#!/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.
#
# Copyright (c) 1994-2007, John Conover, All Rights Reserved.
#
# Comments and/or bug reports should be addressed to:
#
#     john@email.johncon.com (John Conover)
#
# -----------------------------------------------------------------------------
#
# Shell script to analyze the characteristics of the DJIA:
#
tsfraction djia | tsavg -p
#   0.000236
tsfraction djia | tsrms -p
#   0.010950
#
#    P (0.000236, 0.010950)
#        0.51077625570776255708
#
tsfraction djia | tsmath -s 0.000236 | tsrms -p
#   0.010947
#   ln (0.010947) = -4.51468983285971677053
tsmath -l djia | tsderivative | tsmath -s 0.000176 | tsrms -p
#   0.010998
#
wc djia
#   29010  29010 202761 djia
head -1 djia
#   68.13
#
tsgain -p djia
#   1.000176
#   ln (1.000176) = 0.00017598451381701882 ~ 0.000176
tsmath -l djia | tsderivative | tsavg -p
#   0.000176
#
tslsq -e -p djia
#   e^(3.450080 + 0.000172t) = 1.000172^(20062.070643 + t) = 2^(4.977413 + 0.000248t)
#   exp (3.450080) = 31.50291244093657542517
#
R="0.5"
#
> "log"
#
LAST="NOTHING"
#
LOOP="1"
#
while [ "${LOOP}" -eq "1" ]
do
    tsmath -l djia | tsderivative | tsmath -s 0.000176 | tsintegrate | tsrunmagnitude -r "${R}" > "djia.magnitude"
    cut -f1 "djia.magnitude" | tsmath -l > "temp.5"
    cut -f2 "djia.magnitude" | tsmath -l > "temp.6"
    LAST=`paste temp.5 temp.6 | egrep '^[0-5]\.' | tslsq -p`
    echo "${LAST}"
    R=`echo "${LAST}" | sed -e 's/^.* //' -e 's/t.*$//'`
    #
    if grep -e "${LAST}" "log"
    then
        LOOP="0"
    fi
    #
    mv "temp.5" "temp.5.last"
    mv "temp.6" "temp.6.last"
    mv "djia.magnitude" "djia.magnitude.last"
    echo "${LAST}" >> "log"
done
#
mv "temp.5.last" "temp.5"
mv "temp.6.last" "temp.6"
mv "djia.magnitude.last" "djia.magnitude"
#
#   -4.592316 + 0.537435t
#   -4.648576 + 0.541035t
#   -4.653584 + 0.541347t
#   -4.654019 + 0.541375t
#   -4.654057 + 0.541377t
#   -4.654058 + 0.541377t
#   -4.654058 + 0.541377t
#
#   exp (-4.654058) = 0.00952287957071537193
#
#   P(0.000236, 0.010950)
#        0.51077625570776255708
#
# djia.sim:
#
# djia, p = 0.51077625570776255708, f = 0.010950, i = 31.50291244093657542517, h = 0.541377, l = 1
#
tsinvestsim djia.sim 29010 | cut -f3 > sim
#
tsfraction sim | tsavg -p
#   0.000253
tsfraction sim | tsrms -p
#   0.010994
tsmath -l sim > sim.ln
#
tslsq -e -p sim
#   e^(3.548001 + 0.000146t) = 1.000146^(24382.768809 + t) = 2^(5.118683 + 0.000210t)
#
tsfraction djia | tsmath -s 0.000236 | tsnormal -t > djia.distribution
tsfraction djia | tsmath -s 0.000236 | tsnormal -t -f > djia.frequency
tsfraction sim | tsmath -s 0.000236 | tsnormal -t > sim.distribution
tsfraction sim | tsmath -s 0.000236 | tsnormal -t -f > sim.frequency
#
egrep '^-' djia.frequency | wc
#   50     100     950
egrep '^-' djia.frequency  | tail -49 | tslsq -e -p | sed 's/ = .*$//'
#    e^(0.710298 + 147.146009t)
#
tsfraction djia | tsmath -s 0.000236 | sed 's/[0-9][0-9][0-9]$//' | sort -n | tscount -r | tsmath -t -d 29009 | tsintegrate -t > djia.cumulative
tsfraction sim | tsmath -s 0.000236 | sed 's/[0-9][0-9][0-9]$//' | sort -n | tscount -r | tsmath -t -d 29009 | tsintegrate -t > sim.cumulative
