Introductory Time Series with R (Use R!)

✍ Scribed by Paul S.P. Cowpertwait, Andrew V. Metcalfe

• Publisher: Springer
• Year: 2009
• Tongue: English
• Leaves: 262
• Series: Use R!
• Edition: 2009
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Preface
Contents
Time Series Data
Purpose
Time series
R language
Plots, trends, and seasonal variation
A flying start: Air passenger bookings
Unemployment: Maine
Multiple time series: Electricity, beer and chocolate data
Quarterly exchange rate: GBP to NZ dollar
Global temperature series
Decomposition of series
Notation
Models
Estimating trends and seasonal effects
Smoothing
Decomposition in R
Summary of commands used in examples
Exercises
Correlation
Purpose
Expectation and the ensemble
Expected value
The ensemble and stationarity
Ergodic series
Variance function
Autocorrelation
The correlogram
General discussion
Example based on air passenger series
Example based on the Font Reservoir series
Covariance of sums of random variables
Summary of commands used in examples
Exercises
Forecasting Strategies
Purpose
Leading variables and associated variables
Marine coatings
Building approvals publication
Gas supply
Bass model
Background
Model definition
Interpretation of the Bass model
Example
Exponential smoothing and the Holt-Winters method
Exponential smoothing
Holt-Winters method
Four-year-ahead forecasts for the air passenger data
Summary of commands used in examples
Exercises
Basic Stochastic Models
Purpose
White noise
Introduction
Definition
Simulation in R
Second-order properties and the correlogram
Fitting a white noise model
Random walks
Introduction
Definition
The backward shift operator
Random walk: Second-order properties
Derivation of second-order properties
The difference operator
Simulation
Fitted models and diagnostic plots
Simulated random walk series
Exchange rate series
Random walk with drift
Autoregressive models
Definition
Stationary and non-stationary AR processes
Second-order properties of an AR(1) model
Derivation of second-order properties for an AR(1) process
Correlogram of an AR(1) process
Partial autocorrelation
Simulation
Fitted models
Model fitted to simulated series
Exchange rate series: Fitted AR model
Global temperature series: Fitted AR model
Summary of R commands
Exercises
Regression
Purpose
Linear models
Definition
Stationarity
Simulation
Fitted models
Model fitted to simulated data
Model fitted to the temperature series (1970--2005)
Autocorrelation and the estimation of sample statistics
Generalised least squares
GLS fit to simulated series
Confidence interval for the trend in the temperature series
Linear models with seasonal variables
Introduction
Additive seasonal indicator variables
Example: Seasonal model for the temperature series
Harmonic seasonal models
Simulation
Fit to simulated series
Harmonic model fitted to temperature series (1970--2005)
Logarithmic transformations
Introduction
Example using the air passenger series
Non-linear models
Introduction
Example of a simulated and fitted non-linear series
Forecasting from regression
Introduction
Prediction in R
Inverse transform and bias correction
Log-normal residual errors
Empirical correction factor for forecasting means
Example using the air passenger data
Summary of R commands
Exercises
Stationary Models
Purpose
Strictly stationary series
Moving average models
MA(q) process: Definition and properties
R examples: Correlogram and simulation
Fitted MA models
Model fitted to simulated series
Exchange rate series: Fitted MA model
Mixed models: The ARMA process
Definition
Derivation of second-order properties
ARMA models: Empirical analysis
Simulation and fitting
Exchange rate series
Electricity production series
Wave tank data
Summary of R commands
Exercises
Non-stationary Models
Purpose
Non-seasonal ARIMA models
Differencing and the electricity series
Integrated model
Definition and examples
Simulation and fitting
IMA(1, 1) model fitted to the beer production series
Seasonal ARIMA models
Definition
Fitting procedure
ARCH models
S&P500 series
Modelling volatility: Definition of the ARCH model
Extensions and GARCH models
Simulation and fitted GARCH model
Fit to S&P500 series
Volatility in climate series
GARCH in forecasts and simulations
Summary of R commands
Exercises
Long-Memory Processes
Purpose
Fractional differencing
Fitting to simulated data
Assessing evidence of long-term dependence
Nile minima
Bellcore Ethernet data
Bank loan rate
Simulation
Summary of additional commands used
Exercises
Spectral Analysis
Purpose
Periodic signals
Sine waves
Unit of measurement of frequency
Spectrum
Fitting sine waves
Sample spectrum
Spectra of simulated series
White noise
AR(1): Positive coefficient
AR(1): Negative coefficient
AR(2)
Sampling interval and record length
Nyquist frequency
Record length
Applications
Wave tank data
Fault detection on electric motors
Measurement of vibration dose
Climatic indices
Bank loan rate
Discrete Fourier transform (DFT)
The spectrum of a random process
Discrete white noise
AR
Derivation of spectrum
Autoregressive spectrum estimation
Finer details
Leakage
Confidence intervals
Daniell windows
Padding
Tapering
Spectral analysis compared with wavelets
Summary of additional commands used
Exercises
System Identification
Purpose
Identifying the gain of a linear system
Linear system
Natural frequencies
Estimator of the gain function
Spectrum of an AR(p) process
Simulated single mode of vibration system
Ocean-going tugboat
Non-linearity
Exercises
Multivariate Models
Purpose
Spurious regression
Tests for unit roots
Cointegration
Definition
Exchange rate series
Bivariate and multivariate white noise
Vector autoregressive models
VAR model fitted to US economic series
Summary of R commands
Exercises
State Space Models
Purpose
Linear state space models
Dynamic linear model
Filtering
Prediction
Smoothing*
Fitting to simulated univariate time series
Random walk plus noise model
Regression model with time-varying coefficients
Fitting to univariate time series
Bivariate time series -- river salinity
Estimating the variance matrices
Discussion
Summary of additional commands used
Exercises
References
Index