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Is there a measure or statistic that could quantify a steady increase in the spacing between data points in a time series?

For instance, in the figure, the points are clustered and dense near 0, but then they become more and more sparse.

enter image description here

Thanks

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  • $\begingroup$ by "variance" I think you mean "spacing", so the time dependence of the mean spacing should give you the information you want. $\endgroup$
    – Carlo Beenakker
    Commented Jan 28, 2018 at 13:02
  • $\begingroup$ Hi Carlo, thank you for the precision. That's what I meant! Is there any reference or formulation that you know of? $\endgroup$
    – Raskol
    Commented Jan 28, 2018 at 13:21

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Yes, there is the inhomogeneous Poisson process with rate $\lambda(t)$.

In this graph from Wikipedia the rate is increasing then decreasing; in your case it would be everywhere decreasing. enter image description here

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