#
tsmath -l djia | tsderivative | tsmath -s 0.000176 | tsintegrate | tsrunmagnitude > djia.magnitude
tsmath -l sim | tsderivative | tsmath -s 0.000176 | tsintegrate | tsrunmagnitude > sim.magnitude
#
tsmath -l djia | tsderivative | tsmath -s 0.000176 | tsintegrate | tsrunlength | cut -f1,7 > djia.length
tsmath -l sim | tsderivative | tsmath -s 0.000176 | tsintegrate | tsrunlength | cut -f1,7 > sim.length
#
cut -f1 djia.magnitude | tsmath -l > temp.1
cut -f2 djia.magnitude | tsmath -l > temp.2
paste temp.1 temp.2 > djia.magnitude.ln
cut -f1 sim.magnitude | tsmath -l > temp.3
cut -f2 sim.magnitude | tsmath -l > temp.4
paste temp.3 temp.4 > sim.magnitude.ln
#
egrep '^0\.' djia.magnitude.ln | tslsq -p
#    -4.510133 + 0.518242t
egrep '^0\.' sim.magnitude.ln | tslsq -p
#    -4.510679 + 0.569523t
#
tsmath -l djia | tsderivative | tssequence | sort -n | cut -f3 | tsmath -s 0.000176 | tsintegrate > "scrambled"
#
R="0.5"
#
> "log"
#
LAST="NOTHING"
#
LOOP="1"
#
while [ "${LOOP}" -eq "1" ]
do
    tsrunmagnitude -r "${R}" scrambled > "scrambled.magnitude"
    cut -f1 "scrambled.magnitude" | tsmath -l > "temp.7"
    cut -f2 "scrambled.magnitude" | tsmath -l > "temp.8"
    LAST=`paste temp.7 temp.8 | egrep '^[0-5]\.' | tslsq -p`
    echo "${LAST}"
    R=`echo "${LAST}" | sed -e 's/^.* //' -e 's/t.*$//'`
    #
    if grep -e "${LAST}" "log"
    then
        LOOP="0"
    fi
    #
    mv "temp.7" "temp.7.last"
    mv "temp.8" "temp.8.last"
    mv "scrambled.magnitude" "scrambled.magnitude.last"
    echo "${LAST}" >> "log"
done
#
mv "temp.7.last" "temp.7"
mv "temp.8.last" "temp.8"
mv "scrambled.magnitude.last" "scrambled.magnitude"
#
#   -4.498716 + 0.496851t
#   -4.495234 + 0.496649t
#   -4.495005 + 0.496635t
#   -4.494994 + 0.496635t
#   -4.494994 + 0.496635t
#   -4.494994 + 0.496635t
#
R="0.5"
#
> "log"
#
LAST="NOTHING"
#
LOOP="1"
#
while [ "${LOOP}" -eq "1" ]
do
    tsmath -l djia | tsderivative | tsmath -s 0.000176 | tsintegrate | tsrunmagnitude -r "${R}" > "djia.magnitude"
    cut -f1 "djia.magnitude" | tsmath -l > "temp.9"
    cut -f2 "djia.magnitude" | tsmath -l > "temp.10"
    LAST=`paste temp.9 temp.10 | egrep '^[0]\.' | tslsq -p`
    echo "${LAST}"
    R=`echo "${LAST}" | sed -e 's/^.* //' -e 's/t.*$//'`
    #
    if grep -e "${LAST}" "log"
    then
        LOOP="0"
    fi
    #
    mv "temp.9" "temp.9.last"
    mv "temp.10" "temp.10.last"
    mv "djia.magnitude" "djia.magnitude.last"
    echo "${LAST}" >> "log"
done
#
mv "temp.9.last" "temp.9"
mv "temp.10.last" "temp.10"
mv "djia.magnitude.last" "djia.magnitude"
#
#   -4.510133 + 0.518242t
#   -4.539663 + 0.521663t
#   -4.545016 + 0.522309t
#   -4.546053 + 0.522481t
#   -4.546241 + 0.522468t
#   -4.546241 + 0.522468t
#   -4.546241 + 0.522468t
#
sed 's/^/DJIA	/' djia | tsnumber | tsinvest -r | tail -1
# # DJIA, p = 0.510810, f = 0.010949, h = 0.544745, i = 68.130000
#
tsinvestsim djia.sim 29010 | tsinvest -r | tail -1
# # DJIA, p = 0.511489, f = 0.010994, h = 0.548321, i = 31.787033
#
sed 's/^/DJIA    /' djia | tsnumber | tsinvest -its -d5 | egrep DJIA | cut -f3 | tsgain -p
# 1.000535