<p>One thing to consider, is that it looks like you <em>may</em> have a unit root, though not necessarily.</p>
<p>An example of a unit root would be the stochastic process <span class="math-container">$y_k=y_{k−1}+\epsilon_{k−1}$</span>, where the error term is mean-zero.</p>
<p>Unit roots can cause problems. For one, they are not stationary processes. Using OLS relies on stationarity. A violation can lead to a 'spurious regression': invalid estimates but with a high R-squared.</p>
<p>However, these problems are solvable. The first step is to run a unit-root test, of which there are many.</p>
<p>I suggest looking elsewhere for further material on this, e.g. <a href="https://en.wikipedia.org/wiki/Unit_root" rel="nofollow noreferrer">here</a>. There is lots out there and a full treatment would be outside the scope of one answer.</p>

CC BY-SA 4.0
2021-03-10T22:30:03.890Z
+1, although to me it looks like stationary series with break, since the article you linked to does not mention this possibility, but I don't think this warrants separate answer, I will just add that there are also breakpoint unit root tests such as Zivot-Andrews test that might be more appropriate here.
1muflon1
CC BY-SA 4.0
2021-03-10T22:04:28.707Z
2021-03-10T22:04:28.707Z
BB King
<p>What are the possible problems/issues of regressing smooth time series with almost no fluctuation?
Here is a specific example.</p>
<p><a href="https://i.sstatic.net/WiU67.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/WiU67.jpg" alt="My Example" /></a></p>
<p>Is there anything I have to pay attention to when interpreting coefficients? Or is there no proper way to regress time series like these? If so, what are the reasons?</p>

<regression><time-series>
Regressing (Very) Smooth Time Series
chopschoc
# Regressing (Very) Smooth Time Series

(Asked by: username_0 on 2021-03-10)

What are the possible problems/issues of regressing smooth time series with almost no fluctuation?
Here is a specific example.

[![My Example](https://i.sstatic.net/WiU67.jpg)](https://i.sstatic.net/WiU67.jpg)

Is there anything I have to pay attention to when interpreting coefficients? Or is there no proper way to regress time series like these? If so, what are the reasons?

**Tags:** regression, time-series

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## 1 answers

### Answer by username_1 on 2021-03-10. Score: 3

One thing to consider, is that it looks like you *may* have a unit root, though not necessarily.

An example of a unit root would be the stochastic process $y\_k=y\_{k−1}+\epsilon\_{k−1}$, where the error term is mean-zero.

Unit roots can cause problems. For one, they are not stationary processes. Using OLS relies on stationarity. A violation can lead to a 'spurious regression': invalid estimates but with a high R-squared.

However, these problems are solvable. The first step is to run a unit-root test, of which there are many.

I suggest looking elsewhere for further material on this, e.g. [here](https://en.wikipedia.org/wiki/Unit_root). There is lots out there and a full treatment would be outside the scope of one answer.

> **Comments:**
> **username_2**: +1, although to me it looks like stationary series with break, since the article you linked to does not mention this possibility, but I don't think this warrants separate answer, I will just add that there are also breakpoint unit root tests such as Zivot-Andrews test that might be more appropriate here.  

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