1 time series data
1.1 Purpose
1.2 Time series
1.3 language R
1.4 Graphs, trends and seasonal variations
1.4.1 Flight departure: reservations of air passengers
1.4.2 Unemployment: Maine
1.4.3 Multiple time series: data relating to electricity, beer and chocolate
1.4.4 Quarterly exchange rate: GBP to NZ $
1.4.5 Series of global temperatures
1.5 Standard decomposition
1.5.1 Notation
1.5.2 Models
1.5.3 Estimate of seasonal trends and effects
1.5.5 Decomposition in R
1.6 Summary of the commands used in the examples
2 Correlation
2.1 Purpose
2.2 Expectation
2.2.1 Expected value
2.2.2 The stationarity
2.2.4 Variance function
2.2.5 Autocorrelation
2.3 The correlogram
2.3.1 General discussion
2.3.2 Example based on air passenger series
2.4 Covariance of sums of random variables
2.5 Summary of the commands used in the examples
3 Forecasting strategies
3.1 Purpose
3.4.1 Exponential smoothing
4 basic stochastic models
4.1 Purpose
4.2 White noise
4.2.1 Introduction
4.2.2 Definition
4.2.3 Simulation in R
4.2.4 Second order properties and the correlogram
4.2.5 Adapting a white noise model
4.3 Random walk
4.3.1 Introduction
4.3.2 Definition
4.3.3 The backward shift operator
4.3.4 Random walk: second order property
4.3.5 Derivation of second order properties
4.3.7 Simulation
4.5 Auto-regressive models
4.5.1 Definition
4.5.2 Stationary and non-stationary AR processes
4.5.3 Second order properties of an AR model (1)
4.5.5 Correlogram of an AR process (1)
4.5.6 partial autocorrelation
4.5.7 Simulation
4.6 Assembled models
4.6.1 Model mounted on simulated series
4.6.2 Exchange rate series: mounted AR model
4.6.3 Global temperature series: mounted AR model
4.7 Summary of R commands
5 regression
5.1 Purpose
5.2 Linear models
5.2.1 Definition
5.2.2 Stationarity
5.2.3 Simulation
5.3 Assembled models
5.3.1 Model adapted to the simulated data
5.3.2 Model adapted to the temperature series (1970-2005)
5.3.3 Autocorrelation and estimate of sample statistics
5.4 Generalized least squares
5.4.1 GLS suitable for simulated series
5.4.2 Confidence interval for the temperature trend
5.5 Linear models with seasonal variables
5.5.1 Introduction
5.5.2 Variables of the additive seasonal indicator
5.5.3 Example: seasonal model for temperature series
5.6 Harmonic seasonal patterns
5.6.1 Simulation
5.6.2 Suitable for simulated series
5.6.3 Harmonic model adapted to the series of temperatures (1970-2005)
5.7 Logarithmic transformations
5.7.1 Introduction
5.7.2 Example using the air passenger series
5.8 Nonlinear models
5.8.1 Introduction
5.8.2 Example of a simulated and adapted nonlinear series
5.9 Prediction from regression
5.9.1 Introduction
5.9.2 Prediction in R.
5.10 Inverse transformation and diagonal correction
5.10.1 Normal residual errors of the register
5.10.2 Empirical correction factor for forecasting means
5.10.3 Example using air passenger data
5.11 Summary of R commands
6 stationary models
6.1 Purpose
6.2 Strictly fixed series
6.3 Moving average models
6.3.1 MA (q) process: definition and properties
6.3.2 Examples R: Correlogram and simulation
6.4 MA models assembled
6.4.1 Model mounted on simulated series
6.4.2 Exchange rate series: mounted MA model
6.5 Mixed models: the ARMA process
6.5.1 Definition
6.6 ARMA models: empirical analysis
6.6.1 Simulation and adaptation
6.6.2 Series of exchange rates
6.6.4 Data of the wave tank
6.7 Summary of commands R