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time series

May 1st, 2007

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It’s remarkable how Keplerian fitting functions can be pushed to model a wide variety of time series. Anyone recognize this particular data stream?

It shows complicated behavior on timescales ranging from days to years, superimposed on an autoregressive tendency. The downloadable systemic console‘s periodogram points to significant power at low frequencies, reflecting the gradual overall decline during the duration of the time series. There are also a number of distinct peaks at higher frequencies.

A crazy (read eccentric) six-planet Keplerian system does a credible job of fitting the data.

largely because the periastron passages of eccentric planets are capable of producing peaks that ramp up and then decay. To fit a particular peak, the five keplerian parameters can be varied to produce an enormous variety of waveforms.

The Keplerian model can be evaluated at any forward time to make a prediction, albeit in this case, one with presumably zero physical justification…

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  1. fivemack
    May 2nd, 2007 at 10:13 | #1

    From the range of values, that looks like the stock market VIX index, and indeed the charts seem to match.


    I suppose that Keplerian models aren’t very good at matching the secular exponential trend underlying value rather than derivative indices.

    Please don’t go off and turn into a quantitive analyst; extrasolar planets are much more exciting.

  2. May 2nd, 2007 at 11:35 | #2

    The data stream looks vaguely familiar, but I can’t quite remember to which system it belongs. That is truly unbelievable how the “crazy” six-planet Keplerian system does a fine job of fitting the data. Maybe, I should try “crazy” more often in my fits. Just kidding. LOL

  3. greg
    May 2nd, 2007 at 13:21 | #3


    you got it! I wanted to pick (1) something totally unrelated to astronomy that (2) had weird structure in order to show that a multi-Keplerian model can fit just about anything.

    Don’t put any money on that prediction.


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