= Solution
A <causal time-series representation> uses only the present and past driving <white noise>. Thus the coefficient condition is
$$
\boxed{a_r=0\quad\text{for }r<0.}
$$
The series must have its stated convergence meaning. For centered <white noise> of positive finite <variance>, $\sum_{r\geq0}|a_r|^2<\infty$ is sufficient and necessary for <mean-square convergence>. In the usual stable-filter convention one imposes the stronger $\sum_{r\geq0}|a_r|<\infty$. A bilateral stationary <linear process> need not be causal: terms with $r<0$ involve future driving values.
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