Time Series Analysis

Unit 900: Comprehensive Time Series Analysis

1. Introduction to Time Series Analysis

• Definition and scope of time series analysis
• Characteristics of time series data: temporal ordering, autocorrelation
• Types of time series models: deterministic vs. stochastic
• Importance and applications in economics, finance, environmental sciences, and other domains

2. Time Series Components

• Overview of key components:
  • Trend: long-term movement
  • Seasonality: regular periodic fluctuations
  • Cyclic patterns: irregular cycles related to economic/business cycles
  • Irregular fluctuations: random noise and residuals
• Methods to identify components through visual inspection and statistical tests

3. Time Series Decomposition

• Purpose of decomposition in analysis and forecasting
• Additive decomposition model: when components are independent in magnitude
• Multiplicative decomposition model: when components interact proportionally
• Step-by-step decomposition process
• Practical examples and interpretation of decomposed components

4. Time Series Visualization

• Importance of visualization in exploratory data analysis
• Time series plots: line graphs over time
• Seasonal subseries plots: isolating seasonal patterns
• Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) plots
• Other graphical tools: lag plots, boxplots by time periods

5. Time Series Forecasting Methods

• Moving averages: simple and weighted
• Exponential smoothing techniques:
  • Simple exponential smoothing
  • Holt’s linear trend method
  • Holt-Winters seasonal method
• Autoregressive Integrated Moving Average (ARIMA) models:
  • Model identification (p, d, q parameters)
  • Model fitting and diagnostics
• Model selection and validation

6. Seasonal Adjustment

• Rationale and benefits of seasonal adjustment
• Seasonal differencing to remove seasonality
• Ratio-to-moving-average method
• Seasonal decomposition of time series (classical and STL methods)
• Application scenarios and limitations

7. Stationarity in Time Series

• Definition of stationarity and why it matters
• Types of stationarity: strict, weak (covariance)
• Tests for stationarity:
  • Augmented Dickey-Fuller (ADF) test
  • KPSS test
• Transformations to achieve stationarity:
  • Differencing
  • Logarithmic and power transformations

8. Time Series Model Evaluation

• Performance metrics:
  • Mean Squared Error (MSE)
  • Mean Absolute Error (MAE)
  • Akaike Information Criterion (AIC)
  • Bayesian Information Criterion (BIC)
• Residual analysis and diagnostics
• Cross-validation techniques for time series

9. Advanced Time Series Models

• Seasonal ARIMA (SARIMA) models
• Vector Autoregression (VAR): handling multivariate time series
• Vector Error Correction Models (VECM): cointegration and long-term relationships
• Overview of other advanced models:
  • GARCH models for volatility
  • State-space models and Kalman filtering
• Use cases and interpretation

Each section includes theoretical background, practical examples, and hands-on exercises to reinforce learning.