406 Structural Time Series Models
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 20050.00.10.20.30.40.50.60.70.80.91.0Figure 9.5 Relative number of times each quarter is classified as a recessionary period, using
5,000 simulated samples. The shaded areas represent NBER-classified recessions
Figure 9.5 plots the recession frequencies, i.e., the relative number of times each
quarter was classified as a recessionary period. For this purpose 5,000 draws from the
conditional distribution ofμ|ywere extracted; each quarter was classified as reces-
sion or expansion according to the Artis, Marcellino and Proietti (2004) Markov
chain dating algorithm. There is a close agreement with the NBER chronology,
which is not based on GDP alone, and the last recession, which started in March
2001 and ended in October 2001, was really mild in terms of GDP; in fact, the
recession frequency is only in one quarter greater than 0.5.
9.2.8 Ad hocfiltering and the Slutsky–Yule effect
A filter isad hocwhen it is invariant to the properties of the time series under
investigation. An instance is provided by the Leser–HP filter with a fixed smoothing
parameter, and another example is the BK filter. The potential danger associated
with anad hoccycle extraction filter is that the filtered series displays cyclical
features that are absent from the original series. The risk of extracting spurious
cycles is known in the time series literature as the Slutsky–Yule effect.
The distortionary effects of the Leser–HP filter have been discussed by King and
Rebelo (1993), Harvey and Jaeger (1993), and Cogley and Nason (1995). These
authors document that, when the series to which the filter is applied is difference
stationary (e.g., a random walk, or an integrated random walk), the detrended series
can display spurious cyclical behavior. As a matter of fact, the transfer function will
display a distinctive peak at business cycle frequencies, which is only due to the