• 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