Re: Surrogate Data Analysis II

From: Roger L. Bagula (rlbtftn_at_netscape.net)
Date: 09/15/04

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    Date: Wed, 15 Sep 2004 17:15:52 GMT

    Dear Costas Vorlow,
    I would look into using Bescovitch -Ursell functions of Mandelbrot
    cartoons for your functions as they will probably model the data
    better if Dr. Mandelbrot is right in his work on the subject of markets.
    You are certainly deeper into it than I am. I just do fractals from this
    stuff and get noise distributions.
    I have a friend who has done some research into markets and I sent him a
    forward of your questions ( the last two
    with the most information). I hadn't even known when I created the
    permutation models for the Primes digits modulo 10
    that I was doing something that had a technical name, ha, ha...
    I just recognized it when I saw the search results.
    I have been doing work on chaotic integer sequences which is
    a somewhat related area.
    a(n)-->a(k*t)

    As far as I know the object in model formation is to get a model that
    can't be distinuished from the "real" output statistically.
    You might be interested in the cryptographic approach in the 128 to 512
    bit range ( hard to tell these numbers from real numbers!).
    The idea is to figure out the "noise" pattern in both cases!

    The frequency domain type of transform is a good tool as well
    1) you find any linear upward or downward trend and subtract it out.
    (by a linear regression)
    2) you, then, get the noise as integers by doing:
    Floor[large_integer*Noise]
    3) You, then, count the appearance of each integer as a frequency
    and plot the frequency against the appearance number
    In this way you can figure out the "kind" of noise distribution that you
    have as an histogram.
    Another guy who has done a lot of work in this area of noise is Dr.
    Falconer ( fractional Brownian noise).

    I take it the major thing you want to do is
    predict future stockmarket trends for some specific market.
    Costas Vorlow wrote:
    > Thanks for all the answers on my previous question.
    >
    > I have posted this because I am not entirely sure that the experiment I
    > am running is proper.
    >
    > In short, I have a sequence of closing prices from the stock market
    > (daily data). I am generating from the levels (not returns i.e., 1st
    > differences) the surrogates using AAFT (testing for null hypothesis 3
    > i.e., that the series is a monotonic nonlinear transformation of
    > linearly filtered noise). For this reason I do not use a pivotal
    > discriminating statistic. I actually choose to fit a regression model
    > which incorporates a Mackey-Glass component and an error term
    > (heteroskedastic GARCH(1,1)). This has been shown to work fine with
    > data, implying that the actual data generating process can be
    > complex-non-stochastic and still have an error term which is not white
    > noise. This also confirms the fat-tailedness of the stock returns as
    > well as the volatility clustering observed.
    >
    > I found out that creating surrogates on the levels (not the 1st
    > differences of prices), generating returns and then fitting the model on
    > original and surrogate "returns" now sequences, produced meaningfully
    > results on all sequences and that the estimations on the original data
    > set were very different from those of the surrogates. However when
    > returns were used directly in order to generate the surrogates, the
    > results were very but and inconclusive.
    >
    > 1. So I am asking basically, can you actually fit a model on original
    > and surrogate data sets and then compare the estimated coefficient
    > values instead of choosing a discriminating statistic to be computed on
    > all sequences?
    >
    > Or
    >
    > 2. Should I fit the model on surrogates and originals and then use a
    > discriminating statistic on the residuals?
    >
    > I have not seen any clear application as such in Physical Review E,
    > Physica D and other relevant journals. Apologies if I am wrong...
    >
    > Any thoughts?
    >
    > Thanks for your time and patience.
    >
    > Costas 

    -- 
Respectfully, Roger L. Bagula
tftn@earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 
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