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Aparkr -
To answer your question: yes, a neural network can learn any continuous
non-linear or linear function of it's inputs. If this is such a function,
and we can't come up with such a network, then either a) we no damn good
or b) you have come up with a counter example to some fairly well
accepted mathematical proofs (which would not be the first time such a
thing has happened). This learning capability is reasonably well
understood and has been applied successfully to a wide range of problems
(not stock market prediction).
I don't think it's correct to say that if a neural net can't learn a
mathematical algorithm then it cannot predict the market. Here's a simple
function of 1 variable that a neural net can't learn: f(x) = 1 if x is
rational and 0 if x is irrational.
As far as your challenge, I think this is exactly the type of thinking
necessary to prove or disprove a methodology. Several universities keep
databases of test problems for researchers to use as test cases. If we
can't solve this one (and we don't know why), I suggest you submit it to
one of those.
How long do we have to solve it, and will you disclose the function
afterwards?
Larry Lewis
----------
From: Aparkr (reply to: Aparkr@xxxxxxx)[SMTP:Aparkr@xxxxxxx (MIME)
(actually from: owner-realtraders@xxxxxxxxxxxxxx)]
Sent: Friday, May 01, 1998 2:24 PM
To: realtraders
Subject: GOOD LUCK! IT CAN'T BE DONE
I am curious. Do Neural's really learn??
I am proposing a challenge. If a neural cannot learn the
relationship of a mathematical algorithm, then obviously it
cannot even begin to predict the market. So, below is data
which is comprised of the date, the close of SP500, and
an indicator calculated from the last 9 closes. If any
of you really believe in neurals, then I dare you to transfer this data
to
your trusty and favorite neural eg., brainmaker, ngo, neuralware,
neuroshell
etc. and let it
train, to predict the value of the indicator respective to the date,and
close
of the SP. Remember, we are not trying to predict an unknown ( tomorrow's
value, which is a prediction ), we are trying to predict the known value,
which is calculated via a relatively simple mathematical algorithm, from
the
last 9 closes.
We are not trying to predict out into the future.
Apply the data below to a neural or whatever.
When you satisfied of the error rate, then apply it to the attached out
of
sample
data. Email me the out of sample data back with your program's
calculation for
each day of the out of sample data.
MY PREDICTION: NO ONE WILL BE ABLE TO CALCULATE THE
OUT OF SAMPLE DATA'S INDICATOR VALUES WITH INSIGNIFICANT
ERROR'S. AGAIN, REMEMBER THERE IS NO PREDICTING INVOLVED IN
THIS EXERCISE. THINK OF IT AS DECODING A RELATIONSHIP EG.,
1 6 11 16 ....NOW WHAT IS THE VALUE OF THE NEXT NUMBER IN
THE SERIES.. 21. That's exactly what's going on here. My contention is,
if
there is a Neural out there can solve for this indicator, then it is
definitely a neural that can LEARN. I haven't found one Neural that can
learn
this "algorithm" with insignificant errors. Hope to hear from any of you
Realtraders who haved solved this algorithm.
Below is the training data, and below that is the out of sample data.
Good
Luck!
