Использование нечеткой искусственной нейронной сети TSK Takagi Sugeno Kanga в задаче прогнозирования (стр. 6 из 14)

Рассматривалась чувствительность ННС TSK к изменению количества правил. На обучающей выборке при увеличении количества правил уменьшается ошибка по критерию СКО и САПП при прогнозах на 1 и на 3 шага вперед. На проверочной выборке при увеличении количества правил сначала достигается минимум при количества правил

, а затем ошибка увеличивается.

Во время выполнения экспериментальных исследований, были получены результаты, которые могут быть использованы в деятельности банков и других инвесторов.

Литература

1. Лукашин Ю. П. Адаптивные методы краткосрочного прогнозирования временных рядов. – М.: Финансы и статистика, 2003. – 416 с.

2. Згуровский М. З., Подладчиков В. Н. Аналитические методы калмановской фильтрации для систем с априорной неопределенностью. – К.: Наукова думка, 1995. – 584с.

3. Зайченко Ю. П. Нечеткие модели и методы в интеллектуальных системах. К.: Слово, 2008. – 344с.

4. Круглов В. В., Борисов В. В. Искусственные нейронные сети. Теория и практика. – М.: Горячая линия – Телеком, 2001. – 382с.

5. Руденко О. Г., Бодянський Є. В. Штучні нейронні мережі. – Харків: Компанія СМІТ, 2006. – 404с.

6. Хоменко А., Гофман В., Мещеряков Е., Никифоров В. Delphi 7. – Санкт-Петербург: БВХ-Петербург, 2004. – 1200с.

Приложение 1. Результаты экспериментальных исследований.

Первый столбец – реальные данные. Второй столбец – прогноз на 1 шаг вперед. Третий столбец – ошибка прогноза на 1 шаг вперед. Четвертый столбец – прогноз на 3 шага вперед. Пятый столбец – ошибка прогноза на 3 шага вперед.

