In the X-12 filter the data are extended with forecasts and backcasts from a seasonal ARIMA model.
This methodology involves first fitting a time series model to forecast and backcast the series, and then applying the moving average approach to the resulting extended series.
The most surreal episode I ever observed of backcasts
gone awry occurred many years ago on an oceanside flat in the Florida Keys, where a buddy and I had staked out at the edge of a channel in hopes of casting to the schools of big tarpon that were known to cruise there.
We are dealing with unobserved variables here; it only makes sense that, with the passage of time, our backcasts
of potential output would differ significantly from our nowcasts.
t] series padded into the future and past using forecasts and backcasts of the series.
These estimates are computed using a 600-term approximation to the band-pass filters and forecasts and backcasts constructed from an AR(6) model for [DELTA]ln([IP.
2003) discuss, these revisions can be reduced through extending the time series with forecasts and backcasts
Beginning fly-fishers can refine casting and presentation skills along shores of several lakes, including Baum Lake on Hat Creek and Manzanita Lake in Lassen Park, where awkward backcasts
won't get tangled in willows and a little luck will result in big trout.
The model is then estimated by maximum likelihood and used to generate forecasts of future values of y, and backcasts
To reduce revisions for recent periods, and improve inference at the end of the series, the observed series can be extended with forecasts, and backcasts
(see Kaiser and Maravall, 2001).
This approach has the desirable feature that it makes no assumption about reversion to the local mean, in contrast to the mean reversion imposed by the standard approach of using a stationary time-series model to pad the series with forecasts and backcasts
This component will populate LODESTAR databases with profile backcasts
and forecasts on a daily basis.