Keywords: corporate profits, stability ratio, unit root, H-P filter
Finally, we decompose the profit growth series and apply the Hodrick-Prescott  filter, (5) also known as the H-P filter, on the series.
The H-P filter reveals that profit growth was higher than its long-run trend growth during the 2003-06 period, evidence of an above-trend (and unsustainable?) pace of profit growth.
One key advantage of the H-P filter is that once we estimate the [g.sub.t] and [c.sub.t], we can see at any point of time whether a series is moving below the trend growth (slowdown) or above the trend (boom).
With the help of the H-P filter, we can test at any point of time whether a time series is moving below the trend growth (slowdown) or above the trend (boom).
In addition, we decomposed profits series using the H-P filter.
We do not use the H-P filter because we believe that, under fiat money standards, the interesting information in nominal data is the trend induced by monetary policy.
Figure 6 depicts the cross-correlations between detrended output and inflation without the H-P filter. This third method of comparing output and inflation corresponds to a common specification of these variables, as they typically appear in the aggregate supply function of macroeconomic models used by policymakers and their advisors.
We begin by examining interest rates after removing the trend with the H-P filter. Figure 7 shows how the cyclical patterns changed after October 1979.
If we omit those three years and use the H-P filter on interest rates, then we can easily reject the hypothesis that the cyclical patterns are the same before and after October 1979.
Figure 8 shows that, if we do not use the H-P filter, these interest rate correlations, compared with those in Figure 7, are about 0.3 to 0.4 smaller in absolute value in the first period and only about 0.1 smaller in the second period.
If we do not use the H-P filter, the leading correlations appear more similar across policy regimes, but the lagging correlations are significantly different.