USD_EUR

0.6456 0.6467 -0.0011 0.6447 0.0009

0.6415 0.6456 -0.0041 0.6467 -0.0052

0.6447 0.6438 0.0009 0.6474 -0.0027

0.6467 0.6447 0.0020 0.6438 0.0029

0.6441 0.6415 0.0026 0.6456 -0.0015

0.6384 0.6441 -0.0057 0.6415 -0.0031

0.6341 0.6384 -0.0043 0.6441 -0.0100

0.6368 0.6341 0.0027 0.6384 -0.0016

0.6336 0.6368 -0.0032 0.6341 -0.0005

0.6358 0.6336 0.0022 0.6368 -0.0010

0.6399 0.6358 0.0041 0.6336 0.0063

0.6441 0.6399 0.0042 0.6358 0.0083

0.6428 0.6441 -0.0013 0.6399 0.0029

0.6432 0.6428 0.0004 0.6441 -0.0009

0.6472 0.6432 0.0040 0.6428 0.0044

0.6472 0.6472 -0.0000 0.6432 0.0040

0.6427 0.6472 -0.0045 0.6472 -0.0045

0.6356 0.6427 -0.0071 0.6472 -0.0116

0.6363 0.6356 0.0007 0.6427 -0.0064

0.6464 0.6363 0.0101 0.6356 0.0108

0.6427 0.6464 -0.0037 0.6363 0.0064

0.6487 0.6427 0.0060 0.6464 0.0023

0.6508 0.6487 0.0021 0.6427 0.0081

0.6464 0.6508 -0.0044 0.6487 -0.0023

0.6444 0.6464 -0.0020 0.6508 -0.0064

0.6452 0.6444 0.0008 0.6464 -0.0012

0.6451 0.6452 -0.0001 0.6444 0.0007

0.6400 0.6451 -0.0051 0.6452 -0.0052

0.6456 0.6400 0.0056 0.6451 0.0005

0.6414 0.6456 -0.0042 0.6400 0.0014

0.6423 0.6414 0.0009 0.6456 -0.0033

0.6355 0.6423 -0.0068 0.6414 -0.0059

0.6350 0.6355 -0.0005 0.6423 -0.0073

0.6350 0.6350 -0.0000 0.6355 -0.0005

0.6330 0.6350 -0.0020 0.6350 -0.0020

0.6302 0.6330 -0.0028 0.6350 -0.0048

0.6366 0.6302 0.0064 0.6330 0.0036

0.6392 0.6366 0.0026 0.6302 0.0090

0.6389 0.6392 -0.0003 0.6366 0.0023

0.6352 0.6389 -0.0037 0.6392 -0.0040

0.6341 0.6352 -0.0011 0.6389 -0.0048

0.6291 0.6341 -0.0050 0.6352 -0.0061

0.6284 0.6291 -0.0007 0.6341 -0.0057

0.6280 0.6284 -0.0004 0.6291 -0.0011

0.6311 0.6280 0.0031 0.6284 0.0027

0.6306 0.6311 -0.0005 0.6280 0.0026

0.6307 0.6306 0.0001 0.6311 -0.0004

0.6299 0.6307 -0.0008 0.6306 -0.0007

0.6325 0.6299 0.0026 0.6307 0.0018

0.6367 0.6325 0.0042 0.6299 0.0068

0.6376 0.6367 0.0009 0.6325 0.0051

0.6351 0.6376 -0.0025 0.6367 -0.0016

0.6416 0.6351 0.0065 0.6376 0.0040

0.6428 0.6416 0.0012 0.6351 0.0077

0.6414 0.6428 -0.0014 0.6416 -0.0002

0.6424 0.6414 0.0010 0.6428 -0.0004

0.6435 0.6424 0.0011 0.6414 0.0021

0.6466 0.6435 0.0031 0.6424 0.0042

0.6489 0.6466 0.0023 0.6435 0.0054

0.6519 0.6489 0.0030 0.6466 0.0053

0.6646 0.6519 0.0127 0.6489 0.0157

0.6686 0.6646 0.0040 0.6519 0.0167

0.6711 0.6686 0.0025 0.6646 0.0065

0.6714 0.6711 0.0003 0.6686 0.0028

0.6731 0.6714 0.0017 0.6711 0.0020

0.6806 0.6731 0.0075 0.6714 0.0092

0.6789 0.6806 -0.0017 0.6731 0.0058

0.6782 0.6789 -0.0007 0.6806 -0.0024

