<p>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 <a href="https://onlinelibrary.wiley.com/doi/abs/10.1111/jofi.12438" rel="nofollow noreferrer">Kroencke (2017)</a>.</p>

CC BY-SA 4.0
2020-08-07T15:46:43.267Z
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.
user29937
CC BY-SA 4.0
2020-08-07T15:56:27.300Z
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.
kurtosis
CC BY-SA 4.0
2020-08-07T07:40:47.997Z
2020-08-07T07:40:47.997Z
kurtosis
<p>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.</p>
<p>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.</p>
<p>Thanks in advance!</p>

<econometrics><time-series>
Can You Use Filtered Variables in OLS?
user29937
# Can You Use Filtered Variables in OLS?

(Asked by: username_0 on 2020-08-06)

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!

**Tags:** econometrics, time-series

---

## 1 answers

### Answer by username_1 on 2020-08-07. Score: 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)](https://onlinelibrary.wiley.com/doi/abs/10.1111/jofi.12438).

> **Comments:**
> **username_0**: 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.  
> **username_1**: 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.  

---

