Introductory Time Series with R (Use R!)

Description

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. 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