ARIMA
Forecast through autocorrelation and differencing
ARIMA describes a series using autoregressive lags, differencing and moving-average innovations. Seasonal ARIMA adds seasonal counterparts to those terms. The model is primarily a forecasting representation of temporal dependence, not an explanation of the underlying mechanism. Differencing should remove relevant non-stationarity without creating unnecessary noise, and prediction intervals depend on the fitted innovation model.
Choose this for univariate time-series forecasting when historical dependence is informative and future external regressors are unavailable or unnecessary. Compare it with simple baseline forecasts using the intended prediction horizon.
Strengths
- Parsimonious and inspectable modelling of autocorrelation
- Seasonal variants represent repeated calendar patterns
Limitations
- Structural breaks can invalidate extrapolation
- Captures linear dependence and may miss nonlinear or changing dynamics
Know the boundary
A well-fitting ARIMA model does not demonstrate that its lag coefficients are causal mechanisms.