A Nonparametric Method for Asymmetrically Extending Signal Extraction Filters
Tucker McElroy
KEY WORDS: ARIMA model, Nonstationary time series, Seasonal adjustment, X-11
ABSTRACT
Two important problems in the X-11 seasonal adjustment methodology
are the construction of standard errors and the handling of the
boundaries. We adapt the ``implied model approach" of Kaiser and Maravall
to achieve both objectives in a nonparametric fashion.
The frequency response function of an X-11 linear
filter is used, together with the periodogram of the differenced
data, to define spectral density estimates for signal and noise.
These spectra are then used to define a matrix smoother, which in
turn generates an estimate of the signal that is linear in the data. Estimates of the signal are provided
at all time points in the sample, and the associated time-varying
signal extraction mean squared errors are a by-product of the
matrix smoother theory. After explaining our method, it is
applied to popular nonparametric filters such as the
Hodrick-Prescott (HP), the Henderson Trend, and Ideal Low-Pass and
Band-Pass filters, as well as X-11 seasonal adjustment, trend, and irregular
filters. Finally, we illustrate the method on a single time series
and provide comparisons with X-11-ARIMA seasonal adjustments.
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