TRAINING DATA BELOW
" date close indicator "
941130 503.35 518.35 " solve for the value of the indicator (
indicator
is derived
941201 501.05 514.65 from last 9 closes)"
941202 496.10 511.50
941205 501.00 507.60
941206 501.15 506.15
941207 500.95 505.35
941208 499.05 505.05
941209 492.80 506.80
941212 494.85 506.65
941213 497.20 505.00
941214 498.10 504.30
941215 502.05 505.45
941216 502.60 506.00
941219 505.75 507.95
941220 505.90 509.70
941221 504.40 510.80
941222 508.85 512.25
941223
507.20 512.20
941227 507.50 511.90
941228 509.95 511.75
941229 508.25 511.65
941230 508.55 511.15
950103 505.30 511.30
950104 505.40 511.40
950105 507.70 511.10
950106 507.20 510.60
950109 506.95 510.75
950110 507.70 510.70
950111 508.15 509.95
950112 508.40 510.00
950113 508.20 509.80
950116 513.00 513.00
950117 515.70 515.70
950118 515.95 518.15
950119 515.10 519.30
950120 512.55 519.35
950123 511.25 519.05
950124 512.05 518.65
950125 512.30 518.30
950126 513.85 517.25
950127 515.10 517.70
950130 515.50 517.50
950131 513.90 516.90
950201 516.15 517.35
950202 515.85 517.85
950203 518.60 519.20
950206 525.00 525.00
950207 526.70 528.10
950208 526.95 530.95
950209 526.30 532.50
950210 526.60 533.80
950213 527.60 534.00
950214 527.30 533.70
950215 527.65 532.05
950216 530.75 530.75
950217 530.25 531.25
950221 528.40 531.40
950222 528.35 531.55
950223 531.05 532.25
950224 532.65 533.45
950227 532.65 534.45
950228 528.90 534.10
950301 532.50 534.50
950302 530.10 534.50
950303 530.40 534.40
950306 529.80 534.20
950307 530.15 533.95
950308 526.10 534.90
950309 527.40 534.40
950310 527.30 533.50
950313 535.05 535.85
950314 534.10 536.50
950315 537.45 539.25
950316 536.15 540.75
950317 539.60 543.40
950320 539.80 545.40
950321 540.20 546.00
950322 539.40 545.40
950323 539.40 543.00
950324 539.40 543.00
950327 545.45 545.45
950328 547.60 548.40
950329 547.45 550.05
950330 546.50 551.10
950331 546.45 551.85
950403 544.45 551.85
950404 544.65 551.45
950405 547.85 551.25
950406 548.95 549.95
950407 549.65 550.85
950410 548.70 551.30
950411 549.75 551.95
950412 548.05 552.05
950413 550.00 552.60
950417 552.20 553.40
950418 548.45 552.25
950419 547.80 552.20
950420 546.70 552.50
950421 547.35 552.35
950424 550.35 552.75
950425 555.05 555.45
950426 553.45 556.45
950427 554.25 557.65
950428 555.35 558.75
950501 556.80 560.40
950502 555.35 560.75
950503 556.70 560.70
950504 562.65 562.65
950505 563.05 564.65
950508 561.40 565.60
950509 565.35 567.95
950510 564.50 568.90
950511 565.45 569.85
950512 566.70 570.90
950515 567.30 570.70
950516 569.95 570.95
950517 569.55 571.95
950518 567.85 572.25
950519 559.15 573.15
950522 560.40 573.80
950523 565.35 573.95
950524 570.05 574.85
950525 569.50 575.50
950526 569.95 576.15
950530 563.90 575.30
950531 563.55 574.35
950601 573.40 576.60
950602 573.80 577.80
950605 572.20 577.60
950606 576.70 579.90
950607 575.40 581.00
950608 573.35 581.55
950609 571.75 581.75
950612 568.75 580.55
950613 572.40 578.00
950614 576.40 579.00
950615 576.20 579.60
950616 578.40 581.00
950619 579.50 582.10
950620 585.25 586.45
950621 584.90 589.30
950622 584.55 590.95
950623 590.95 593.55
950626 590.50 595.10
950627 583.80 594.80
950628 582.75 593.75
950629 585.00 593.00
950630 584.05 592.05
950703 582.75 592.15
950705 585.15 592.15
