<p>Yes, if the series is already stationary then there is no need to difference the data to remove a trend. In fact, there is a cost associated with unnecessarily differencing the data such that you are removing / losing relevant information. More generally this is related to the concept of cointegration where even if series are non-stationary, if they are co-trending then you lose more information by differencing than by including the lagged levels in the model specification.</p>
<p>You might also find the following question and answers helpful for thinking about this in a slightly different context: <a href="https://stats.stackexchange.com/questions/415914/is-it-a-valid-claim-that-by-differencing-a-time-series-it-loses-its-memory-an">https://stats.stackexchange.com/questions/415914/is-it-a-valid-claim-that-by-differencing-a-time-series-it-loses-its-memory-an</a></p>

CC BY-SA 4.0
2020-11-17T04:21:10.230Z
But if you take a look at the federal funds rate, it is not mean stationary. The series trends upwards until about the mid-1980s and trends downwards after that. Anyway, I will check later if it passes unit root tests. I will send an update on that.
Emmanuel Ameyaw
CC BY-SA 4.0
2020-11-17T20:18:14.437Z
Yes, for various subsamples you might have what appear to be upward or downward trends. So for some subsamples might have what appears to be non-stationarity. But over the full historical sample least until 2010 it seemed to fluctuate around a pretty constant mean: https://fred.stlouisfed.org/series/FEDFUNDS.  Ofcourse there are different non-stationarity concerns that you might be worried about. For instance, I would be much more worried about structural breaks than trends. And structural breaks aren't just simply eliminated by differencing the data.
Andrew M
CC BY-SA 4.0
2020-11-18T10:41:33.850Z
*there is no need to difference the data to remove a trend*: note that this holds only for stochastic trends. Deterministic trends should not be removed by differencing as this would lead to overdifferencing.
Richard Hardy
CC BY-SA 4.0
2020-11-18T19:58:55.980Z
@Richard Hardy. Any references to your statement? That would be great. Does the federal funds rate has a deterministic trend from 1960 to 2000? It does not seem it does. I mean, it goes up until the mid-1980s and then it trends downwards after that.
Emmanuel Ameyaw
CC BY-SA 4.0
2020-11-18T20:10:27.787Z
@ Andrew M. Yeah, I guess VAR models ignore structural breaks and variance stationary. Actually, I applied the Dickey-Fuller test to a series that is variance non-stationary, and it passed. So, I guess variance non-stationarity is not really a big deal in VAR models. By the way, by eyeballing the federal funds rate (https://fred.stlouisfed.org/series/FEDFUNDS), what would say is the stationary mean? 7.5?
Emmanuel Ameyaw
CC BY-SA 4.0
2020-11-18T20:54:27.137Z
@EmmanuelAmeyaw, no comment on a concrete variable, just a general note on time series analysis. A reference could be found in a decent time series textbook, though it seems not even all textbooks get this one unambiguously right as the malpractice is getting pretty widespread...
Richard Hardy
CC BY-SA 4.0
2020-11-19T02:13:10.533Z
@Richard Hardy. Thanks!! Given a series like this - https://fred.stlouisfed.org/series/FEDFUNDS , would you transform it? If yes, why? If no, why not? It seems the answer depends on the researcher, and what he wants to do. Some people transform it, others don't. Both are correct, it seems.
Emmanuel Ameyaw
CC BY-SA 4.0
2020-11-16T20:10:48.817Z
2020-11-16T20:10:48.817Z
Andrew M
<p>In FAVAR (factor augmented VAR) paper (<a href="https://faculty.wcas.northwestern.edu/%7Elchrist/finc520/QJE.pdf" rel="nofollow noreferrer">https://faculty.wcas.northwestern.edu/~lchrist/finc520/QJE.pdf</a>), the following transformation code is applied to the data:
1—no transformation; 2—first difference;
4 —logarithm; 5—first difference of logarithm.</p>
<p>There is no transformation for the federal funds rate, among several others. The paper does not say why, but is it because these series are already stationary in levels? Would it hurt to detrend them even if they are stationary in levels?</p>

CC BY-SA 4.0
2020-11-16T20:13:06.043Z
In addition to the answer you already got I would like to point out that in this case since the interest rate can be negative 4-5 would be non-starters from the get go. Generally taking logs of interest rates in to a good idea
1muflon1
CC BY-SA 4.0
2020-11-17T04:12:17.157Z
Yeah, of course.
Emmanuel Ameyaw
<macroeconomics><econometrics>
Why the Federal Funds rate isn't detrended in a VAR model?
Emmanuel Ameyaw
# Why the Federal Funds rate isn't detrended in a VAR model?

