I want to develop an estimate of the "complexity" of any time series trend line
in terms of its "cumulative trend-line distance".
I need help in how to calculate the "cumulative distance" or sum of lengths of
individual lines connecting each data point to its next data point - like
tracing the (jagged) time series plot line with your finger and measuring the
total length traced.
Consider a regular time series plotted using ts.plot()
The index of complexity I am toying with would use as a reference the Minimum
Length where each data point would have the same value across all time periods
(observation points): a straight horizontal line. The Maximal Length would then
be where maximal data value variability occurs between every adjacent data
point in the series (sorta like a massive earthquake). Intermediate lengths
would represent intermediate forms of time series data variability.
Obviously I need to "stabilize" the data ranges being referenced and eliminate
influences of scale. That comes later ..
But I am stuck initially with just how to use S-Plus commands to sum the
sequential series of plotted time series plot lengths between adjacent points
from the starting point to the ending point.
Note: I believe this measure is different in principle than just measuring
variance. For the following reason: I ran some time series test cases for 36
time periods: (1) same value repeated = straight horizontal line, (2) a
steadily rising value = forms a straight angled line across the time series
plot, (3) flat for half the points then steady decline, (4) max variation or
seesaw between two extreme data values = maximum jaggy plot, and (5) a random
series of values set by rnorm(). Now the variance of # 2 is greater than #5
(random) and yet #2 is far more regular and "less complex" in my view than the
random changes in direction and length of #5.
Anyone have a method or can suggest some S-Plus standard functions to measure
the cumulative line lengths - or get a better measure of the "complexity" of a
time series plot-line?
Many thanks in advance.
Andy White
Andrew N. White, Ph.D. - Manager Research Unit
Financial Reporting & Medical Economics Dept.
Hawaii Medical Service Association
- Blue Cross Blue Shield of Hawaii
An Independent Licenseee of the Blue Cross and Blue Shield Association -
818 Keeaumoku Street, Honolulu, HI 96814
Ph. 808-948-5344 - Email: andrew_white@hmsa.com
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