Attrasoft
Table of Contents
6.1 Lottery
6.2 A simple Dynamic System
6.3 A simple Markov Chain
6.4 Attrasoft Dow 56.4.1 Attrasoft Dow 5: Game Rules
6.4.2 Game data
6.4.3 Results
Attrasoft PredictorPro is a universal PredictorPro, which can be applied to any prediction problem. The PredictorPro reads a sequence of numbers and predicts the distribution for the next row of numbers in line.
Lottery numbers are random numbers and therefore they are unpredictable. The problem most people have is they do not know what to pick. The PredictorPro can help.
Let use 3-digit lottery as an example. Let the 3 digits be (x, y, z).
You can build 7 files for
Predicting x;
Predicting y;
Predicting z;
Predicting xy;
Predicting xz;
Predicting yz;
Predicting xyz.
Use the directory input, a single operation will predict all 7 files.
Find the output with the highest weight, say (x1, y1, z1), then (x1, y1,
z1) will be the PredictorPro�s pick.
To increase the chance, pick up 3 numbers for x: x1-1, x1, x1+1; pick up 3 numbers for y: y1-1, y1, y1+1; and pick up 3 numbers for z: z1-1, z1, z1+1. Have fun!
Clicking �Example/Cask 3, Batch� command will generate the lottery example. You must be in the home directory to run this example. If you are not in the home directory, close and restart the PredictorPro. The parameters are: Trend = 4, Precision = 10, Command = 10 = "Integer\+ Linear".
Click "Batch\Run" to get the results. This batch file uses the �Integer/+ Linear� command. The results are:
File Results
Confidence
X
1
660
Y
8
516
Z
0, 4 64
XY 3 0
360
XZ 1 0
256
YZ No results
XYZ No results
Use the �Integer/- Linear� command, and you will get
File Results
Confidence
X
1
1280
Y
2,7 16
Z
4
528
XY 3 2
28
XZ No results
YZ No results
XYZ No results
Assume the minimum confidence number is 100, then the Predictor picks 184. The winning number on that day is 645.
Let a system be defined by a triplet (x, y, z) which obeys:
x (n+1) = ( x (n) + y(n)
+ z(n) ) Mod 7;
y (n+1) = x
( n );
z (n+1 ) = y
( n) Mod 5;
This is a finite dynamic system. The domains are:
x in { 0, 1, 2, 3,
4, 5, 6 };
y in { 0, 1,
2, 3, 4, 5, 6 };
z in { 0, 1,
2, 3, 4 }.
The possible states are 000, 001, . . ., 100, 101, . . . , 775.
Assume initially that (x, y, z) is in state (1 0 0), then it will generate
the following sequence by a computer simulation:
1 0 0
1 1 0
2 1 1
4 2 1
0 4 2
6 0 4
3 6 0
2 3 1
6 2 3
4 6 2
5 4 1
3 5 4
5 3 0
1 5 3
2 1 0
3 2 1
6 3 2
4 6 3
6 4 1
4 6 4
0 4 1
5 0 4
2 5 0
0 2 0
2 0 2
4 2 0
6 4 2
5 6 4
1 5 1
0 1 0
1 0 1
2 1 0
3 2 1
6 3 2
4 6 3
6 4 1
4 6 4
0 4 1
5 0 4
2 5 0
0 2 0
2 0 2
4 2 0
6 4 2
5 6 4
1 5 1
0 1 0
1 0 1
2 1 0
3 2 1
6 3 2
4 6 3
6 4 1
4 6 4
0 4 1
5 0 4
2 5 0
0 2 0
2 0 2
4 2 0
6 4 2
5 6 4
1 5 1
0 1 0
1 0 1
2 1 0
3 2 1
6 3 2
4 6 3
6 4 1
The next row is 4 6 4.
Step 1. Data and Input File;
The data set is {x, y, z}. The input Data file is math1a.txt, which contains the above. The file is in the software.Step 2. Link the data;
To generate data from software, click: �File/Open� to open "math1a.txt".Step 3: Running
Click: "10-Average/+ Integer Linear", this click produces the output data file, which will be opened at this point. It looks like this:
4 6 4 384000
0 4 1 384000
5 0 4 384000
2 5 0 384000
0 2 0 384000
2 0 2 384000
4 2 0 384000
6 4 2 384000
5 6 4 384000
1 5 1 384000In the output data file, the first line is 4 6 4, 38400. 464 is the next row predicted, and 38,400 is the confidence number of 464. The larger the confidence number is, the more reliable the prediction is. This is the correct answer.
The command predicts next 10 rows. In this case, they are all correct.
Let a system be defined by ( x, y, z , s, t), which obeys
the following rule:
x (n+1) = ( x (n) + y(n)
+ z(n) ) Mod 7;
y (n+1) = x
( n );
z (n+1 ) = y
( n) Mod 5;
60%
z (n+1 ) = (
y ( n)+ 1 ) Mod 5; 40%
s (n+1 ) = (
s(n) + 1 ) Mod 5; 60%
s (n+1 ) = (
s(n) + 2 ) Mod 5; 40%
t (n+1 ) = s
( n) Mod 3.
