5. Measures of uncertainty in market network analysis? V.A. Kalyagina , A.P. Koldanov b , P.A. Koldanov b , P.M. Pardalos a,c , V.A. Zamaraev
6. 1975год Кендэл ранговые корреляции
7. Гмурман В.Е.. вероятностей и математическая статистика: Учебное пособие для вузов. - 10-е издание, стереотипное. - Москва: Высшая школа, 2004
8. G. Bonanno, G. Caldarelli, F. Lillo, S. Miccichи, N. Vandewalle, R.N. Mantegna, Networks of equities in financial markets, Eur. Phys. J. B 38 (2004) 363-371.
9. [4] V. Boginski, S. Butenko, P.M. Pardalos, Statistical analysis of financial networks, Comput. Statist. Data Anal. 48 (2005) 431-443.
10. [11] G.-J. Wang, C. Xie, S. Chen, J.-J. Yang, M.-Y. Yang, Random matrix theory analysis of cross-correlations in the us stock market: evidence from Pearson correlation coefficient and detrended cross-correlation coefficient, Physica A 392 (2013) 3715-3730.
11. ] E.L. Lehmann, A theory of some multiple decision problems, i, Ann. Math. Statist. (1957) 1-25
Приложения
1. Получение матрицы активов(PYTHON)
import yfinance as yf
import datetime
import pandas as pd
import numpy as np
pd.core.common.is_list_like = pd.api.types.is_list_like
import matplotlib
import pandas_datareader as pdr
import seaborn as sns
import matplotlib.pyplot as plt
from scipy.stats import norm
import scipy
yf.pdr_override()
import math
import networkx
stocks = ['AC','AI','AIR','MT','ATO','NIE','AVID','AETG.SG','AKRN.ME','YNDX','AMOT','AMZN','AXP','UA','NLY','AET','EA','AMBA','AGI','RAD','SKAS','ORLY','GAS','AKS','AGIO',
'AEE','ARLP','ACCO','ABC','AVB','LH','AUY','AOXY','LIFE','WMC','LAQ','JBK','Y','MTGE','AAON','XLRN','VJET','ATLS','APO','RBA','NOG','ARE','AWI','AHGP','AT']
start = datetime.datetime(2017, 1, 1)
end = datetime.datetime(2018, 1, 1)
data = yf.download(stocks, start=start, end=end)
corrmat = data1.corr()
f, ax = plt.subplots(figsize =(10, 5))
sns.heatmap(corrmat, ax = ax, cmap ="YlGnBu", linewidths = 0.1)
corrmat.to_csv(r'C:\Users\Слава\xyz.txt', index=None, sep=' ', mode='a')
2. Генерация данных.(MATLAB)
3. n_iter=10000;
4.
5. % ex1
6. % задаем корреляционную матрицу
7. %sigma = [1 0.4;
8. % 0.4 1];
9. sigma = [ 1.0 0.5152069095021041 -0.05667063800581024 0.21839819234745073 -0.11978697428769702 0.10134316213830274 -0.27930042323620646 -0.4937875319087946 -0.13441786463182895 -0.1836749290873235 0.11698986458082533 0.18175869300869307 -0.34871474191929114 -0.1342360821653816 0.40489536189017655 0.260063797670438 0.2548499854932075 0.29532475281709664 0.08139420182318309 0.0723879441020065 0.14464560368345275 0.06312533983311353 -0.305092931720633 0.019354875832787697 -0.4423264379020519 0.35610313572502006 0.46212696244334805 0.15651283859728718 0.007618983460007782 -0.012677439764108069 -0.036936104794969074 0.1603238801134231 -0.14332873809686122 -0.049348225393366314 0.15362053650432672 -0.18539257761698458 0.06564455952968465 0.11033996698050869 0.14256059978184252 0.017956642020051882 0.09620366938762362 -0.1525516822970671 -0.03849103833892827 -0.03241155562817533 -0.009266143558943502 0.2304392037698104 -0.15969307044404427 -0.0913459631861964 0.16536797295920186 -0.01650931041916315;
10. 0.5152069095021041 1.0 -0.059717066603911816 -0.08056516212596171 -0.5185975015422378 -0.2369181070279052 -0.5592302844787413 -0.014798320332459858 -0.45173846828148734 -0.060951529222418754 0.4994002416738101 -0.26848057884695986 -0.4907354914247383 0.3239221310532368 0.1370961415046379 -0.010665514016118465 -0.11581464912395888 -0.050804209625297685 -0.3082513350985703 -0.11871076449764302 0.33540482870335275 -0.19763045258584208 0.1430593539367036 -0.3129835880301045 -0.06643125022733737 0.24505576446204216 0.4080139007716837 -0.24246587687577864 -0.3172972922324646 -0.23676000028603122 -0.2170518968835467 -0.2910302827135299 -0.4850062821327649 -0.15087961825175186 -0.21241592797134562 -0.3256364391356128 -0.2066309821487786 -0.24166295747138053 -0.0543624254297931 0.336397747950471 0.24044109793905327 0.24542096405601993 0.24702159713769137 0.13248763665800542 0.3836318694712589 -0.07711843148143416 -0.05174925556241794 -0.40863386078084674 0.48331852305308454 -0.3685366218425072;
