<p>What you want is to detect <em>statistical stationarity</em>, which is a pretty tough problem and research papers <a href="http://arxiv.org/abs/gr-qc/9910027" rel="nofollow">[1]</a>, <a href="http://arxiv.org/abs/1001.1831" rel="nofollow">[2]</a>, <a href="http://www.sciencedirect.com/science/article/pii/S0378375801000817" rel="nofollow">[3]</a> are written about it. First you will need to decide on the algorithm that actually is able do detect stationarity before you even begin to consider how you would implement it using any programming language (be it Unix utilities, Python with numpy/scipy, or whatever you choose). Perhaps a good book on time-series analysis will help you here.</p>
Spotting the point at which data stabilises using standard Bash utilities
<p>I have a set of data (two columns of CSV numbers) which varies quite a bit initially and then stabilises around a certain number. I'm trying to spot the point at which the graph first seems to stabilise in an automated way using standard Bash utilities. In an ASCII graph, the data may look like something such as this:</p>

<pre><code>y
^                                     ___ stabilised
| .                                  |
|  .                                 |
|    .    .                          |
|     .  . .    .       .            ▾
|      .    .  . .   . . .  . . . . . . . . . . . . . . . .
|             .   . .              .
------------------------------------------------------------&gt; x
</code></pre>

<p>Note that the data do not reach a constant value, but fluctuate slightly around the stable value. Is there some way I may spot the first point at which the graph seems to become stable using standard Bash utilities?</p>