Time Series Decomposer

Time series decomposition separates a time series into three components:

• Trend (T): Long-term progression of the series (increasing/decreasing pattern)
• Seasonal (S): Repeating patterns at fixed intervals (daily, weekly, monthly, yearly)
• Residual (R): Random fluctuations (noise) after removing trend and seasonality

• Additive: Y = T + S + R
  Use when seasonal variations are roughly constant over time
  Residuals should be independent of trend/seasonal components
• Multiplicative: Y = T × S × R
  Use when seasonal variations change proportionally with the level
  Often converted to additive via log transformation

• Seasonal Period: Number of observations in one seasonal cycle
  • Daily data with weekly pattern: 7
  • Monthly data with yearly pattern: 12
  • Hourly data with daily pattern: 24
• Trend Window: Size of moving average window for trend extraction
  • Larger window = smoother trend
  • Smaller window = more responsive to changes
  • Typically set to seasonal period or slightly larger
  • Must be odd number

• Trend: Shows overall direction (growth, decline, stability)
• Seasonal: Reveals cyclical patterns (peak days, slow periods)
• Residual: Should resemble white noise if decomposition is good
  • Random scatter around zero
  • No patterns or trends
  • Approximately normal distribution

• Sales Forecasting: Separate trend from seasonal patterns
• Anomaly Detection: Identify unusual values in residuals
• Pattern Analysis: Understand cyclical behavior
• Deseasonalization: Remove seasonal effects for clearer trends
• Model Preparation: Understand components before forecasting

• Regularly spaced time series (no gaps)
• At least 2 complete seasonal cycles recommended
• More data = better seasonal pattern estimation
• CSV format: timestamp, value
• Timestamps can be dates or sequential integers