algo-forecast-arima

# ARIMA Time Series Model ## Overview ARIMA(p,d,q) combines autoregression (AR), differencing (I), and moving average (MA) for time series forecasting. Seasonal variant: SARIMA(p,d,q)(P,D,Q,s). Requires stationary data (achieved through differencing). Best for univariate series with clear trend/seasonality patterns. ## When to Use **Trigger conditions:** - Forecasting univariate time series (sales, demand, traffic) - Data has clear trend and/or seasonal patterns - Need interpretable model with statistical properties **When NOT to use:** - For multivariate forecasting with many external features (use ML models) - For very long-range forecasts (ARIMA confidence intervals widen rapidly) - For irregular/event-driven data (use causal models) ## Algorithm ``` IRON LAW: ARIMA Requires STATIONARY Data Non-stationary data (trend, changing variance) violates ARIMA assumptions. Test stationarity with ADF test (p < 0.05 = stationary). If non-stationary: difference the series (d=1 usually suffices). If still non-stationary after d=2, ARIMA may not be appropriate. ``` ### Phase 1: Input Validation Check: regular time intervals, no missing values (impute if needed), minimum 50 observations (ideally 2+ full seasonal cycles). Test stationarity with ADF test. **Gate:** Data is regular, sufficient length, stationarity assessed. ### Phase 2: Core Algorithm 1. **Stationarity**: ADF test. If p > 0.05, difference (d=1). Retest. 2. **Parameter selection**: Examine ACF/PACF plots. Or use aut...