Learn→Time Series Forecasting→Statistical Models (ARIMA, Exponential Smoothing)→3 of 6

Time Series Forecasting • Statistical Models (ARIMA, Exponential Smoothing)Medium⏱️ ~3 min

ARIMA: Modeling Momentum and Shocks

Core Idea
ARIMA forecasts by modeling momentum (values stay high if they were high) and shock recovery (surprises fade). Written as ARIMA(p, d, q).
AR: MOMENTUM
Predicts today from recent days. If prices were rising, they tend to keep rising. today = w₁×yesterday + w₂×2_days_ago. Parameter p = past days used. AR(1) uses yesterday; AR(2) uses two days.
MA: SHOCK RECOVERY
Models how prediction errors (shocks) fade. A surprise causes a spike, then dissipates. Parameter q = past errors that matter. MA(1) = yesterday shock affects today; MA(2) = shocks linger 2 periods.
💡 Insight: AR = "values have inertia." MA = "shocks fade." Most real data has both momentum and shock effects.
I: REMOVING TRENDS
ARIMA needs stationary data (no trend). Differencing removes trends: diff = today - yesterday. Parameter d = times to difference. d=1 handles linear trends; d=2 (rare) handles accelerating trends.
CHOOSING P, D, Q
Start with d: difference until data looks flat (usually 0 or 1). Then examine correlations to pick p and q. Automated tools test combinations. Common start: ARIMA(1,1,1). For seasonal data, SARIMA adds seasonal terms.
⚠️ Trade-off: ARIMA is flexible but harder to tune. Clear trend/seasonality → ETS. Complex autocorrelation → ARIMA.

💡 Key Takeaways

✓AR (autoregressive) captures momentum—if values were high, they tend to stay high

✓MA (moving average) captures shock recovery—unexpected events that fade over time

✓I (integrated) = differencing to remove trends; d=1 handles most trending data

✓ARIMA(p,d,q): p=past values used, d=differencing times, q=past errors used

✓More flexible than ETS but harder to tune; use when autocorrelation patterns are complex

📌 Interview Tips

1Explain AR as momentum (inertia) and MA as shock recovery (fading surprises)

2Know that differencing removes trends—subtract today from yesterday to get stationary data

← Back to Statistical Models (ARIMA, Exponential Smoothing) Overview