Juan Alberto Zapata May 27, 2020
## [[1]]
## [1] "pdfetch" "stats" "graphics" "grDevices" "utils" "datasets"
## [7] "methods" "base"
##
## [[2]]
## [1] "tseries" "pdfetch" "stats" "graphics" "grDevices" "utils"
## [7] "datasets" "methods" "base"
##
## [[3]]
## [1] "forcats" "stringr" "dplyr" "purrr" "readr" "tidyr"
## [7] "tibble" "ggplot2" "tidyverse" "tseries" "pdfetch" "stats"
## [13] "graphics" "grDevices" "utils" "datasets" "methods" "base"
##
## [[4]]
## [1] "forecast" "forcats" "stringr" "dplyr" "purrr" "readr"
## [7] "tidyr" "tibble" "ggplot2" "tidyverse" "tseries" "pdfetch"
## [13] "stats" "graphics" "grDevices" "utils" "datasets" "methods"
## [19] "base"
NASDAQdata <- pdfetch_YAHOO("^IXIC",from = as.Date("2019-01-01"),to = as.Date("2020-01-01"), interval = '1d') #DATOS DE S&P500
tsNASDAQ <- ts(NASDAQdata$`^IXIC.close`,start = c(2019,1),frequency=356.25)Retornos *(Discretos)
## Time Series:
## Start = 2019.00280701754
## End = 2019.70456140351
## Frequency = 356.25
## ^IXIC.close
## [1,] -0.03036930167
## [2,] 0.04260228406
## [3,] 0.01255558859
## [4,] 0.01077601025
## [5,] 0.00871104509
## [6,] 0.00416694154
## [7,] -0.00208841944
## [8,] -0.00940403733
## [9,] 0.01707377979
## [10,] 0.00154614546
## [11,] 0.00707494153
## [12,] 0.01027178069
## [13,] -0.01912333646
## [14,] 0.00077063813
## [15,] 0.00678785967
## [16,] 0.01292152674
## [17,] -0.01105111454
## [18,] -0.00809945349
## [19,] 0.02202385476
## [20,] 0.01373507673
## [21,] -0.00245409977
## [22,] 0.01151864236
## [23,] 0.00742289783
## [24,] -0.00362064348
## [25,] -0.01178662905
## [26,] 0.00135148516
## [27,] 0.00132905466
## [28,] 0.01460340405
## [29,] 0.00077681202
## [30,] 0.00088544146
## [31,] 0.00612094599
## [32,] 0.00192171785
## [33,] 0.00030718240
## [34,] -0.00392036177
## [35,] 0.00909285728
## [36,] 0.00357619114
## [37,] -0.00068306087
## [38,] 0.00069012506
## [39,] -0.00290951785
## [40,] 0.00833986918
## [41,] -0.00234094199
## [42,] -0.00015967665
## [43,] -0.00929733306
## [44,] -0.01125244632
## [45,] -0.00179477139
## [46,] 0.02023718764
## [47,] 0.00436219423
## [48,] 0.00690029844
## [49,] -0.00163539569
## [50,] 0.00755082000
## [51,] 0.00337518300
## [52,] 0.00122758955
## [53,] 0.00064992910
## [54,] 0.01423084097
## [55,] -0.02504031657
## [56,] -0.00067121609
## [57,] 0.00706771823
## [58,] -0.00625885870
## [59,] 0.00337416685
## [60,] 0.00784307854
## [61,] 0.01288474721
## [62,] 0.00252650556
## [63,] 0.00597040581
## [64,] -0.00047748670
## [65,] 0.00594417955
## [66,] 0.00191340663
## [67,] -0.00560733864
## [68,] 0.00694885634
## [69,] -0.00211952057
## [70,] 0.00463050543
## [71,] -0.00102081995
## [72,] 0.00303663294
## [73,] -0.00051872284
## [74,] 0.00024761896
## [75,] 0.00215176691
## [76,] 0.01316858992
## [77,] -0.00231627575
## [78,] 0.00205756479
## [79,] 0.00341431432
## [80,] 0.00189656734
## [81,] -0.00814275688
## [82,] -0.00565136445
## [83,] -0.00159884377
## [84,] 