📊 SARIMA Model Interactive Visualization

Seasonal ARIMA with Classic Airline Passenger Dataset

Created by Dr. Pedram Jahangiry | Enhanced with Claude

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This tool approximates how a Seasonal ARIMA model behaves on the classic Box-Jenkins airline passenger counts (1949-1960), directly in your browser. Move the sliders for the orders and seasonal period below and the chart redraws the forecast against the actual monthly data, so you can see exactly how each parameter changes what the model captures.

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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