11. -0.05667063800581024 -0.059717066603911816 1.0 0.433583151989103 -0.04710667937211029 -0.22647409603619834 0.21686384877693915 0.12984743384236955 0.16050517631694103 0.41079039316417615 0.033256052584630574 -0.04998529089162265 0.10970795851395435 0.2852127684563238 0.08279658821869301 -0.2424204386140238 -0.3023946429878101 -0.40013704336394545 -0.19684702621295103 -0.1807210138766501 0.31202808173806323 0.1970176251480292 0.24300842889410987 -0.29613532695569156 0.14769298774278458 -0.5007049846168339 -0.09531449062010268 0.03449285968678694 0.012371924971937093 -0.26071289142264586 -0.031933106991026805 -0.29192766451640556 -0.00012415185842763683 -0.21696590598144797 0.5203263798463259 0.26559234875449195 -0.3570485929571797 -0.06115114836175263 -0.3224574428380354 0.23786943010290434 0.30616411572191904 0.1624414830443728 0.28799185801660027 0.4240118917432622 -0.07598795328094629 -0.19457201183908696 -0.13429508269769933 -0.05233410268262804 0.1920784365868285 -0.16119479829430602;
12. 0.21839819234745073 -0.08056516212596171 0.433583151989103 1.0 -0.14055915161906407 -0.2701140712456958 -0.040956702726441994 -0.00690095037038205 -0.19273620799385674 0.29948164349568507 0.08407048522495275 0.05395867917458333 0.2579320118858664 0.3183858825152628 0.3783099714970756 -0.12812236627379806 -0.15473684063202123 -0.2697865603640341 -0.2808556453689714 -0.18716028968328746 0.45126529939525867 0.32290087932426137 0.25752941678280117 -0.3606474451954933 0.2087708631338578 -0.42828716953841106 0.3379757674143984 0.10825277435325598 -0.028227109737660534 -0.6336117632365837 0.06849769832843755 -0.1440684308579454 -0.22244317822226026 -0.3776404390282153 0.19820201955544428 0.19759945485870997 -0.5467518142757012 -0.08672837114744691 -0.5224029800928205 0.5081085066042312 0.5806588929994452 0.3303660104930506 0.29336470391528763 0.5545083825689011 0.01868848375203422 -0.38595112006955845 -0.3541602051049346 -0.20827353172454463 0.38036937261460185 -0.3110679915778835;
13. -0.11978697428769702 -0.5185975015422378 -0.04710667937211029 -0.14055915161906407 1.0 0.8786255618810025 0.7744462585639723 -0.5169618504012967 0.764340460852915 -0.47015455392506694 -0.9033972567098696 0.8337143492491901 0.6110848315066317 -0.7906645615540191 0.060143203119427745 0.7150411075293192 0.8096558906226151 0.3394573064094056 0.8534016358235347 0.8049419469419031 -0.7974293610950415 0.0306019402444824 -0.6999261603269422 0.9061851316159119 -0.38737549556416684 0.052419222689392315 0.031621861108973554 0.8036624413338576 0.8559554906938531 0.6961617484434709 0.712426138277753 0.8060543785192517 0.8131477243346036 0.7026521751600782 0.4927683895299173 0.6476147212597423 0.6418318565673476 0.8486072503983056 0.5752133813905576 -0.7494107552827466 -0.5421229306321893 -0.8086691209265592 -0.7333852557479283 -0.5782676860849572 -0.8725838247930258 0.63839829382416 0.04774247239784669 0.8024623178223143 -0.6808164813443078 0.8424111278994232;
