Causal time-series representation ($X_t={\sum }_{r\ge 0}{a}_r{ϵ}_{t-r}$)

A causal time-series representation expresses a time series using present and past driving white noise. Its coefficients vanish at negative lags. Square summability ensures mean-square convergence for a white-noise input; absolute summability is the stronger stable-filter convention. Causality refers to the particular driving sequence, not merely to stationary existence.