I have two variables that are non-stationary and contain stochastic trends. I used the Hamilton filter( an improvement over the HP filter) to remove the trend and isolate the cyclical component. My question is can I use these filtered variables (i.e. the cyclical component of the original data) in a standard OLS regression? Although the variables are now stationary will the application of the filter bias the estimates or generate spurious regression results? I know this is the case with the HP filter, although the Hamilton filter should correct for that.

The reason I am doing this is because I want to preserve the long-run properties of the data for my analysis. If I first difference the data to make it stationary all of that long-run information is lost. I am trying to figure out the best way to preserve the long-run information while making the variables stationary. Any other suggestions are welcome.

Thanks in advance!


1 Answer 1


You can use the filtered components as many researchers have done before in researching the equity risk premium and consumption-based asset pricing. However, you may want to use the unsmoothed variables for some models -- since the variation may contain useful information for asset pricing or inferring volatility. For an example about how unfiltered NIPA was more informative, see Kroencke (2017).

  • $\begingroup$ Thanks for your reply Kurtosis. Can you reference some of these papers on the equity risk premium and asset pricing that use filtered data? I am not very familiar with this literature. $\endgroup$
    – user29937
    Aug 7, 2020 at 15:46
  • $\begingroup$ Kroencke (2017) references many, so I would start there first. It's a vast field and he pointed out that many many people were making a simple mistake by forgetting the data were filtered. $\endgroup$
    – kurtosis
    Aug 7, 2020 at 15:56

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