TSCOINS(1) TSCOINS(1) NAME tscoins - generate an unfair coins toss time series SYNOPSIS tscoins [-b n] [-f fraction] [-i value] [-p probability] [-t] [-v] number DESCRIPTION tscoins is for generating fractional brownian noise, with unfair bias, and cumulative sum-generates a time series. The idea is to produce a 1/f squared power spectrum distribution by running a cumulative sum on a Gaussian power spectrum distribution. The program accepts an unfair bias and a wager factor. See "Fractals", Jens Feder, Plenum Press, New York, New York, 1988, ISBN 0-306-42851-2, pp 172. The name, tscoins, was chosen since pitching many coins, at once, and counting the number of heads, many times, will approach a gaussian dis- tribution, if the number of coins is large, and the number of times is large. See "Fractals", Jens Feder, Plenum Press, New York, New York, 1988, ISBN 0-306-42851-2, pp 154. The discreet time formula is: x[t] = x[t - 1] + f * R * x[t - 1] where f is the fraction of the capital to be wagered, and R is a Gaus- sian function, with the mean offset appropriately to provide a Shannon probability, P. For the logistic function, the discreet time formula is: x[t] = x[t - 1] + f * R * x[t - 1] + n * x[t - 1]^2 Note: these programs use the following functions from other references: ran1, which returns a uniform random deviate between 0.0 and 1.0. See "Numerical Recipes in C: The Art of Scientific Computing," William H. Press, Brian P. Flannery, Saul A. Teukolsky, William T. Vetterling, Cambridge University Press, New York, 1988, ISBN 0-521-35465-X, page 210, referencing Knuth. gasdev, which returns a normally distributed deviate with zero mean and unit variance, using ran1 () as the source of uniform deviates. See "Numerical Recipes in C: The Art of Scientific Computing," William H. Press, Brian P. Flannery, Saul A. Teukolsky, William T. Vetterling, Cambridge University Press, New York, 1988, ISBN 0-521-35465-X, page 217. gammln, which returns the log of the results of the gamma function. See "Numerical Recipes in C: The Art of Scientific Computing," William H. Press, Brian P. Flannery, Saul A. Teukolsky, William T. Vetterling, Cambridge University Press, New York, 1988, ISBN 0-521-35465-X, page 168. The general outline of this program is: 1) given the Shannon probability, compute the abscissa value that divides the area under the normal curve, into two sections, such that the area to the left of the value, divided by the total area under the normal curve is the Shannon probability-a Newton-Raphson iterated approach using Romberg integration to find the area is used for this 2) for each record: a) compute a gaussian distributed random number b) add the computed abscissa value from 1) above to the gaussian distributed number c) multiply this number by the fraction of cumulative sum to be wagered d) multiply this number by the cumulative sum e) add this number to the cumulative sum This program will require finding the value of the normal function, given the standard deviation. The method used is to use Romberg/trape- zoid integration to numerically solve for the value. This program will require finding the functional inverse of the normal, ie., Gaussian, function. The method used is to use Romberg/trapezoid integration to numerically solve the equation: x 2 | 1 - t / 2 F(x) = integral | ------ * e dt + 0.5 | 2 * pi 0 which has the derivative: 2 1 - x / 2 f(x) = ------ * e 2 * pi Since F(x) is known, and it is desired to find x, x 2 | 1 - t / 2 F(x) - integral | ------ * e dt + 0.5 = P(x) | 2 * pi 0 = 0 and the Newton-Raphson method of finding roots would be: P(x) P = P - ---- n + 1 n f(x) As a reference on Newton-Raphson Method of root finding, see "Numerical Recipes in C: The Art of Scientific Computing," William H. Press, Brian P. Flannery, Saul A. Teukolsky, William T. Vetterling, Cambridge Uni- versity Press, New York, 1988, ISBN 0-521-35465-X, pp 270. As a reference on Romberg integration, see "Numerical Recipes in C: The Art of Scientific Computing," William H. Press, Brian P. Flannery, Saul A. Teukolsky, William T. Vetterling, Cambridge University Press, New York, 1988, ISBN 0-521-35465-X, page 124. As a reference on trapezoid iteration, see "Numerical Recipes in C: The Art of Scientific Computing," William H. Press, Brian P. Flannery, Saul A. Teukolsky, William T. Vetterling, Cambridge University Press, New York, 1988, ISBN 0-521-35465-X, page 120. As a reference on polynomial interpolation, see "Numerical Recipes in C: The Art of Scientific Computing," William H. Press, Brian P. Flan- nery, Saul A. Teukolsky, William T. Vetterling, Cambridge University Press, New York, 1988, ISBN 0-521-35465-X, page 90. OPTIONS -b n Logistic nonlinear term, x(t) = x(t - 1) * (m - n * x(t - 1)). -f fraction Fraction of reserves to be wagered, (0 <= fraction <= 1) -i value Initial value of cash reserves -p probability Shannon probability, (0.5 <= probability <= 1.0) -t Sample's time will be included in the output time series. -v Print the version and copyright banner of the program. number Number of data points in the output time series. WARNINGS There is little or no provision for handling numerical exceptions. SEE ALSO tsderivative(1), tshcalc(1), tshurst(1), tsintegrate(1), tslogre- turns(1), tslsq(1), tsnormal(1), tsshannon(1), tsblack(1), tsbrown- ian(1), tsdlogistic(1), tsfBm(1), tsfractional(1), tsgaussian(1), tsin- tegers(1), tslogistic(1), tspink(1), tsunfairfractional(1), tswhite(1), tscoin(1), tsunfairbrownian(1), tsfraction(1), tsshannonmax(1), tschangewager(1), tssample(1), tsrms(1), tscoins(1), tsavg(1), tsXsquared(1), tsstockwager(1), tsshannonwindow(1), tsmath(1), tsavg- window(1), tspole(1), tsdft(1), tsbinomial(1), tsdeterministic(1), tsnumber(1), tsrmswindow(1), tsshannonstock(1), tsmarket(1), tsstock(1), tsstatest(1), tsunfraction(1), tsshannonaggregate(1), tsin- stant(1), tsshannonvolume(1), tsstocks(1), tsshannonfundamental(1), tstrade(1), tstradesim(1), tsrunlength(1), tsunshannon(1), tsroot- mean(1), tsrunmagnitude(1), tskurtosis(1), tskurtosiswindow(1), tsroot- meanscale(1), tsscalederivative(1), tsgain(1), tsgainwindow(1) tscauchy(1), tslognormal(1), tskalman(1), tsroot(1), tslaplacian(1) DIAGNOSTICS Error messages for incompatible arguments, failure to allocate memory, inaccessible files, and opening and closing files. AUTHORS ---------------------------------------------------------------------- A license is hereby granted to reproduce this software source code and to create executable versions from this source code for personal, non-commercial use. The copyright notice included with the software must be maintained in all copies produced. THIS PROGRAM IS PROVIDED "AS IS". THE AUTHOR PROVIDES NO WARRANTIES WHATSOEVER, EXPRESSED OR IMPLIED, INCLUDING WARRANTIES OF MERCHANTABILITY, TITLE, OR FITNESS FOR ANY PARTICULAR PURPOSE. THE AUTHOR DOES NOT WARRANT THAT USE OF THIS PROGRAM DOES NOT INFRINGE THE INTELLECTUAL PROPERTY RIGHTS OF ANY THIRD PARTY IN ANY COUNTRY. Copyright (c) 1994-2006, John Conover, All Rights Reserved. Comments and/or bug reports should be addressed to: john@email.johncon.com (John Conover) ---------------------------------------------------------------------- January 17, 2006 TSCOINS(1)