Re: [Phys-L] Timing Statistic

[John Denker <jsd@av8n.com>]

On 11/6/18 12:19 PM, Paul Nord wrote in part:

>  I don't think that
> is valid in this case because the samples are correlated.

Previously I wrote: That hypothesis is

> >   a) interesting, and
> >   b) easily testable.

Here's another test, in addition to the previously-mentioned
straight-line test: Plot the lagged residuals.  That is:

Fit the data to a suitable model.  If you think the data should
be constant, fit to a one-parameter model, i.e. a horizontal
straight line.  In any case, calculate the residuals Δ_i, that
is, the difference between the ith data point and the model.

Plot the *lagged residuals*.  That is, make a scatter plot
where one axis is Δ_i and the other axis is Δ_(i+1).

Example:  plain Gaussian white noise, subjected to almost
the mildest possible smoothing, i.e. an RC filter with a
time constant equal to the timestep between samples:
  https://www.av8n.com/physics/img48/lagged-residuals-white-rc.png

Without smoothing, the dots would be spread out with perfect
radial symmetry, but here you can see the cloud is elongated
in one direction.

Example:  roundoff error (for 10 π t, rounded to the nearest
integer) subjected to slightly more rounding, i.e. RC=2)
  https://www.av8n.com/physics/img48/lagged-residuals-roundoff-rc.png

Roundoff errors are not random.  They're just not.

Bottom line:  You can learn a lot by looking at lagged residuals.