Terry Fields wrote:
The Natural Philosopher wrote:

What you are essentially doing when analysing, smoothing, or whatever a
time series, is applying a low pass filter to it: What the filter has as
output is critically dependent on the form of the filter. You are merely
comparing two different forms of filter..and if they give different
results, that merely calls into question the validity of using ANY of them.

I know it's a been as while since I did any statistics in anger, but
from my first lecture in college in 1963 up to what's laughingly
called retirement, I've never heard of statistics being called a LPF.


Note that I did say with respect to a *time series*.

Indeed you probabably would not, but let me assure you that the digital
implementation of a low pass filter is a statistically weighted moving
average of a sort.

Juts like e.g. a 'moving average'.

A resistor and a capacitor does a beautiful moving average as it happens ;-)
More resistors and capacitors change its characteristics.

Anyway, as ypu know my background is in analog and digital electronics,
and thats a unique viewpoint that allows me to see the things that you
regard - possibly because the methodology you use appears oo different,
to be different things: They are not. They are data compressors. Of
which a low pass filter - or indeed any filter - is a classic example,
but done 'analogue'




Perhaps the picture in my mind, of a LPF rejecting HF components of
something, isn't what I see as being done by statistics, which is to
discard nothing in orderto return the best estimates of the provenance
of the data.

An average is a complete and most basic reduction of a data set to ONE
data point.

Low pass filters discard nothing: its simply that the shorter the
duration of a section of the raw graph is, the less it affects the final
output.



How would a comparison of say, satellite data analysed by two
different organisations, with ditto from ground-based data, by putting
them through an analysis of variance, be classed as low-pass
filtering?

Sounds a perfect description to me.A differential amplifier and low pass
filter..


Apologies if I appear dim, but I'm struggling to visualise the LPF
concept.

That, I am afraid, is your problem.

Broadly speaking, any device which allows the time variance of a signal
to affect the amplitude of the output as well as the amplitude of that
signal does, is some kind of filter.

The moment you derive an output at a given time, not just from the input
data at that time, but from other times as well, you are applying some
sort of frequency style filter in practice, even if you think you are
doing statistics.