If I'm not mistaken, one half the mean of the *squared* first order
differences is essentially the sample variance, so one can draw the
connection with acf and pacf based on that, I'd guess. Not sure what it is
if you average the *absolute* first order differences.
Andy
> -----Original Message-----
> From: Spencer Graves [mailto:spencer.graves@PDF.COM]
> Sent: Tuesday, August 19, 2003 9:04 PM
> To: Andrew White
> Cc: S-News List (E-mail)
> Subject: Re: [S] How to Sum the Lengths of Plotted Lines in a
> Time Series
>
>
> For the total distance, if y = a vector of
> observations at equally
> spaced points in time, sum(abs(diff(y))) should give you the total
> length of the line; mean(abs(diff(y))) should normalize it for the
> number of observations.
>
> Are you familiar with the use of autocorrelation
> (acf) and partial
> autocorrelations (pacf; function acf with type="partial") for model
> identification, as described, e.g., in Box, Jenkens, Reinsel
> (1994) Time
> Series Analysis, Forecasting and Control (Prentice Hall)? My
> preference
> today for basic time series analysis is to use ACF and PACF for model
> identification and then use state space techniques a la West and
> Harrison (1997) Bayesian Forecasting and Dynamic Models (Springer).
> There should be some relationship between your "total
> distance" and the
> ACF, but I'm not certain what.
>
> hope this helps. spencer graves
>
> Andrew White wrote:
> > 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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