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- 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

- Examples of time series
- 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

- The periodogram
- 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

- Relationship between input and output
processes
- 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

- Recursive LS
- 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

Click on the chapter titles to see more.