Preface
1
Introduction
1.1
Topics to cover
1.2
Multivariate time series models
2
R Time series environment
3
Plots, Trends
4
Basic Stochastic Models
4.1
Modelling time series
4.2
Residual error series
4.3
Stationary models
4.3.1
White noise models
4.4
Non-stationary models
4.4.1
Random walks
5
Stationary models
5.1
Univariate Time Series
5.2
Introduction
5.3
Autogregressive Models
5.3.1
Expected Value of AR(1)
5.3.2
Variance of AR(1)
5.3.3
Covariances of AR(1)
5.4
Moving Average Models
5.4.1
Mean of MA(1)
5.4.2
Variance of MA(1)
5.4.3
Covariance of MA process
5.5
Comparing AR(1) and MA(1)
6
General ARMA models
6.1
MA(q) process: Definition and properties
6.1.1
MA equation with backshift operator
6.1.2
Mean and variance of MA process
6.1.3
Autocorrelation function and MA process
6.1.4
R codes
6.1.5
Autocovariance function
6.1.6
Fitted MA models
6.1.7
Stationarity
6.1.8
Autocorreation function (ACF)
6.2
Formulating ARMA process
6.2.1
Lag operator
6.2.2
Characteristics of Lag Polynomial
6.3
From
\(MA(1)\)
to AR(
\(\infty\)
)}
6.4
Parsimonious representation of ARMA
6.5
Invertibility of Lag Polynomial
6.5.1
Second Order Polynomial
6.6
Mixed models: The ARMA process
7
Regression models
7.1
Introduction
7.2
Conditions for Stationarity
7.3
Spurious Regression
7.4
Statistical properties of regression
7.4.1
Deterministic Trends
7.4.2
Stochastic Trend
7.4.3
Time series Regression
7.5
Generalised least square (GLS)
7.5.1
GLS fit to simulated series
7.5.2
Fitting simulated data
7.5.3
Linear models with seasonal variables
7.5.4
Introduction
7.5.5
Additive seasonal indicator variables
7.6
Unit root
8
VAR and VECM Models
Time Series Analysis
3
Plots, Trends