Solved – Detrending a time series

Question

I have time series data from 1947-1971 for prices and quantity indices. In the original paper from 1975 which I obtained the data the authors did not detrend the data. Here is how I detrended the data:

1. I applied the Hodrick Prescott filter to each of the variables via Eviews
2. I obtained the residuals values from the Hodrick Prescott and examined them.
3. It was good because of no trend so I took the residuals and replaced them for each of the variables. Then I proceeded to the estimation of the model.

Would this be correct approach to detrend the data?

Answer 1

The HP filter was not conceived as a simple detrending method, it proposes a way to estimate the cyclical component of a time series, leaving you with the potential long-run component.

Many scholars argue against its use, as for example James Hamilton in his article "Why You Should Never Use the Hodrick-Prescott Filter" (shorter presentation). You should be careful whenever you use it.

That being said, if you simply want to detrend the data, you could estimate:

$$ y_t=\beta t + \varepsilon_t $$

and then use the residuals $\varepsilon$ as your detrended series, just like you did with the HP estimation.