0.6803 0.6782 0.0021 0.6789 0.0014

0.6724 0.6803 -0.0079 0.6782 -0.0058

0.6757 0.6724 0.0033 0.6803 -0.0046

0.6756 0.6757 -0.0001 0.6724 0.0032

0.6822 0.6756 0.0066 0.6757 0.0065

0.6811 0.6822 -0.0011 0.6756 0.0055

0.6809 0.6811 -0.0002 0.6822 -0.0013

0.6818 0.6809 0.0009 0.6811 0.0007

0.6887 0.6818 0.0069 0.6809 0.0078

0.6903 0.6887 0.0016 0.6818 0.0085

0.6965 0.6903 0.0062 0.6887 0.0078

0.7007 0.6965 0.0042 0.6903 0.0104

0.7081 0.7007 0.0074 0.6965 0.0116

0.7056 0.7081 -0.0025 0.7007 0.0049

0.7134 0.7056 0.0078 0.7081 0.0053

0.7176 0.7134 0.0042 0.7056 0.0120

0.7057 0.7176 -0.0119 0.7134 -0.0077

0.7052 0.7057 -0.0005 0.7176 -0.0124

0.7067 0.7052 0.0015 0.7057 0.0010

0.7076 0.7067 0.0009 0.7052 0.0024

0.6953 0.7076 -0.0123 0.7067 -0.0114

0.6950 0.6953 -0.0003 0.7076 -0.0126

0.6806 0.6950 -0.0144 0.6953 -0.0147

0.6786 0.6806 -0.0020 0.6950 -0.0164

0.6825 0.6786 0.0039 0.6806 0.0019

0.6830 0.6825 0.0005 0.6786 0.0044

0.6852 0.6830 0.0022 0.6825 0.0027

0.6954 0.6852 0.0102 0.6830 0.0124

0.7103 0.6954 0.0149 0.6852 0.0251

0.7114 0.7103 0.0011 0.6954 0.0160

0.7219 0.7114 0.0105 0.7103 0.0116

0.7238 0.7219 0.0019 0.7114 0.0124

0.7403 0.7238 0.0165 0.7219 0.0184

0.7327 0.7403 -0.0076 0.7238 0.0089

0.7311 0.7327 -0.0016 0.7403 -0.0092

0.7329 0.7311 0.0018 0.7327 0.0002

0.7425 0.7329 0.0096 0.7311 0.0114

0.7381 0.7425 -0.0044 0.7329 0.0052

0.7322 0.7381 -0.0059 0.7425 -0.0103

0.7372 0.7322 0.0050 0.7381 -0.0009

0.7454 0.7372 0.0082 0.7322 0.0132

0.7430 0.7454 -0.0024 0.7372 0.0058

0.7512 0.7430 0.0082 0.7454 0.0058

0.7632 0.7512 0.0120 0.7430 0.0202

0.7792 0.7632 0.0160 0.7512 0.0280

0.7766 0.7792 -0.0026 0.7632 0.0134

0.7902 0.7766 0.0136 0.7792 0.0110

0.8035 0.7902 0.0133 0.7766 0.0269

0.8016 0.8035 -0.0019 0.7902 0.0114

0.7782 0.8016 -0.0234 0.8035 -0.0253

0.7783 0.7782 0.0001 0.8016 -0.0233

0.7886 0.7783 0.0103 0.7782 0.0104

0.7863 0.7886 -0.0023 0.7783 0.0080

0.7681 0.7863 -0.0182 0.7886 -0.0205

0.7669 0.7681 -0.0012 0.7863 -0.0194

0.7840 0.7669 0.0171 0.7681 0.0159

0.7828 0.7840 -0.0012 0.7669 0.0159

0.7838 0.7828 0.0010 0.7840 -0.0002

0.7966 0.7838 0.0128 0.7828 0.0138

0.7984 0.7966 0.0018 0.7838 0.0146

0.7856 0.7984 -0.0128 0.7966 -0.0110

0.7858 0.7856 0.0002 0.7984 -0.0126

0.7882 0.7858 0.0024 0.7856 0.0026

0.7939 0.7882 0.0057 0.7858 0.0081

0.7986 0.7939 0.0047 0.7882 0.0104

0.7983 0.7986 -0.0003 0.7939 0.0044

0.7758 0.7983 -0.0225 0.7986 -0.0228

0.7675 0.7758 -0.0083 0.7983 -0.0308