950706 587.60 592.60
950707 593.45 594.05
950710 595.65 596.85
950711 596.80 600.20
950712 593.35 601.15
950713 599.70 604.30
950714 599.60 606.00
950717 598.35 605.55
950718 601.05 605.25
950719 596.50 603.10
950720 589.50 604.50
950721 591.85 604.85
950724 590.95 604.95
950725 596.00 605.00
950726 598.90 604.90
950727
599.65 604.85
950728 603.15 606.75
950731 599.90 606.30
950801 598.75 606.75
950802 597.00 605.80
950803 594.95 605.35
950804 596.05 603.85
950807 596.20 603.80
950808 596.85 603.65
950809 597.45 603.25
950810 597.50 600.50
950811 594.10 599.70
950814 592.80 599.40
950815 597.30 599.50
950816 595.65 599.45
950817 596.20 599.60
950818 596.20 599.60
950821 597.20 599.60
950822 594.45 599.25
950823 595.50 598.70
950824 593.40 598.80
950825 594.70 598.50
950828 597.65 598.65
950829 595.00 598.60
950830 596.15 598.55
950831 596.75 598.75
950901 598.45 599.45
950905 600.55 601.15
950906 604.95 605.15
950907 606.75 608.35
950908 606.60 610.40
950911 609.05 613.05
950912 609.55 614.55
950913 612.30 616.50
950914 615.10 618.50
950915 619.80 621.80
950918 620.00 623.80
950919 618.65 624.85
950920 620.80 626.40
950921 623.05 627.65
950922 617.55 626.75
950925 618.15 625.35
950926 616.90 623.90
950927 616.85 623.45
950928 616.35 623.55
950929 620.10 623.50
951002 619.10 623.70
951003 615.95 623.15
951004 617.20 620.60
951005 615.80 620.60
951006 617.50 620.50
951009 617.50 620.50
951010 612.65 621.65
951011 612.15 622.15
951012 614.25 620.85
951013 618.40 620.60
951016 619.10 621.50
951017 616.00 621.40
951018 620.80 623.00
951019 621.85 624.45
951020 624.85 627.25
951023 620.55 627.35
951024 618.70 626.30
951025 620.15 625.35
951026 614.85 626.25
951027 609.55 628.35
951030 614.40 628.40
951031 617.60 628.00
951101 614.75 626.95
951102 619.15 624.35
951103 623.25 625.65
951106 623.40 627.20
951107 622.20 628.00
951108 619.10 628.10
951109 625.00 628.20
951110 625.60 629.00
951113 625.35 629.95
951114 624.80 628.60
951115 621.35 628.15
951116 627.20 629.20
951117 630.80 632.00
951120 632.05 634.45
951121 629.30 634.10
951122 632.65 635.85
951124 631.30 636.70
951127 632.45 637.65
951128 632.70 638.10
951129 638.80 638.80
951130 638.95 640.55
951201 638.15 641.95
951204 639.20 643.20
951205 645.70 646.90
951206 649.65 651.65
951207 650.70 655.10
951208 647.35 655.75
951211 649.15 655.75
951212 650.85 657.05
951213 649.95 657.35
951214 652.50 656.90
951215 648.70 653.70
951218 647.70 653.10
951219 636.55 658.15
951220 642.80 657.80
951221 638.00 658.60
951222 640.90 658.10
951226 643.30 656.50
951227 644.50 654.90
951228 644.15 651.75
951229 642.70 649.70
960102 643.40 647.80
960103 650.05 650.25
960104 651.90 653.50
960105 644.75 652.75
960108 644.25 652.45
960109 647.35 652.75
960110 633.45 656.05
960111 625.70 660.30
960112 630.60 661.00
960115 629.90 660.90
960116 628.15 658.15
960117 635.85 652.85
960118 633.25 649.85
960119 635.45 646.85
960122 639.10 641.50
960123 638.65 643.05
960124 641.10 644.50
960125 646.90 648.90
960126 643.95 650.35
960129 649.10 652.10
960130 651.15 655.35
960131 656.90 659.50
960201 662.90 665.50
960202 664.60 670.40
960205 663.30 672.50
960206 666.85 674.65
960207 673.15 679.55
960208 676.70 682.50
960209 683.30 687.90
960212 684.20 690.80
960213 689.20 695.40
960214 686.75 697.95
960215 680.85 697.45
