by WebHubbleTelescope » Sun 20 Feb 2011, 18:30:52
$this->bbcode_second_pass_quote('Xenophobe', '
')I don't need a list of what Excel does, or does not have, to fit time series data with the identical level of predictive ability you have demonstrated.
Afraid you are wrong on that account. If you want to do time-series analysis of a response function against an impulse, you need to learn how to do a convolution. I take it you are not an engineer. Enough people reading this thread are engineers and they would switch over to Matlab to do this kind of work. You can do a convolution in Excel and I describe it briefly in the book, but it is painful.
$this->bbcode_second_pass_quote('Xenophobe', '
')Any time you want to show us how predictive this method is, knock yourself out. The day long movement of the DJIA sits there, no more than a day or two in the future, ready to test your trendology on.
Let us know how it goes.
Movements of the DJIA are pretty much a random walk with a long-term shifting bias. Statistically the big boys make the money by executing trades faster than the next guy. Long term I have modeled this with a dispersion formulation.
Consider a typical stock market. It consists of a number of stocks that show various rates of growth, R. Say that these have an average growth rate, r. Then by the Maximum Entropy Principle, the probability distribution function is:
pr(R) = 1/r*exp(-R/r)
We can solve this for an expected valuation, x, of some arbitrary stock after time, t.
n(x|t) = ∫ pr(R) δ(x-Rt) dR
This reduces to the marginal distribution:
n(x|t) = 1/(rt) * exp(-x/(rt))
In general, the growth of a stock only occurs over some average time, τ, which has its own Maximum Entropy probability distribution:
p(t) = 1/τ *exp(-t/τ)
So when the expected growth is averaged over expected times we get this integral:
n(x) = ∫ n(x|t) p(t) dt
We have almost solved our problem, but this integration reduces to an ugly transcendental function K0 otherwise known as a modified Bessel function of the second kind and order 0.
n(x) = 2/(rτ) * K0(2*sqrt(x/(rτ) ))
Fortunately, the K0 function is available on any spreadsheet program (Excel, OpenOffice, etc) as the function BESSELK(X;0).
Let us try it out. I took 3500 stocks over the last decade (since 1999), and plotted the histogram of all rates of return below.

Like I said, I interpreted this more completely here:
http://mobjectivist.blogspot.com/2010/1 ... s-toy.htmlNow if you want me to confirm that I can predict the movement of the DJIA a day or two in advance, you would have to be insane. I understand exactly how the stock market works and know that it is a sucker's bet. The random walk component is much bigger than anything else and I can only suggest a statistical ensemble movement long-term.
Incidentally, the kind of analysis I presented falls under the umbrella of Econophysics. This isn't the quant stuff that ruined Wall Street but straightforward applications of statistical mechanics formulations from the physics world. Like my work on oil depetion, this stuff will eventually take over mainstream economics thought. It essentially explains and helps us understand what is going on. As a benefit, with a constrained resource, it actually allows you to peek into the future.
Next question please?