0.7798 0.7675 0.0123 0.7758 0.0040

0.7798 0.7798 -0.0000 0.7675 0.0123

0.7916 0.7798 0.0118 0.7798 0.0118

0.7859 0.7916 -0.0057 0.7798 0.0061

0.7893 0.7859 0.0034 0.7916 -0.0023

0.7789 0.7893 -0.0104 0.7859 -0.0070

0.7903 0.7789 0.0114 0.7893 0.0010

0.7730 0.7903 -0.0173 0.7789 -0.0059

0.7729 0.7730 -0.0001 0.7903 -0.0174

0.7680 0.7729 -0.0049 0.7730 -0.0050

0.7523 0.7680 -0.0157 0.7729 -0.0206

0.7492 0.7523 -0.0031 0.7680 -0.0188

0.7320 0.7492 -0.0172 0.7523 -0.0203

0.7242 0.7320 -0.0078 0.7492 -0.0250

0.6968 0.7242 -0.0274 0.7320 -0.0352

0.6996 0.6968 0.0028 0.7242 -0.0246

0.7211 0.6996 0.0215 0.6968 0.0243

0.7168 0.7211 -0.0043 0.6996 0.0172

0.7162 0.7168 -0.0006 0.7211 -0.0049

0.7162 0.7162 0.0000 0.7168 -0.0006

0.7130 0.7162 -0.0032 0.7162 -0.0032

0.7027 0.7130 -0.0103 0.7162 -0.0135

0.7100 0.7027 0.0073 0.7130 -0.0030

0.7184 0.7100 0.0084 0.7027 0.0157

0.7172 0.7184 -0.0012 0.7100 0.0072

0.7366 0.7172 0.0194 0.7184 0.0182

0.7439 0.7366 0.0073 0.7172 0.0267

0.7290 0.7439 -0.0149 0.7366 -0.0076

0.7293 0.7290 0.0003 0.7439 -0.0146

0.7411 0.7293 0.0118 0.7290 0.0121

0.7493 0.7411 0.0082 0.7293 0.0200

0.7579 0.7493 0.0086 0.7411 0.0168

0.7591 0.7579 0.0012 0.7493 0.0098

0.7638 0.7591 0.0047 0.7579 0.0059

0.7553 0.7638 -0.0085 0.7591 -0.0038

0.7725 0.7553 0.0172 0.7638 0.0087

0.7772 0.7725 0.0047 0.7553 0.0219

0.7720 0.7772 -0.0052 0.7725 -0.0005

0.7782 0.7720 0.0062 0.7772 0.0010

0.7603 0.7782 -0.0179 0.7720 -0.0117

0.7601 0.7603 -0.0002 0.7782 -0.0181

0.7552 0.7601 -0.0049 0.7603 -0.0051

0.7700 0.7552 0.0148 0.7601 0.0099

0.7811 0.7700 0.0111 0.7552 0.0259

0.7809 0.7811 -0.0002 0.7700 0.0109

0.7687 0.7809 -0.0122 0.7811 -0.0124

0.7779 0.7687 0.0092 0.7809 -0.0030

0.7791 0.7779 0.0012 0.7687 0.0104

0.7769 0.7791 -0.0022 0.7779 -0.0010

0.7656 0.7769 -0.0113 0.7791 -0.0135

0.7714 0.7656 0.0058 0.7769 -0.0055

0.7757 0.7714 0.0043 0.7656 0.0101

0.7800 0.7757 0.0043 0.7714 0.0086

0.7766 0.7800 -0.0034 0.7757 0.0009

0.7832 0.7766 0.0066 0.7800 0.0032

0.7957 0.7832 0.0125 0.7766 0.0191

0.7971 0.7957 0.0014 0.7832 0.0139

0.7891 0.7971 -0.0080 0.7957 -0.0066

0.7881 0.7891 -0.0010 0.7971 -0.0090

0.7846 0.7881 -0.0035 0.7891 -0.0045

0.7849 0.7846 0.0003 0.7881 -0.0032

0.7856 0.7849 0.0007 0.7846 0.0010

0.7835 0.7856 -0.0021 0.7849 -0.0014

0.7899 0.7835 0.0064 0.7856 0.0043

0.7950 0.7899 0.0051 0.7835 0.0115

0.7970 0.7950 0.0020 0.7899 0.0071

0.7933 0.7970 -0.0037 0.7950 -0.0017

0.7959 0.7933 0.0026 0.7970 -0.0011