0.01583098430
## [85,] -0.00498652144
## [86,] -0.01963862822
## [87,] -0.00256661961
## [88,] -0.00412044091
## [89,] 0.00080273369
## [90,] -0.03409397103
## [91,] 0.01143847064
## [92,] 0.01133360640
## [93,] 0.00970320231
## [94,] -0.01035319123
## [95,] -0.01457213727
## [96,] 0.01082007552
## [97,] -0.00448004424
## [98,] -0.01581248761
## [99,] 0.00114442328
## [100,] -0.00388367554
## [101,] -0.00789237228
## [102,] 0.00270429542
## [103,] -0.01513934312
## [104,] -0.01611800159
## [105,] 0.02646932594
## [106,] 0.00642474974
## [107,] 0.00528941072
## [108,] 0.01661735479
## [109,] 0.01047129629
## [110,] -0.00007670778
## [111,] -0.00381583158
## [112,] 0.00569886596
## [113,] -0.00516384539
## [114,] 0.00620263844
## [115,] 0.01387630149
## [116,] 0.00420423007
## [117,] 0.00801520678
## [118,] -0.00243808899
## [119,] -0.00323838462
## [120,] -0.01511173002
## [121,] 0.00320239645
## [122,] 0.00730591259
## [123,] 0.00482952161
## [124,] 0.01060671670
## [125,] 0.00221596009
## [126,] 0.00753970386
## [127,] -0.00103301144
## [128,] -0.00776914815
## [129,] 0.00535293449
## [130,] 0.00746773636
## [131,] -0.00079124780
## [132,] 0.00586864007
## [133,] 0.00170433576
## [134,] -0.00428551815
## [135,] -0.00457141666
## [136,] 0.00269147317
## [137,] -0.00740200095
## [138,] 0.00707659524
## [139,] 0.00576059709
## [140,] 0.00849548024
## [141,] -0.00996935180
## [142,] 0.01112696201
## [143,] -0.00442724531
## [144,] -0.00237778140
## [145,] -0.01186790601
## [146,] -0.00786501557
## [147,] -0.01319796667
## [148,] -0.03473605192
## [149,] 0.01387903511
## [150,] 0.00377365493
## [151,] 0.02242577752
## [152,] -0.00995377844
## [153,] -0.01202767879
## [154,] 0.01945081128
## [155,] -0.03024064864
## [156,] -0.00094158484
## [157,] 0.01665719644
## [158,] 0.01352836336
## [159,] -0.00677886887
## [160,] 0.00901419898
## [161,] -0.00359340019
## [162,] -0.02998478524
## [163,] 0.01315444263
## [164,] -0.00341111855
## [165,] 0.00382392723
## [166,] 0.01482907410
## [167,] -0.00131816628
## [168,] -0.01114166336
## [169,] 0.01304516608
## [170,] 0.01754447817
## [171,] -0.00169527437
## [172,] -0.00192888416
## [173,] -0.00040554057
## [174,] 0.01057871422
## [175,] 0.00303433555
## [176,] -0.00216728679
## [177,] -0.00283364851
## [178,] 0.00398354345
## [179,] -0.00105422207
## [180,] 0.00067133228
## [181,] -0.00796907225
## [182,] -0.00064180498
## [183,] -0.01464784770
## [184,] 0.01047709254
## [185,] -0.00578402003
## [186,] -0.01133534121
## [187,] 0.00752049678
## [188,] -0.01133339373
## [189,] -0.01560692470
## [190,] 0.01117623275
## [191,] 0.01399984913
## [192,] -0.00327970857
## [193,] -0.01665477922
## [194,] 0.01022018145
## [195,] 0.00595155580
## [196,] 0.01336475879
## [197,] -0.00104134235
## [198,] 0.01243190600
## [199,] -0.00301026606
## [200,] 0.00402131923
## [201,] -0.00825196714
## [202,] 0.00907965034
## [203,] -0.00718981982
## [204,] 0.00191135994
