= Solution
An <invertible time-series representation> recovers the driving <white noise> from current and past observations. In the inverse series the support condition is therefore
$$
\boxed{b_r=0\quad\text{for }r<0.}
$$
Again the series must converge. Stable invertibility uses $\sum_{r\geq0}|b_r|<\infty$, which ensures <mean-square convergence> when $X_t$ has finite <variance>. Merely writing a bilateral inverse is not invertibility in this one-sided sense: it may require future observations. For a general correlated input $X$, square summability of $b_r$ alone is not the same sufficient condition as it is for a <white noise> input.
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