14. 0.10134316213830274 -0.2369181070279052 -0.22647409603619834 -0.2701140712456958 0.8786255618810025 1.0 0.6748007053243326 -0.6842625060006611 0.7015332955518834 -0.6055245673999506 -0.8855539035976255 0.9022852434250145 0.5321452679323031 -0.8113083053953809 0.044513536819400616 0.89513726208298 0.9414524707182306 0.5044793133225134 0.9204440775197781 0.9117114740814513 -0.8453221627021947 -0.1632381820751957 -0.7631210452112223 0.9191255688427585 -0.517000663620482 0.13777107520170528 0.16358269169639322 0.8413266747977295 0.9177687230632536 0.7729350283894064 0.7974327355828325 0.8467417677963788 0.7870665371478723 0.8356197395476984 0.4241642204923972 0.6235281548682241 0.7463530325030987 0.9262283175496876 0.6712340814507656 -0.798490018329909 -0.6544381342581354 -0.8687828609551554 -0.7914209401017089 -0.7586689190404102 -0.7981044702796161 0.7635007878598138 0.07636650260694473 0.8647315172782226 -0.6454307579456039 0.9121980077070948;
15. -0.27930042323620646 -0.5592302844787413 0.21686384877693915 -0.040956702726441994 0.7744462585639723 0.6748007053243326 1.0 -0.32537154852156225 0.7798827333175862 -0.21430773448379442 -0.7344156148367197 0.6727282552277346 0.6791583854941139 -0.5245302416235416 -0.19184383630114338 0.48221337429655475 0.5324073806059051 0.19133760945577818 0.6945410092599472 0.579626960562211 -0.6114320461778822 0.017580770213575122 -0.44349065575539237 0.6039826560162879 -0.09343911031518108 -0.32029211884246783 -0.14223243388160503 0.7002788894649958 0.7549313172430814 0.5527136171685318 0.6795910863343405 0.5696131846812409 0.8326375500126522 0.531013048080443 0.6136755242638764 0.6284411938137932 0.5336707045807044 0.7337755315663507 0.41610114621078303 -0.6167908453447952 -0.448785396285333 -0.5907448366230487 -0.4329966048063916 -0.4461250517936547 -0.664991274201634 0.5630255963954727 0.16694982003599168 0.8038142580255461 -0.7577133900525099 0.7579748854439583;
16. -0.4937875319087946 -0.014798320332459858 0.12984743384236955 -0.00690095037038205 -0.5169618504012967 -0.6842625060006611 -0.32537154852156225 1.0 -0.3417760210247947 0.36782419529089927 0.5700930648560674 -0.6980635072922411 -0.24644417363030888 0.620304878764959 -0.36476410422102473 -0.7546357409812899 -0.7317341634068543 -0.5172205312947072 -0.6129965213414632 -0.6217393014894486 0.4036538282306985 0.14454499190830816 0.5444799379458836 -0.5615721272053228 0.6767868924052948 -0.1962884776592149 -0.3324008607816942 -0.6164882259253625 -0.5950265408314271 -0.483707427611835 -0.5088060482431039 -0.6011962879763976 -0.42170206211569966 -0.42354814510407435 -0.40934598734057315 -0.2961452532753129 -0.44983849836488077 -0.6734509308661046 -0.3789137911337018 0.48792070888130373 0.31866417619685455 0.6021298068909278 0.47543246751820734 0.5055226659285306 0.5351672523438092 -0.6747509209296408 0.1644841729451815 -0.4687807659526227 0.34503499207551847 -0.6150185691205592;
17. -0.13441786463182895 -0.45173846828148734 0.16050517631694103 -0.19273620799385674 0.764340460852915 0.7015332955518834 0.7798827333175862 -0.3417760210247947 1.0 -0.3418268623831907 -0.770893419328504 0.6546586212914677 0.3759381059135233 -0.6770481927858347 -0.2295970006985888 0.45689380276052927 0.5537268903447857 0.32102840714160874 0.7751545390989869 0.5599208686846732 -0.7164584241532858 0.11826323347859431 -0.6919306187208663 0.7391919622779003 -0.4324978463570861 0.003914920191634363 -0.2779135355632455 0.672732864908302 0.7169676283656337 0.7409459334265505 0.4777430159863355 0.6744350007330361 0.900026269948939 0.7325443917609195 0.6868254566877956 0.5223116554329571 0.6988398581355059 0.7004164930977116 0.6543723173572822 -0.815510717780411 -0.6797025944796127 -0.7861040912569135 -0.5950208118582677 -0.48816311980743543 -0.7261228648630156 0.545727389592372 0.23875269952655812 0.83071301235432 -0.6428566762001433 0.7821165308828467;
