On exit: the filtered output series. If the ARIMA model for the time series was known, and hence
${Q}_{y}^{\prime}$ backforecasts were supplied in
y, then
b contains
${Q}_{y}^{\prime}$ ‘filtered’ backforecasts followed by the filtered series. Otherwise, the filtered series begins at the start of
b just as the original series began at the start of
y. In either case, if the value of the series at time
$t$ is held in
${\mathbf{y}}\left(t\right)$, then the filtered value at time
$t$ is held in
${\mathbf{b}}\left(t\right)$.