Detrending with antilog of intercept in regression


There are different methods to obtain cycle of a time series such as first difference or hodrick-prescot filter and etc.

We can estimate this regression.
We can obtain stationary time series (cycle of the time series) with antilog of the intercept.

I saw this method to derive cycle of a time series.My question is that when we regress this equation, for intercept we have only one scalar parameter and when we employ the antilog we have only a scalar parameter.How we can obtain the time series of cycle by this method?

In some thesis researchers used this method to stationarizing a time series.They mentioned that they used antilog of intercept to obtain cycle.

I cannot really follow your post. Your formula was not explained and does not even contain an intercept. What is the paper your are referring to?