📊 SARIMA Model Interactive Visualization

Seasonal ARIMA with Classic Airline Passenger Dataset

Created by Dr. Pedram Jahangiry | Enhanced with Claude

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Current Model: SARIMA(1,1,0)(0,1,0)₁₂

📚 Understanding SARIMA Models

SARIMA(p,d,q)(P,D,Q)ₘ

SARIMA (Seasonal ARIMA) extends ARIMA by adding seasonal components to capture repeating patterns at fixed intervals (like monthly or quarterly seasonality).

Non-Seasonal Parameters (p,d,q)

  • p: AR order - captures short-term autocorrelation
  • d: Differencing degree - removes trend
  • q: MA order - models error terms

Seasonal Parameters (P,D,Q)ₘ

  • P: Seasonal AR - relates current to m periods ago
  • D: Seasonal differencing - removes seasonal trend
  • Q: Seasonal MA - seasonal error structure
  • m: Season length (12 for monthly, 4 for quarterly)

Airline Passenger Dataset

  • Period: Monthly, Jan 1949 - Dec 1960 (144 observations)
  • Pattern: Clear upward trend + strong yearly seasonality
  • Optimal Model: SARIMA(1,1,0)(0,1,0)₁₂
  • Features: Parsimonious model with differencing handling both trend and seasonality

Model Selection Tips

  • Use ACF/PACF plots to identify p and q
  • Apply differencing (d,D) until series is stationary
  • Set m to match your data frequency (12 for monthly)
  • Compare models using AIC, AICc, or BIC criteria

Educational Insight: The optimal model SARIMA(1,1,0)(0,1,0)₁₂ uses:
• d=1 to remove the trend through first differencing
• D=1 to remove seasonal pattern through seasonal differencing
• p=1 for short-term AR(1) autocorrelation
• P=0, Q=0 meaning seasonal differencing alone handles seasonality without additional AR/MA terms
• This is a parsimonious model that captures both trend and seasonality efficiently