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

  1. Detrending: removing trend
  1. Differencing: eliminate trend/seasonality
  1. Seasonal adjustment: seasonality
  1. Transformation: variance stabilization
  1. ADF test: stationarity determination

Methods Analyzing Time Series

  1. ARIMA models
  1. SARIMA models
  1. VAR
  1. Exponential Smoothing
  1. Prophet model

Models include

  1. Curve fitting
  1. Descriptive analysis
  1. Explanative analysis
  1. Exploratory analysis
  1. Forecasting
  1. Intervention analysis
  1. Segmentation
  1. 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

  1. Reduced form VAR models
  1. Recursive VAR models
  1. Structural VAR models

Advantages

Systematic and flexible

Improved forecasting

Captures intertwined dynamics