18. -0.1836749290873235 -0.060951529222418754 0.41079039316417615 0.29948164349568507 -0.47015455392506694 -0.6055245673999506 -0.21430773448379442 0.36782419529089927 -0.3418268623831907 1.0 0.4326746678962012 -0.46230426068718705 -0.13361443278425264 0.4512215665963065 0.22863196326458052 -0.535809863729071 -0.5886322553254439 -0.3221261043897046 -0.4688331811478582 -0.5183347661828519 0.7774496412444644 -0.013017307319593583 0.5364900033244916 -0.6118209691855105 0.5276395775570745 -0.30348004323193806 -0.13031883568512376 -0.46450015309078657 -0.49709148392397634 -0.4546036412946931 -0.38190135539952547 -0.4911927821811086 -0.3098738560953582 -0.5890263423940294 -0.0697039561404624 -0.17517255941155474 -0.5643985100945634 -0.43519728980899347 -0.5630237440414676 0.5077592478444082 0.4845191226386972 0.5134994968594869 0.6150702187918048 0.55122980340681 0.3310980215539028 -0.45436013934701586 -0.09498814188671253 -0.4662151147094583 0.3177545534940276 -0.4426138682026305;
19. 0.11698986458082533 0.4994002416738101 0.033256052584630574 0.08407048522495275 -0.9033972567098696 -0.8855539035976255 -0.7344156148367197 0.5700930648560674 -0.770893419328504 0.4326746678962012 1.0 -0.8539284574170825 -0.6579731719510626 0.7699432331831564 -0.04686009818832572 -0.7469511643387945 -0.8154584671215852 -0.348766733766984 -0.8322777006964144 -0.7816826607791825 0.7739383738489795 0.03866720266316449 0.6676493610264771 -0.8411132688360475 0.4052843008193604 0.04964040090544838 -0.01638821266147812 -0.8162542832003147 -0.8944149364979572 -0.6453937516738721 -0.7575096935657769 -0.8001996894172448 -0.8041307928496843 -0.7778421998387383 -0.49061217229770165 -0.7328694749698564 -0.5492753553686857 -0.8506227489574081 -0.4717605270809031 0.7227918794208043 0.5814802874443689 0.8144132965262475 0.7788620597469198 0.5852417483629363 0.876343950003402 -0.55084949123312 0.11656800129399988 -0.8265130380449413 0.5901749710386411 -0.8390531077005865;
20. 0.18175869300869307 -0.26848057884695986 -0.04998529089162265 0.05395867917458333 0.8337143492491901 0.9022852434250145 0.6727282552277346 -0.6980635072922411 0.6546586212914677 -0.46230426068718705 -0.8539284574170825 1.0 0.6450286059738541 -0.7161888503449563 0.19245903624189736 0.8655797978056533 0.8918120081295908 0.42603574104591824 0.8551552371951722 0.8707211644677872 -0.6858338115635352 -0.0871616352430539 -0.6764593998134961 0.8048828091061176 -0.4490866949387792 -0.07218549062872134 0.2941981805979403 0.9095930757945694 0.9437112878266696 0.5705143069854287 0.849717370506264 0.8051690980147017 0.7430852876829893 0.7118283420979424 0.5526064134604418 0.7358556890883805 0.5842079046875794 0.9487962357120235 0.5014906824046875 -0.6229218865366423 -0.45407072710623697 -0.7758162565966303 -0.6925320661028456 -0.5789402516787967 -0.8161712864439359 0.6694384735304882 0.003292133726180623 0.7862050382555064 -0.5313789101031088 0.8291020524414462;
21. -0.34871474191929114 -0.4907354914247383 0.10970795851395435 0.2579320118858664 0.6110848315066317 0.5321452679323031 0.6791583854941139 -0.24644417363030888 0.3759381059135233 -0.13361443278425264 -0.6579731719510626 0.6450286059738541 1.0 -0.25648723918002864 0.0890360351235502 0.48643739208076087 0.47936888073669354 0.000584210844355103 0.4333232249594746 0.5585080020266553 -0.408736288179181 -0.1073793149498603 -0.11281886808952095 0.38840951772837007 0.16977796839658657 -0.5953867201186013 0.2626201998044791 0.6622859744348892 0.7184768849101569 0.08166722813786231 0.829349055984347 0.3972455878762209 0.49252889796675414 0.3824251424466229 0.2523841229730625 0.8409501575419677 0.09420414897071339 0.6057125648802427 -0.03534739272385971 -0.16356881158190217 -0.07093038838854399 -0.2807025489442869 -0.36828524791744566 -0.24520942346796173 -0.5598789037147551 0.19787159414256772 -0.17367263285251777 0.560057691866568 -0.38068970552689363 0.5154724386129322;
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