One issue is whether you want to test some properties of the series or whether you want to test for similarity in the sense of correlation.

If the first, then one would have thought you would want to measure the autocorrelations and partial autocorrelations and then compare them with the mean in some arbitrary way.

If the second then you might consider cumulating the observations and using something like the Kolmorgorov-type tests to see whether the series are similar.

Alternatively and very crudely you might take first differences and calculate the Baumol efficiency criterion which = mean - k * standard deviation (k being arbittrarily chosen to reflect a weighting or trade-off between the "risingness" reflected in the mean and the unsmoothness reflected in the standard deviation. This is an old measure suggested to measure investment performance but it might get you started even though it ignores the statistical properties of the time series.

Charles Ward

(1)

On 16 April 2010 17:09, robert pisani <r.pisani@mac.com> wrote:

Two simple time series questions:

1- I want a measure of a time series that describes how closely it
resembles a given collection of time series. Thus, the time series
collection may be contained in column 2 to n of an Excel file, with
each column containing one of the collection, with the time series to
be measured in column 1.

2- Define a measure of a time series that measures how close it is to
a smoothly rising (but not necessarily monotonically rising)
series. Thus using such a measure, one could rank a collection of
time series so that those most smoothly rising and fastest rising
rank highest/lowest using the measure. Thus the time series to be
measured may reside in column 1 of an Excel spread sheet, with the
second column being the numbers 1, 2, 3, . . . etc.

The proximity of the given series to the collection or to "smooth
rising" should be measured in some rms sense. I realize that these
requirements are not completely defined. I'm looking for ideas.

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