(Asked by: username_0 on 2020-11-16)

In FAVAR (factor augmented VAR) paper ([https://faculty.wcas.northwestern.edu/~lchrist/finc520/QJE.pdf](https://faculty.wcas.northwestern.edu/%7Elchrist/finc520/QJE.pdf)), the following transformation code is applied to the data:
1—no transformation; 2—first difference;
4 —logarithm; 5—first difference of logarithm.

There is no transformation for the federal funds rate, among several others. The paper does not say why, but is it because these series are already stationary in levels? Would it hurt to detrend them even if they are stationary in levels?

**Tags:** macroeconomics, econometrics
> **Comments:**
> **username_1**: In addition to the answer you already got I would like to point out that in this case since the interest rate can be negative 4-5 would be non-starters from the get go. Generally taking logs of interest rates in to a good idea  
> **username_0**: Yeah, of course.  

---

## 1 answers

### Answer by username_2 on 2020-11-16. Score: 2 | Accepted answer

Yes, if the series is already stationary then there is no need to difference the data to remove a trend. In fact, there is a cost associated with unnecessarily differencing the data such that you are removing / losing relevant information. More generally this is related to the concept of cointegration where even if series are non-stationary, if they are co-trending then you lose more information by differencing than by including the lagged levels in the model specification.

You might also find the following question and answers helpful for thinking about this in a slightly different context: <https://stats.stackexchange.com/questions/415914/is-it-a-valid-claim-that-by-differencing-a-time-series-it-loses-its-memory-an>

> **Comments:**
> **username_0**: But if you take a look at the federal funds rate, it is not mean stationary. The series trends upwards until about the mid-1980s and trends downwards after that. Anyway, I will check later if it passes unit root tests. I will send an update on that.  
> **username_2**: Yes, for various subsamples you might have what appear to be upward or downward trends. So for some subsamples might have what appears to be non-stationarity. But over the full historical sample least until 2010 it seemed to fluctuate around a pretty constant mean: https://fred.stlouisfed.org/series/FEDFUNDS.  Ofcourse there are different non-stationarity concerns that you might be worried about. For instance, I would be much more worried about structural breaks than trends. And structural breaks aren't just simply eliminated by differencing the data.  
> **username_3**: *there is no need to difference the data to remove a trend*: note that this holds only for stochastic trends. Deterministic trends should not be removed by differencing as this would lead to overdifferencing.  
> **username_0**: @Richard Hardy. Any references to your statement? That would be great. Does the federal funds rate has a deterministic trend from 1960 to 2000? It does not seem it does. I mean, it goes up until the mid-1980s and then it trends downwards after that.  
> **username_0**: @ Andrew M. Yeah, I guess VAR models ignore structural breaks and variance stationary. Actually, I applied the Dickey-Fuller test to a series that is variance non-stationary, and it passed. So, I guess variance non-stationarity is not really a big deal in VAR models. By the way, by eyeballing the federal funds rate (https://fred.stlouisfed.org/series/FEDFUNDS), what would say is the stationary mean? 7.5?  
> **username_3**: @EmmanuelAmeyaw, no comment on a concrete variable, just a general note on time series analysis. A reference could be found in a decent time series textbook, though it seems not even all textbooks get this one unambiguously right as the malpractice is getting pretty widespread...  
> **username_0**: @Richard Hardy. Thanks!! Given a series like this - https://fred.stlouisfed.org/series/FEDFUNDS , would you transform it? If yes, why? If no, why not? It seems the answer depends on the researcher, and what he wants to do. Some people transform it, others don't. Both are correct, it seems.  

---