## [205,] 0.00812949173
## [206,] 0.00700240824
## [207,] 0.01005324632
## [208,] -0.00590207574
## [209,] 0.00327792110
## [210,] -0.00139934301
## [211,] 0.01134056348
## [212,] 0.00558043998
## [213,] 0.00017543672
## [214,] -0.00285130033
## [215,] 0.00284041128
## [216,] 0.00483608329
## [217,] -0.00130134444
## [218,] 0.00257665983
## [219,] -0.00047020890
## [220,] -0.00036312684
## [221,] 0.00728982246
## [222,] 0.00106668227
## [223,] 0.00242337665
## [224,] -0.00512558965
## [225,] -0.00240660920
## [226,] 0.00160705203
## [227,] 0.01321736369
## [228,] 0.00178852841
## [229,] 0.00662008158
## [230,] -0.00456164748
## [231,] -0.01124918742
## [232,] -0.00552645191
## [233,] 0.00540220874
## [234,] 0.00047045970
## [235,] 0.01001436009
## [236,] -0.00400855700
## [237,] -0.00065535854
## [238,] 0.00439523297
## [239,] 0.00731108665
## [240,] 0.00201433117
## [241,] 0.00908433625
## [242,] 0.00103581169
## [243,] 0.00049639614
## [244,] 0.00673779375
## [245,] 0.00424657375
## [246,] 0.00231826586
## [247,] 0.00080815723
## [248,] 0.00776395595
## [249,] -0.00174782199
## [250,] -0.00673170204
## [251,] 0.00297444713
Retornos *(Continuo)
## Time Series:
## Start = 2019.00280701754
## End = 2019.70456140351
## Frequency = 356.25
## ^IXIC.close
## [1,] -0.03084000335
## [2,] 0.04171978408
## [3,] 0.01247742080
## [4,] 0.01071836282
## [5,] 0.00867332285
## [6,] 0.00415828389
## [7,] -0.00209060322
## [8,] -0.00944853448
## [9,] 0.01692966094
## [10,] 0.00154495141
## [11,] 0.00705003155
## [12,] 0.01021938444
## [13,] -0.01930855256
## [14,] 0.00077034134
## [15,] 0.00676492588
## [16,] 0.01283875606
## [17,] -0.01111263175
## [18,] -0.00813243225
## [19,] 0.02178483276
## [20,] 0.01364160548
## [21,] -0.00245711600
## [22,] 0.01145280786
## [23,] 0.00739548370
## [24,] -0.00362721388
## [25,] -0.01185664206
## [26,] 0.00135057273
## [27,] 0.00132817225
## [28,] 0.01449780121
## [29,] 0.00077651045
## [30,] 0.00088504969
## [31,] 0.00610228909
## [32,] 0.00191987372
## [33,] 0.00030713523
## [34,] -0.00392806653
## [35,] 0.00905176615
## [36,] 0.00356981177
## [37,] -0.00068329426
## [38,] 0.00068988704
## [39,] -0.00291375872
## [40,] 0.00830528462
## [41,] -0.00234368628
## [42,] -0.00015968940
## [43,] -0.00934082303
## [44,] -0.01131623406
## [45,] -0.00179638392
## [46,] 0.02003513716
## [47,] 0.00435270744
## [48,] 0.00687660034
## [49,] -0.00163673441
## [50,] 0.00752245525
## [51,] 0.00336949985
## [52,] 0.00122683668
## [53,] 0.00064971799
## [54,] 0.01413053308
## [55,] -0.02535915917
## [56,] -0.00067144145
## [57,] 0.00704285898
## [58,] -0.00627852747
## [59,] 0.00336848712
## [60,] 0.00781248147
## [61,] 0.01280244506
## [62,] 0.00252331931
## [63,] 0.00595265356
## [64,] -0.00047760073
## [65,] 0.00592658261
## [66,] 0.00191157840
## [67,] -0.00562311878
## [68,] 0.00692482431
## [69,] -0.00212176993
## [70,] 0.00461981762
## [71,] -0.00102134135
## [72,] 0.00303203168
