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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?

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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.

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  • $\begingroup$ Interesting, I had never heard of the HP filter before! It is essentially Tikhonov regression with a curvature penalty (e.g. as here). If you make the penalty coefficient $\lambda$ large, the HP result should converge to the linear fit, I would think (?) The issue in Hamilton seems to be "not appropriate for a random walk" (?), which could also apply to a purely linear trend. (Or is Hamilton only arguing against "certain values of $\lambda$?) $\endgroup$
    – GeoMatt22
    May 29 '17 at 3:57

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