How do ARIMA models forecast financial time series?

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AcadiFi · Accepted Answer

ARIMA(p,d,q) combines autoregression of order p, differencing of order d, and moving average of order q to forecast non-stationary time series.

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Forecasting proceeds recursively: use estimated coefficients to predict one step ahead, treat the forecast as known for two-step ahead, etc. Forecast intervals widen with horizon because uncertainty compounds through both AR persistence and accumulated shock variance. Example: ARIMA(1,1,1) on quarterly EBITDA where first differences follow xt = 0.4 xt-1 + et - 0.3 et-1. A one-step forecast inherits the AR(1) carry and last shock; two-step loses the MA(1) effect after one period.

Model diagnostics require stationarity testing before fitting, residual autocorrelation checks via Ljung-Box, and information criteria (AIC, BIC) for order selection. Overfitting is common with high p or q—parsimony principle favors simpler models that fit comparably. For financial returns that are typically already stationary, d=0 suffices; for price levels or accumulated quantities, d=1 is standard. Seasonal ARIMA extends this to handle periodic patterns.

How do ARIMA models forecast financial time series?

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