The RATS Software Forum

Dear Tom:


In the trend cycle decomposition of logarithmic time series multiplied by 100, why is the cycle exactly as a percentage ? Is there a certain allocation mechanism for the variance of trends and cyclic components within it? Why does the cyclic component happen to be a percentage of the trend, rather than a tenfold percentage, or a thousandth or even a ten thousandth ratio. When decomposition of seasonally unadjusted time series, does the seasonal component also show a percentage? Why?

Best Regard
Hardmann

I'm not sure I understand what you are asking. If you do an additive decomposition of data in 100 x logs, any "zero mean" component will have an interpretation of percentage differences.

Dear Tom:

What I mean is why in trend/cycle decomposition, the amplitude of the cycle is mostly between positive or negative 5, rather than positive or negative 50, or positive or negative 0.5.


Best Regard
Hardmann

While it would certainly depend upon the series in question, for most macro aggregates a cycle that is even +/- 10 percentage points would be rather extreme. Again, if you are modeling a series at 100 x log, any of the components which aren't capturing the overall log level are going to be percentage deviations. If you have a cycle that is straying way off of zero (particularly if it's very persistent) then it's probably picking up something that maybe should be in the trend.