0.7892 0.7959 -0.0067 0.7933 -0.0041

0.7914 0.7892 0.0022 0.7959 -0.0045

0.7842 0.7914 -0.0072 0.7892 -0.0050

0.7829 0.7842 -0.0013 0.7914 -0.0085

0.7814 0.7829 -0.0015 0.7842 -0.0028

0.7759 0.7814 -0.0055 0.7829 -0.0070

0.7695 0.7759 -0.0064 0.7814 -0.0119

0.7710 0.7695 0.0015 0.7759 -0.0049

0.7628 0.7710 -0.0082 0.7695 -0.0067

0.7310 0.7628 -0.0318 0.7710 -0.0400

0.7372 0.7310 0.0062 0.7628 -0.0256

0.7371 0.7372 -0.0001 0.7310 0.0061

0.7395 0.7371 0.0024 0.7372 0.0023

0.7387 0.7395 -0.0008 0.7371 0.0016

0.7376 0.7387 -0.0011 0.7395 -0.0019

0.7516 0.7376 0.0140 0.7387 0.0129

0.7609 0.7516 0.0093 0.7376 0.0233

0.7542 0.7609 -0.0067 0.7516 0.0026

0.7563 0.7542 0.0021 0.7609 -0.0046

0.7431 0.7563 -0.0132 0.7542 -0.0111

0.7437 0.7431 0.0006 0.7563 -0.0126

0.7484 0.7437 0.0047 0.7431 0.0053

0.7530 0.7484 0.0046 0.7437 0.0093

0.7526 0.7530 -0.0004 0.7484 0.0042

0.7606 0.7526 0.0080 0.7530 0.0076

0.7489 0.7606 -0.0117 0.7526 -0.0037

0.7533 0.7489 0.0044 0.7606 -0.0073

0.7587 0.7533 0.0054 0.7489 0.0098

0.7579 0.7587 -0.0008 0.7533 0.0046

0.7675 0.7579 0.0096 0.7587 0.0088

0.7751 0.7675 0.0076 0.7579 0.0172

0.7706 0.7751 -0.0045 0.7675 0.0031

0.7686 0.7706 -0.0020 0.7751 -0.0065

0.7665 0.7686 -0.0021 0.7706 -0.0041

0.7532 0.7665 -0.0133 0.7686 -0.0154

0.7613 0.7532 0.0081 0.7665 -0.0052

0.7657 0.7613 0.0044 0.7532 0.0125

0.7506 0.7657 -0.0151 0.7613 -0.0107

0.7552 0.7506 0.0046 0.7657 -0.0105

0.7539 0.7552 -0.0013 0.7506 0.0033

0.7483 0.7539 -0.0056 0.7552 -0.0069

0.7478 0.7483 -0.0005 0.7539 -0.0061

0.7513 0.7478 0.0035 0.7483 0.0030

0.7458 0.7513 -0.0055 0.7478 -0.0020

0.7412 0.7458 -0.0046 0.7513 -0.0101

0.7343 0.7412 -0.0069 0.7458 -0.0115

0.7343 0.7412

0.7458

0.7343

USD_GBR

0.5135 0.5135 0.0007 0.5098 0.0044

0.5142 0.5098 0.0037 0.5133 0.0002

0.5131 0.5142 -0.0011 0.5135 -0.0004

0.5108 0.5131 -0.0023 0.5142 -0.0034

0.5129 0.5108 0.0021 0.5131 -0.0002

0.5076 0.5129 -0.0053 0.5108 -0.0032

0.5084 0.5076 0.0008 0.5129 -0.0045

0.5054 0.5084 -0.0030 0.5076 -0.0022

0.5046 0.5054 -0.0008 0.5084 -0.0038

0.5062 0.5046 0.0016 0.5054 0.0008

0.5049 0.5062 -0.0013 0.5046 0.0003

0.5061 0.5049 0.0012 0.5062 -0.0001

0.5053 0.5061 -0.0008 0.5049 0.0004

0.5085 0.5053 0.0032 0.5061 0.0024

0.5089 0.5085 0.0004 0.5053 0.0036

0.5116 0.5089 0.0027 0.5085 0.0031

0.5112 0.5116 -0.0004 0.5089 0.0023

0.5078 0.5112 -0.0034 0.5116 -0.0038

0.5061 0.5078 -0.0017 0.5112 -0.0051

0.5117 0.5061 0.0056 0.5078 0.0039

0.5090 0.5117 -0.0027 0.5061 0.0029

