Unit 3: Time Series Analysis
behavior
Stationarity
Non-Stationarity
- Stationarity defined as constancy over time
- Key characteristics: mean, variance, autocorrelation
- Simplifies analysis and modeling
- Easier forecasting, reliable properties
- Non-stationary: changing over time
- Varying mean, variance, autocorrelation
- Shows trends, seasonality, patterns
- Must address before analysis
- Avoids spurious correlations, incorrect models
Approaches
- Detrending: removing trend
- Differencing: eliminate trend/seasonality
- Seasonal adjustment: seasonality
- Transformation: variance stabilization
- ADF test: stationarity determination
Methods Analyzing Time Series
- ARIMA models
- SARIMA models
- VAR
- Exponential Smoothing
- Prophet model
Models include
- Curve fitting
- Descriptive analysis
- Explanative analysis
- Exploratory analysis
- Forecasting
- Intervention analysis
- Segmentation
- Classification
Autoregressive Component
Moving Average
Integration
Time Series
Forecasting:
- Box-Jenkins Model (ARIMA: p, d, q)
- Rescaled range analysis for trend stability
- Cross-sectional analysis for stock evaluation
Models and Techniques:
- Box-Jenkins ARIMA models (univariate)
- Box-Jenkins Multivariate Models (multivariate)
- Holt-Winters Method for seasonal data.
Types
- Reduced form VAR models
- Recursive VAR models
- Structural VAR models
Advantages
Systematic and flexible
Improved forecasting
Captures intertwined dynamics