UsefulLinks
Statistics
Time Series Analysis
1. Introduction to Time Series
2. Foundational Concepts and Data Preparation
3. Descriptive Analysis and Decomposition
4. Stationarity and Unit Root Analysis
5. Autocorrelation and Dependence Structure
6. Classical Forecasting Methods
7. ARIMA Modeling
8. Seasonal ARIMA Models
9. Advanced Univariate Models
10. Volatility Modeling
11. Multivariate Time Series
12. State Space Models and Kalman Filtering
13. Machine Learning for Time Series
14. Forecasting Evaluation and Model Selection
15. Practical Forecasting Considerations
16. Software and Implementation
5.
Autocorrelation and Dependence Structure
5.1.
Measuring Temporal Dependence
5.1.1.
Covariance and Correlation
5.1.2.
Lag Relationships
5.1.3.
Serial Dependence
5.2.
Autocorrelation Function
5.2.1.
Definition and Properties
5.2.2.
Sample ACF
5.2.3.
Theoretical ACF Patterns
5.2.4.
Confidence Intervals
5.2.5.
Interpretation Guidelines
5.3.
Partial Autocorrelation Function
5.3.1.
Definition and Calculation
5.3.2.
Sample PACF
5.3.3.
Theoretical PACF Patterns
5.3.4.
Model Identification Uses
5.4.
Cross-Correlation Analysis
5.4.1.
Cross-Correlation Function
5.4.2.
Lead-Lag Relationships
5.4.3.
Prewhitening
5.4.4.
Spurious Correlation
5.5.
Spectral Analysis
5.5.1.
Frequency Domain Analysis
5.5.2.
Periodogram
5.5.3.
Spectral Density
5.5.4.
Fourier Transform
5.6.
Nonlinear Dependence
5.6.1.
Higher-Order Moments
5.6.2.
Conditional Heteroskedasticity
5.6.3.
Nonlinear Correlation Measures
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4. Stationarity and Unit Root Analysis
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6. Classical Forecasting Methods