This is a Markov chain. Each state can go to one of 4 different states with the probability: 36%, 24%, 24%, and 16%. The possible domains are:
x in { 0, 1,
2, 3, 4, 5, 6 };
y in { 0, 1,
2, 3, 4, 5, 6 };
z in { 0, 1,
2, 3, 4 };
s in { 0, 1,
2, 3, 4 };
t in { 0, 1,
2 }.
The possible states are 00000, 00001, . . ., 10000, 10001, . . . , 77553. A computer simulates this Markov chain 20,000 times and the following data is generated:
1 0 0 0 0The next configuration generated by the computer is (6 6 1 0 1). Of course, any one out of 4 possibilities are correct. The data set is {x, y, z, s, t}, i.e. five variables. You can complete this problem in a similar way as the last example:
1 1 0 1 0
2 1 2 3 1
5 2 1 0 0
1 5 3 2 0
2 1 0 4 2
3 2 2 1 1
0 3 3 2 1
6 0 4 4 2
3 6 0 1 1
2 3 1 2 1
6 2 3 3 2
4 6 2 0 0
5 4 1 1 0
3 5 4 2 1
5 3 0 3 2
1 5 4 0 0
3 1 0 2 0
4 3 2 4 2
2 4 3 0 1
2 2 0 1 0
4 2 2 2 1
1 4 2 3 2
0 1 4 4 0
5 0 1 0 1
6 5 0 1 0
4 6 0 3 1
�
- The data file is "math2a.txt"; click �File/Open� to open and link to the file;
- To run, click "Integer/ +Linear".
The result is a distribution:
Possibility Confidence*Probability
1 3 0 2 0 443
6 3 2 1 1 139
3 4 0 0 1 405
0 3 4 1 0 500
6 6 1 0 1 4000
6 6 1 1 0 42000
2 5 4 0 1 101
5 1 3 1 1 367
4 2 2 0 1 44
3 0 3 1 1 481
6 5 1 0 1 253
2 4 0 0 1 24000
2 4 1 0 1 12000
0 2 4 1 0 481
4 5 2 0 1 750
2 4 1 1 0 2500
6 2 4 2 0 310
5 6 1 0 1 424
5 3 1 2 0 120
6 6 2 2 0 5000
1 1 0 0 1 101
6 2 0 1 0 44
4 1 3 2 0 291
0 6 1 2 0 215
---------------------------------------------------
Weighted Average
4 5 1 1 0
Highest Probability
6 6 1 1 0 42000
Error of each number
0.33 0.33 0.22 0.22 0.11
The most likely possibility is ( 6, 6, 1, 1, 0). This is very close
to the computer-simulated result, ( 6, 6, 1, 0, 1). Ignoring everything
below 1000, the probability of the above configuration is roughly:
42000/(4000+42000+24000+12000+2500+5000) = 47%.
The confidence of this prediction is 42,000.
Attrasoft Dow 5 is very similar to the Dogs of the Dow. The Dogs of the Dow is a stock picking system that has been reported on periodically in the popular press. Attrasoft Dow 5 uses Attrasoft Predictor to pick up 5 "top" stocks among the 30 Dow stocks. Basically, you hold the Attrasoft Dow 5 for a 6-months period. At the end of the period, you pick up the new Attrasoft Dow 5.
To predict a stock trend with the Attrasoft Predictor, you will need a "Model" and data. A model is a set of relevant variables. The data is the historical values of the chosen variables. The Attrasoft Dow 5 uses the simplest model: to predict a stock, there is only one variable in the model, the 5-month moving average of the stock.
Attrasoft Predictor 2.6, with a Single-Stock-Model, outperforms Dow Jones 30 by a factor of 2 from Feb. 1997 to Jan 30, 2001: 112.4 % vs. 58.15 %.
6.4.1 Attrasoft Dow 5: Game Rules
Assumption:
1. You start with $100,000 paper money, which must be equally invested in 5 stocks, from the Dow Jones 30 stocks <http://attrasoft.com/stock/data/Excel/> ;
2. You update your Attrasoft Dow 5 once every 6 months.
The data is obtained from Microsoft Network:
http://investor.msn.com/quotes/quotes.asp?beenthere=1&Page=Research&Item=QuoteDetail,
see the last chapter.