0.5137 0.5090 0.0047 0.5117 0.0020

0.5129 0.5137 -0.0008 0.5090 0.0039

0.5093 0.5129 -0.0036 0.5137 -0.0044

0.5117 0.5093 0.0024 0.5129 -0.0012

0.5110 0.5117 -0.0007 0.5093 0.0017

0.5069 0.5110 -0.0041 0.5117 -0.0048

0.5068 0.5069 -0.0001 0.5110 -0.0042

0.5100 0.5068 0.0032 0.5069 0.0031

0.5074 0.5100 -0.0026 0.5068 0.0006

0.5083 0.5074 0.0009 0.5100 -0.0017

0.5058 0.5083 -0.0025 0.5074 -0.0016

0.5016 0.5058 -0.0042 0.5083 -0.0067

0.5024 0.5016 0.0008 0.5058 -0.0034

0.5012 0.5024 -0.0012 0.5016 -0.0004

0.5019 0.5012 0.0007 0.5024 -0.0005

0.5045 0.5019 0.0026 0.5012 0.0033

0.5077 0.5045 0.0032 0.5019 0.0058

0.5080 0.5077 0.0003 0.5045 0.0035

0.5048 0.5080 -0.0032 0.5077 -0.0029

0.5057 0.5048 0.0009 0.5080 -0.0023

0.5027 0.5057 -0.0030 0.5048 -0.0021

0.5018 0.5027 -0.0009 0.5057 -0.0039

0.4988 0.5018 -0.0030 0.5027 -0.0039

0.5002 0.4988 0.0014 0.5018 -0.0016

0.4991 0.5002 -0.0011 0.4988 0.0003

0.5004 0.4991 0.0013 0.5002 0.0002

0.5006 0.5004 0.0002 0.4991 0.0015

0.5014 0.5006 0.0008 0.5004 0.0010

0.4995 0.5014 -0.0019 0.5006 -0.0011

0.5030 0.4995 0.0035 0.5014 0.0016

0.5015 0.5030 -0.0015 0.4995 0.0020

0.5049 0.5015 0.0034 0.5030 0.0019

0.5048 0.5049 -0.0001 0.5015 0.0033

0.5049 0.5048 0.0001 0.5049 0.0000

0.5065 0.5049 0.0016 0.5048 0.0017

0.5100 0.5065 0.0035 0.5049 0.0051

0.5120 0.5100 0.0020 0.5065 0.0055

0.5134 0.5120 0.0014 0.5100 0.0034

0.5144 0.5134 0.0010 0.5120 0.0024

0.5210 0.5144 0.0066 0.5134 0.0076

0.5223 0.5210 0.0013 0.5144 0.0079

0.5262 0.5223 0.0039 0.5210 0.0052

0.5353 0.5262 0.0091 0.5223 0.0130

0.5344 0.5353 -0.0009 0.5262 0.0082

0.5363 0.5344 0.0019 0.5353 0.0010

0.5356 0.5363 -0.0007 0.5344 0.0012

0.5360 0.5356 0.0004 0.5363 -0.0003

0.5370 0.5360 0.0010 0.5356 0.0014

0.5331 0.5370 -0.0039 0.5360 -0.0029

0.5393 0.5331 0.0062 0.5370 0.0023

0.5380 0.5393 -0.0013 0.5331 0.0049

0.5438 0.5380 0.0058 0.5393 0.0045

0.5459 0.5438 0.0021 0.5380 0.0079

0.5477 0.5459 0.0018 0.5438 0.0039

0.5498 0.5477 0.0021 0.5459 0.0039

0.5600 0.5498 0.0102 0.5477 0.0123

0.5620 0.5600 0.0020 0.5498 0.0122

0.5654 0.5620 0.0034 0.5600 0.0054

0.5654 0.5654 0.0000 0.5620 0.0034

0.5701 0.5654 0.0047 0.5654 0.0047

0.5659 0.5701 -0.0042 0.5654 0.0005

0.5699 0.5659 0.0040 0.5701 -0.0002

0.5715 0.5699 0.0016 0.5659 0.0056

0.5588 0.5715 -0.0127 0.5699 -0.0111

0.5589 0.5588 0.0001 0.5715 -0.0126

0.5610 0.5589 0.0021 0.5588 0.0022

0.5589 0.5610 -0.0021 0.5589 -0.0000

0.5499 0.5589 -0.0090 0.5610 -0.0111