960216 676.35 694.95
960220 675.35 692.75
960221 668.45 694.25
960222 676.65 694.25
960223 684.90 694.50
960226 684.20 694.60
96022
7 673.80 691.60
960228 672.55 688.75
960229 668.45 688.25
960301 663.20 689.60
960304 672.20 689.40
960305 675.65 689.45
960306 682.40 691.20
960307 676.15 688.15
960308 679.20 686.00
960311 656.90 689.10
960312 663.85 689.05
960313 659.80 689.60
960314 662.65 689.65
960315 666.40 689.20
960318 665.90 687.50
960319 678.40 685.40
960320 676.20 685.40
960321 675.05 683.65
960322 673.55 683.75
960325 675.25 684.85
960326 674.80 684.00
960327 677.70 683.50
960328 670.20 682.60
960329 673.65 680.25
960401 670.15 679.55
960402 676.30 679.70
960403 677.50 680.50
960404 678.00 681.40
960408 678.50 682.30
960409 665.90 683.90
960410 663.90 684.30
960411 652.15 689.55
960412 652.50 690.90
960415 659.50 690.50
960416 664.70 688.10
960417 666.20 684.80
960418 663.75 680.15
960419 664.85 673.45
960422 665.95 673.55
960423 670.95 675.95
960424 673.90 678.10
960425 670.60 676.20
960426 673.95 677.15
960429 675.35 678.95
960430 674.05 680.05
960501 673.75 679.75
960502 675.35 679.15
960503 664.75 679.75
960506 662.40 681.80
960507 661.80 682.40
960508 657.95 683.75
960509 666.40 682.40
960510 666.25 680.25
960513 673.80 680.00
960514 682.65 684.85
960515 686.20 690.00
960516 686.25 695.25
960517 685.95 698.75
960520 690.40 702.00
960521 695.15 703.55
960522 694.70 704.90
960523 699.80 705.00
960524 697.35 703.95
960528 699.50 705.10
960529 692.70 704.70
960530 688.00 704.40
960531 692.30 703.10
960603 685.85 704.25
960604 688.35 704.15
960605 692.10 703.90
960606 697.65 702.85
960607 692.15 701.55
960610 692.75 698.75
960611 690.30 698.50
960612 690.45 698.45
960613 688.65 698.25
960614 687.70 697.70
960617 683.60 699.00
960618 684.55 699.15
960619 680.55 696.95
960620 681.75 695.95
960621 679.90 694.30
960624 686.50 692.90
960625 688.20 691.80
960626 687.20 691.40
960627 681.70 690.30
960628 686.10 690.90
960701 689.85 692.65
960702 693.85 695.65
960703 691.85 696.85
960705 689.15 695.95
960708 674.15 699.55
960709 669.35 702.55
960710 672.20 702.80
960711 674.75 702.95
960712 661.40 704.80
960715 661.10 703.10
960716 643.30 702.50
960717 645.15 697.15
960718 650.85 687.85
960719 660.50 684.30
960722 655.05 681.65
960723 650.60 676.80
960724 641.20 669.00
960725 643.75 666.15
960726 648.25 662.25
960729 652.40 662.60
960730 644.05 662.85
960731 650.75 662.75
960801 655.45 660.05
960802 666.10 666.50
960805 679.40 679.80
960806 674.75 685.35
960807 677.30 690.10
960808 679.25 694.25
960809 679.25 697.25
960812 675.50 694.30
960813 680.80 692.00
960814 674.85 686.05
960815 676.65 682.45
960816 676.65 681.85
960819 681.15 682.95
960820 681.25 683.85
960821 681.00 684.40
960822 679.05 684.25
960823 684.90 686.30
960826 681.85 686.65
960827 677.25 686.05
960828 679.75 685.75
960829 678.75 685.35
960830 670.20 688.20
960903 664.40 691.00
960904 668.90 690.70
960905 669.65 690.05
960906 662.05 687.85
960909 671.30 684.70
960910 678.10 685.10
960911 678.20 684.40
960912 680.05 684.85
960913 685.15 689.75
960916 695.90 698.30
960917 697.80 705.00
960918 697.00 709.40
960919 694.25 707.85
960920 696.90 708.10
960923 698.95 709.15
960924 699.45 708.45
960925 699.10 705.70
96092
6 698.10 701.10
960927 699.00 701.40
