Contents

• Preface
• Notation
• Chapter 1: Introduction
  • Examples of time series
    • Dollar to Euro exchange rate
    • Number of monthly airline passengers
    • Heat dynamics of a building
    • Prefator-prey relationship
  • A first crash course
  • Contents and scope of the book
• Chapter 2: Multivariate random variables
  • Joint and marginal densities
  • Conditional distributions
  • Expectations and moments
  • Moments of multivariate random variables
  • Conditional expectation
  • The multivariate normal distibution
  • Distributions derived from the normal distribution
  • Linear projections
  • Problems
• Chapter 3: Regression-based methods
  • The regression model
  • The general linear model (GLM)
    • Least squares (LS) estimates
    • Maximum likelihood (ML) estimates
  • Prediction
    • Predictions in the general linear model
  • Regression and exponential smoothing
    • Predictions in the constant mean model
    • Locally constant mean model and simple exponential smoothing
    • Predictions in trend models
    • Local trend and exponential smoothing
  • Time series with seasonal variations
    • The classic decomposition
    • Holt-Winters procedure
  • Global and local trend model - an example
  • Problems
• Chapter 4: Linear dynamic systems
  • Linear systems in the time domain
  • Linear systems in the frequency domain
  • Sampling
  • The z-transform
  • Frequently used operators
  • The Laplace transform
  • A comparison between transformations
  • Problems
• Chapter 5: Stochastic processes
  • Introduction
  • Stochastic processes and their moments
    • Characteristics for stochastic processes
    • Covariance and correlation functions
  • Linear processes
    • Processes in discrete time
    • Processes in continuous time
  • Stationary processes in the frequency domain
  • Commonly used linear processes
    • The MA process
    • The AR process
    • The ARMA process
  • Non-stationary models
    • The ARIMA process
    • Seasonal models
    • Models with covariates
    • Models with time-varying mean values
    • Models with time-varying coefficients
  • Optimal prediction of stochastic processes
    • Prediction in the ARIMA process
  • Problems
• Chapter 6: Identification, estimation, and model checking
  • Introduction
  • Estimation of covariance and correlation functions
    • Autocovariance and autocorrelation function
    • Cross-covariance and cross-correlation functions
  • Identification
    • Identification of the degree of differencing
    • Identification of the ARMA part
    • Cointegration
  • Estimation of parameters in standard models
    • Moment estimates
    • The LS estimator for linear dynamic models
    • The prediction error method
    • The ML method for dynamic models
  • Selection of the model order
    • The autocorrelation functions
    • Testing the model
    • Information criteria
  • Model checking
    • Cross-validation
    • Residual analyse
  • Case study: Electricity consumption
  • Problems
• Chapter 7: Spectral analysis
  • The periodogram
    • Harmonic analysis
    • Properties of the periodogram
  • Consistent estimates of the spectrum
    • The truncated periodogram
    • Lag- and spectral windows
    • Approximative distributions for spectral estimates
  • The cross-spectrum
    • The co-spectrum and the quadrature spectrum
    • Cross-amplitude spectrum, phase spectrum, coherence spectrum, gain spectrum
  • Estimation of the cross-spectrum
  • Problems
• Chapter 8: Linear systems and stochastic processes
  • Relationship between input and output processes
    • Moment relations
    • Spectral relations
  • Systems with measurement noise
  • Input-output models
    • Transfer function models
    • Difference equation models
    • Output error models
  • Identification of transfer function models
  • Multiple-input models
    • Moment relations
    • Spectral relations
    • Identification of multiple-input models
  • Estimation
    • Moment estimates
    • LS estimates
    • Prediction error method
    • ML estimates
    • Output error method
  • Model checking
  • Prediction in transfer function models
    • Minimum variance controller
  • Intervention models
  • Problems
• Chapter 9: Multivariate time series
  • Stationary stochastic processes and their moments
  • Linear processes
  • The multivariate ARMA process
    • Theoretical covariance matrix functions
    • Partial correlation matrix
    • q-conditioned partial correlation matrix
    • VAR representation
  • Non-stationary models
    • The multivariate ARIMA process
    • The multivariate seasonal model
    • Time-varying models
  • Prediction
    • Missing values for some signals
  • Identification of multivariate models
    • Identification using pre-whitening
  • Estimation of parameters
    • Least squares estimation
    • An extended LS method for multivariate ARMAX models (the Spliid method)
    • ML estimates
  • Model checking
  • Problems
• Chapter 10: State space models of dynamic systems
  • The linear stochastic state space model
  • Transfer function and state space formulations
  • Interpolation, reconstruction, and prediction
    • The Kalman filter
    • k-step predictions in state space models
    • Empirical Bayesian description of the Kalman filter
  • Some common models in state space form
    • Signal extraction
  • Time series with missing observations
    • Estimation of autocorrelation functions
  • ML estimates of space state models
  • Problems
• Chapter 11: Recursive estimation
  • Recursive LS
    • Recursive LS with forgetting
  • Recursive pseudo-linear regression (RPLR)
  • Recursive prediction error methods (RPEM)
  • Model-based adaptive estimation
  • Models with time-varying parameters
    • The regression model with time-varying parameters
    • Dynamic models with time-varying parameters
• Chapter 12: Real life inspired problems
  • Prediction of wind power production
  • Prediction of the consumption of medicine
  • Effect of chewing gum
  • Prediction of stock prices
  • Wastewater treatent: Using root zone plants
  • Scheduling system for oil delivery
  • Warning system for slippery roads
  • Statistical quality control
  • Wastewater treatment: Modeling and control
  • Sales numbers
  • Modeling and prediction of stock prices
  • Adaptive modeling of interest rates
• Appendix A: The solution to difference equations
• Appendix B: Partial autocorrelations
• Appendix C: Some results from trigonometry
• Appendix D: List of acronyms
• Appendix E: List of symbols
• Bibliography
• Index