#!/bin/sh
#
# 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.
#
# So there.
#
# Copyright (c) 1994-2005, John Conover, All Rights Reserved.
#
# Find the root, (reciprocal of the Hausdorff fractal dimension,) of
# the DJIA time series, djia1900-2004, to three decimal places, by
# iterating the tsrunmagnitude(1) program. (Note: the iteration
# technique is "fragile," and convergence is not guaranteed.)
#
# The program uses the last calculated value of the root of the
# fractional Brownian equivalent of the time series for the DJIA, to
# calculate a new root value. In pseudo code:
#
#     using the tsmath program, take the log of the time series of the
#     DJIA to produce the fractional Brownian equivalent of the DJIA
#     time series; use the tslsq program to LSQ the linear trend
#
#     while the error is more than 0.000
#
#     use the tsrunmagnitude program to make a time series of the
#     root of the fractional Brownian equivalent of the DJIA time
#     series
#
#     take the log, using the tsmath program, of both axis of the
#     fractional Brownian equivalent of the DJIA time series,
#     i.e., make a log-log plot; the slope of the plot is the root
#     of the fractional Brownian equivalent of the DJIA time
#     series
#
#     we need 843 days of data, (ln (843) = 6.7, grep'ing 0-5 will
#     give 5.999 ... which is close,) and use the tslsq program to
#     LSQ the slope; strip out the root value, and calculate the
#     error from the last iteration
#
# On the DJIA time series, from January 2, 1900, to October 12, 2004,
# inclusive, (it takes about 22 minutes on a half GHz. Pentium class
# machine):
#
# LSQ Approximation = -4.588093 + 0.537910t, Error = 0.03791
# LSQ Approximation = -4.645150 + 0.541671t, Error = 0.003761
# LSQ Approximation = -4.650391 + 0.542009t, Error = 0.000338
# Final LSQ Approximation -4.650391 + 0.542009t
#
# The deviation is e^(-4.650391) = 0.00955786407, and the root is
# 0.542009, or the formula for the deviation of the DJIA, t many days
# into the future will be 0.00955786407 * t^0.542009.
#
# John Conover, john@email.johncon.com
#
tsmath -l djia1900-2004 | tslsq -o > djia1900-2004.brownian
#
ROOT="0.5"
#
while [ "1" != "2" ]
do
    tsrunmagnitude -r "${ROOT}" djia1900-2004.brownian > djia1900-2004.brownian.root
    cut -f1 djia1900-2004.brownian.root | tsmath -l > 1.tmp
    cut -f2 djia1900-2004.brownian.root | tsmath -l > 2.tmp
    SLOPE=`paste 1.tmp 2.tmp | egrep '^[0-5]\.' | tslsq -p`
    paste 1.tmp 2.tmp > djia1900-2004.brownian.root.log-log
    rm -f 1.tmp 2.tmp
    LASTROOT="${ROOT}"
    ROOT=`echo "${SLOPE}" | sed -e 's/^.* + //' -e 's/t$//'`
    DIFF=`calc "${ROOT}" - "${LASTROOT}" | sed 's/^[^0-9]//'`
    echo "LSQ Approximation = ${SLOPE}, Error = ${DIFF}"
    #
    if echo "${DIFF}" | egrep '0\.000' > /dev/null
    then
        echo "Final LSQ Approximation ${SLOPE}"
        break;
    fi
    #
done