1. Results From 1/97 to 7/97, UP 23.4 %, http://attrasoft.com/stock/data/a2_97_6a.txt
rank stock
Feb-97 Jul-97
grow rate
Dj 30 6877.7
8222.6 19.5545
SP 500 790.82
954.31 20.67348
1 mrk
92.125 103.875
12.75441
2 AXP
65.625 83.75
27.61905
3 utx
75.25 84.563
12.37608
4 uk
47.25 55.375
17.19577
5 ibm
71.875 105.75
47.13043
avg
23.41515
2. Results From 8/97 to 1/98, Down 2.45%, http://attrasoft.com/stock/data/a8_97_6a.txt
rank stock Aug-97
Jan-98 grow rate
Dj 30
7622.4 7906.5 1.037272
SP 500
899.47 980.28 1.089842
1 xon
61.188 59.313 0.969357
2 axp
77.75 83.688
1.076373
3 utx
78.063 81.25
1.040826
4 ibm
105.75 98.75
0.933806
5 cat
56
48 0.857143
avg 0.975501
3. Results From 2/98 to 7/98, Up 1.94%, http://attrasoft.com/stock/data/a2_98_6a.txt
rank stock Feb-98
Jul-98 grow rate
Dj 30
8545.72 8883.29 1.039502
SP 500
980.28 1120.67
1.143214
1 Ald
42.563 43.5
1.022014
2 AA
73.375 69.313
0.944641
3 Uk
46.438 48
1.033636
4 Ibm
104.438 132.5
1.268695
5 Hwp
67 55.5
0.828358
Avg 1.019469
4. Results From 8/98 to 1/99, Up 44.17%, http://attrasoft.com/stock/data/a8_98_6a.txt
rank Stock Aug-98
Jan-99 grow rate
Dj 30
7539.07 9358.83 24.13773
SP 500
957.28 1279.64 33.67458
1 Ko
65.125 65.313
0.288676
2 Axp
78
102.875 31.89103
3 Utx
72.563 119.438 64.59904
4 Ibm
112.625 183.25 62.7081
5 Hwp
48.563 78.375
61.3883
Avg 44.17503
5. Results From 2/99 to 7/99, up 31.92 %, http://attrasoft.com/stock/data/jan1999a.txt
rank Stock 2-1-99
7-30-99 grow rate
Dj 30
9345.7 10655.15 14.01
SP 500
1273 1328.72
4.3
1 Axp
100.75 137.288
36.626
2 Ald
39.125 64.688
65.336
3 Cat
43.688 58.625
34.19
4 chv
73.688 91.25
23.83
5 wmt
42.25 42.25
0
avg 31.92
6. Results From 8/99 to 1/2000, Up 9.17%, http://attrasoft.com/stock/data/a8_99_6a.txt
rank stock 8-2-99
1-31-00 grow rate
Dj 30
10645.96 10940.53 2.77%
SP 500
1328.05 1394.46
5%
1 msft
84.914 97.875
1.152
2 cat
58.563 42.4375
0.725
3 axp
130.063 164.75
1.267
4 pg
90.125 100.875
1.119
5 c
44.125 57
1.229
avg up 9.1%
7. Results From 2/2000 to 7/2000, down 7.1%, http://attrasoft.com/stock/data/a2_00_6a.txt
rank stock 2-1-99
7-31-00 grow rate
Dj 30
11041.05 10521.98 down 4.7%
SP 500
1409.28 1430.83
up 1.5 %
1 axp
56.33 56.6875
1.006
2 c
58.25 70.5
1.210
3 hd
62.00 51.75
0.835
4 aa
36.06 30.25
0.839
5 dd
59.875 45.31
0.757
avg
down 7.1%
8. Results From 8/2000 to 1/2001, down 5.0%, http://attrasoft.com/stock/data/a8_00_6a.txt
rank stock
7-1-00 1-31-01
grow rate
Dj 30
10606.95 10877.36
+ 2.5%
SP 500
1438.11 1366.01
down 5 %
1 Msft
68.688 61.06
0.89
2 Axp
56.938 47.17
0.83
3 Ibm
110.5
112.0
1.01
4 Utx
59.25
74.98
1.27
5 T
31.813 23.99
0.75
Avg down 5 %
Evaluation: Feb 1997 - Jan 31, 2000
Predicted GrowthAttrasoft Predictor, with a Single-Stock-Model, outperforms Dow Jones 30 by a factor of 2 from Feb. 1997 to Jan 30, 2001: 112.4 % vs. 58.15 %. The �Attrasoft Dow 5� prediction for the period August 2000 to January 2001 is in the software. To generate this example:
= 1.234151478 * 0.975501* 1.019468885* 1.441750282 * 1.3192* 1.091*0.929 *0.95
= 2.124
Up 112.4% in 4 years.Dow Jones 30:
Feb 1, 1997: 6877.7; Jan 31, 2001: 10877.36
Up : 58.15% in 4 years.
- Make sure you are in the home directory;
- Click �Example\Attrasoft DJ 30, Batch�;
- Click �Batch\Run�.
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Version 2.8 ($494.99 + $5 US Shipping and Handling)
Mail Order: 499.99 (S&H included)
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Attrasoft, Attn.: Gina
P. O. Box 13051
Savannah, GA. 31406, USA
or contact us at:webmaster@attrasoft.com
Attrasoft, P. O. Box 13051, Savannah, GA. 31406, USA
Copyright © 2001 Attrasoft, Inc. All rights reserved.