Can You Use Filtered Variables in OLS? 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!
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).