; 12.8 Summary of additional commands used; 12.9 Exercises; References; Index

Contributor: Metcalfe, Andrew V. [Other]; Cowpertwait, Paul S. P. [Other]

Published: New York, NY: Springer New York, 2009

Extent: Online-Ressource (XVI, 256p, digital)

Language: English

DOI: 10.1007/978-0-387-88698-5

ISBN: 9780387886985; 1282364561; 9780387886978

Identifier:

RVK notation: QH 237 : Zeitreihenanalyse. Anwendungen stochastischer Prozesse, stochastische Prozesse, stochastische Differentialgleichungen
SK 845 : Sequentialanalyse, Zeitreihenanalyse

Keywords: Zeitreihenanalyse > R
Zeitreihenanalyse > R

Origination:

Footnote: Includes bibliographical references and index

Description: Time Series Data -- Correlation -- Forecasting Strategies -- Basic Stochastic Models -- Regression -- Stationary Models -- Non-stationary Models -- Long-Memory Processes -- Spectral Analysis -- System Identification -- Multivariate Models -- State Space Models.

Yearly global mean temperature and ocean levels, daily share prices, and the signals transmitted back to Earth by the Voyager space craft are all examples of sequential observations over time known as time series. This book gives you a step-by-step introduction to analysing time series using the open source software R. Each time series model is motivated with practical applications, and is defined in mathematical notation. Once the model has been introduced it is used to generate synthetic data, using R code, and these generated data are then used to estimate its parameters. This sequence enhances understanding of both the time series model and the R function used to fit the model to data. Finally, the model is used to analyse observed data taken from a practical application. By using R, the whole procedure can be reproduced by the reader. All the data sets used in the book are available on the website http://staff.elena.aut.ac.nz/Paul-Cowpertwait/ts/. The book is written for undergraduate students of mathematics, economics, business and finance, geography, engineering and related disciplines, and postgraduate students who may need to analyse time series as part of their taught programme or their research. Paul Cowpertwait is an associate professor in mathematical sciences (analytics) at Auckland University of Technology with a substantial research record in both the theory and applications of time series and stochastic models. Andrew Metcalfe is an associate professor in the School of Mathematical Sciences at the University of Adelaide, and an author of six statistics text books and numerous research papers. Both authors have extensive experience of teaching time series to students at all levels.

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