See figure I for an explanation of the detrending
Given the lack of a structural interpretation of the error term, combined with the likely distortions introduced by the detrending
filter, I do not want to put too much emphasis on the point estimate.
The problem with linear detrending
, however, is that it is not well supported by the data.
Also, the slope of the line relating the elevation profile detrending
length to some power of the detrended root mean squared (RMS) value is used.
We measure the business cycle using seven popular detrending
methods, and a turning point rule that does not involve a trend-cycle decomposition per se.
But for the early '60s and the late '90s the message would be quite different, with lower interest rates indicated by the gap based on the log-linear detrending
. According to the Figure 13 version of the Taylor rule, the federal funds rate was too high by about 300 basis points throughout 1995-1998!
To meet the assumption of a stationary time series (Gottman 1981), cross-correlation analysis was performed on the residuals of each pollen record after detrending
it with the highest order polynomial in which all parameters were significant at the P [less than] 0.05 level.
(8.) The complete set of filters considered were (i) demeaning and detrending
. (ii) firs-differenced, (iii) demeaning and detrending
the first-differenced data, (iv) using first-differenced output and the second-differenced price level, and (v) demeaning and detrending
first-differenced output and second-differenced price level.
Dating the peak of the cycle by reference to a subsequent absolute decline in output no longer seems such a 'rare event' activity as it did before the first oil shock; moreover, the intervening popularity of the growth cycle has suffered from the realization that detrending
techniques may spuriously create cycles of their own and shift the timing of the turning points in undesirable ways.
Watson, Mark W "Univariate Detrending
Methods with Stochastic Trends." Journal of Monetary Economics, 18(1), 1986, 49-75.
Two series - investment and net exports - are not logged, but taken as a ratio to GDP in order to convert to proportionate measures before detrending
Effects of detrending
and rescaling on correspondence analysis: solution stability and accuracy.