Hi.

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.

Log(yt)=log(y0)+Ut

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.