Causal time-series representation
= Causal time-series representation
{title2=$X_t=\sum_{r\geq0}a_r\epsilon_{t-r}$}
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.