Introductory Time Series with R

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