Applied Time Series Analysis with R
I Foundation
1
Introduction
1.1
Conventions
1.2
Bibliographic Note
1.3
Acknowledgements
1.4
License
2
Basic Elements of Time Series
2.1
The Wold Decomposition
2.1.1
The Deterministic Component (Signal)
2.1.2
The Random Component (Noise)
2.2
Exploratory Data Analysis for Time Series
2.3
Dependence in Time Series
2.4
Basic Time Series Models
2.4.1
White Noise
2.4.2
Random Walk
2.4.3
First-Order Autoregressive Model
2.4.4
Moving Average Process of Order 1
2.4.5
Linear Drift
2.5
Composite Stochastic Processes
3
Fundamental Properties of Time Series
3.1
The Autocorrelation and Autocovariance Functions
3.1.1
A Fundamental Representation
3.1.2
Admissible Autocorrelation Functions 😱
3.2
Stationarity
3.2.1
Assessing Weak Stationarity of Time Series Models
3.3
Estimation of Moments (Stationary Processes)
3.3.1
Estimation of the Mean Function
3.3.2
Sample Autocovariance and Autocorrelation Functions
3.3.3
Robustness Issues
4
The Family of Autoregressive Moving Average Models
4.1
Linear Processes
4.2
Autoregressive Models - AR(p)
4.2.1
Properties of AR(p) models
4.2.2
Estimation of AR(p) models
4.2.3
Forecasting AR(p) Models
4.3
Diagnostic Tools for Time Series
4.3.1
The Partial AutoCorrelation Function (PACF)
4.3.2
Portmanteau Tests
4.4
Inference for AR(p) Models
4.5
Model Selection
4.6
Moving Average Models
4.6.1
The Autocovariance Function of MA processes
4.6.2
Selecting and Forecasting MA(
\(q\)
) Models
4.7
Autoregressive Moving Average Models ⚠️
4.7.1
Autocovariance of ARMA Models
4.8
ARIMA Models ⚠️
4.9
SARIMA Models ⚠️
References
Appendix
A
Proofs 😱
A.1
Proof of Theorem 3.1
A.2
Proof of Theorem 4.1
A.3
Proof of Theorem 4.2
B
Robust Regression Methods
B.1
The Classical Least-Squares Estimator
B.2
Robust Estimators for Linear Regression Models
B.3
Applications of Robust Estimation
C
Proofs
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Applied Time Series Analysis with R
References