960930 698.45 701.45
961001 698.45 701.65
961002 702.15 702.15
961003 706.40 706.40
961004 704.75 707.35
961007 714.25 714.25
961008 715.25 718.65
961009 711.80 720.20
961010 707.55 720.15
961011 705.45 719.25
961014 712.95 719.15
961015 714.55 719.55
961016 713.70 720.10
961017 715.65 720.05
961018 718.05 721.45
961021 722.90 724.90
961022 721.45 727.05
961023 716.15 726.75
961024 718.10 724.50
961025 710.80 725.00
961028 712.40 725.20
961029 707.40 726.60
961030 713.30 726.50
961031 709.85 726.25
961101 716.70 723.70
961104 713.55 720.75
961105 718.30 721.50
961106 722.45 723.85
961107 736.45 736.45
961108 738.00 743.20
961111 741.30 749.10
961112 741.15 753.75
961113 739.05 754.65
961114 741.20 756.20
961115 746.30 756.10
961118 747.90 755.10
961119 747.40 751.20
961120 753.35 754.95
961121 753.20 757.20
961122 752.50 758.70
961125 758.25 762.05
961126 767.00 768.20
961127 764.40 770.40
961129 763.00 771.80
961202 765.30 773.30
961203 765.05 773.05
961204 752.55 773.15
961205 754.70 772.90
961206 752.40 773.00
961209 747.55 774.75
961210 758.55 772.35
961211 755.10 770.50
961212 746.55 769.75
961213 734.50 770.30
961216 736.40 766.80
961217 727.75 768.95
961218 733.25 767.05
961219 738.15 764.55
961220 753.50 766.30
961223 757.25 765.85
961224 754.10 765.30
961226 759.05 769.65
961227 764.60 775.60
961230 764.60 779.80
961231 759.10 777.30
970102 744.50 773.90
970103 744.70 771.70
970106 757.20 772.00
970107 750.70 771.70
970108 759.65 772.45
970109 755.50 771.90
970110 758.90 769.90
970113 766.60 771.00
970114 764.30 772.70
970115 773.20 777.20
970116 771.65 778.25
970117 775.25 782.25
970120 780.75 785.55
970121 780.15 788.75
970122 786.95 792.15
970123 791.60 796.20
970124 780.25 795.85
970127 769.75 794.35
970128 768.95 794.95
970129 771.50 795.10
970130 778.30 795.30
970131 787.95 797.35
970203 787.50 799.10
970204 789.75 799.95
970205 793.70 800.90
970206 780.50 800.90
970207 782.65 800.25
970210 794.35 801.35
970211 788.05 798.85
970212 794.85 799.65
970213 807.25 808.05
970214 814.15 817.35
970218 812.20 822.80
970219 818.35 829.75
970220 814.30 831.10
970221 804.35 828.15
970224 804.45 827.65
970225 812.55 824.55
970226 814.15 821.75
970227 803.75 822.55
__________________________________
OUT OF SAMPLE DATA
"DATE CLOSE INDICATOR ? "
910130 413.00 " what is the value of the indicator for this date
calculated from
910131 415.40 last 9 closes? That's the problem.
910201 414.15
910204 419.70
910205 423.55
910206 430.60
910207 428.65
910208 431.45
910211 440.65
910212 437.05
910213 441.00
910214 436.10
910215 440.20
910219 440.90
910220 437.25
910221 436.65
910222 437.60
910225 438.80
910226 434.55
910227 439.85
910228 437.55
910301 442.00
910304 440.40
910305 448.10
910306 447.35
910307 446.40
910308 446.15
910311 444.25
910312 441.45
910313 446.30
910314 444.20
910315 442.80
910318 443.25
910319 437.25
910320 438.65
910321 436.90
910322 438.45
910325 440.10
910326 446.95
910327 445.80
910328 443.50
910401 440.85
910402 449.30
910403 447.90
910404 449.25
910405 444.65
910408 448.35
910409 442.85
910410 443.05
910411 448.35
910412 449.6
5
910415 449.65
910416 456.40
910417 459.40
910418 458.00
910419 453.60
910422 450.55
910423 450.00
910424 451.00
910425 447.45
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