## [73,] -0.00051885742
## [74,] 0.00024758830
## [75,] 0.00214945518
## [76,] 0.01308263780
## [77,] -0.00231896246
## [78,] 0.00205545090
## [79,] 0.00340849878
## [80,] 0.00189477113
## [81,] -0.00817609019
## [82,] -0.00566739383
## [83,] -0.00160012329
## [84,] 0.01570698128
## [85,] -0.00499899562
## [86,] -0.01983402857
## [87,] -0.00256991903
## [88,] -0.00412895332
## [89,] 0.00080241167
## [90,] -0.03468872800
## [91,] 0.01137354596
## [92,] 0.01126986226
## [93,] 0.00965642857
## [94,] -0.01040715833
## [95,] -0.01467935372
## [96,] 0.01076195735
## [97,] -0.00449010971
## [98,] -0.01593883871
## [99,] 0.00114376893
## [100,] -0.00389123659
## [101,] -0.00792368189
## [102,] 0.00270064539
## [103,] -0.01525511292
## [104,] -0.01624930944
## [105,] 0.02612507484
## [106,] 0.00640419901
## [107,] 0.00527547092
## [108,] 0.01648079729
## [109,] 0.01041685200
## [110,] -0.00007671072
## [111,] -0.00382313044
## [112,] 0.00568268886
## [113,] -0.00517722411
## [114,] 0.00618348126
## [115,] 0.01378090709
## [116,] 0.00419541699
## [117,] 0.00798325563
## [118,] -0.00244106597
## [119,] -0.00324363953
## [120,] -0.01522707574
## [121,] 0.00319727970
## [122,] 0.00727935369
## [123,] 0.00481789689
## [124,] 0.01055086010
## [125,] 0.00221350847
## [126,] 0.00751142236
## [127,] -0.00103354536
## [128,] -0.00779948521
## [129,] 0.00533865846
## [130,] 0.00743999086
## [131,] -0.00079156100
## [132,] 0.00585148668
## [133,] 0.00170288503
## [134,] -0.00429472731
## [135,] -0.00458189754
## [136,] 0.00268785764
## [137,] -0.00742953170
## [138,] 0.00705167364
## [139,] 0.00574406830
## [140,] 0.00845959674
## [141,] -0.01001937855
## [142,] 0.01106551277
## [143,] -0.00443707458
## [144,] -0.00238061281
## [145,] -0.01193889180
## [146,] -0.00789610794
## [147,] -0.01328583381
## [148,] -0.03535369372
## [149,] 0.01378360329
## [150,] 0.00376655255
## [151,] 0.02217801708
## [152,] -0.01000364849
## [153,] -0.01210059659
## [154,] 0.01926406199
## [155,] -0.03070732965
## [156,] -0.00094202841
## [157,] 0.01651998694
## [158,] 0.01343767208
## [159,] -0.00680194977
## [160,] 0.00897381360
## [161,] -0.00359987196
## [162,] -0.03044352228
## [163,] 0.01306867429
## [164,] -0.00341694968
## [165,] 0.00381663461
## [166,] 0.01472019841
## [167,] -0.00131903582
## [168,] -0.01120419660
## [169,] 0.01296081073
## [170,] 0.01739235057
## [171,] -0.00169671297
## [172,] -0.00193074685
## [173,] -0.00040562282
## [174,] 0.01052315114
## [175,] 0.00302974125
## [176,] -0.00216963876
## [177,] -0.00283767089
## [178,] 0.00397563015
## [179,] -0.00105477816
## [180,] 0.00067110704
## [181,] -0.00800099502
## [182,] -0.00064201103
## [183,] -0.01475618668
## [184,] 0.01042258817
## [185,] -0.00580081225
## [186,] -0.01140007585
## [187,] 0.00749235883
## [188,] -0.01139810604
## [189,] -0.01572999493
## [190,] 0.01111424013
## [191,] 0.01390275638
## [192,] -0.00328509861
## [193,] -0.01679502946
## [194,] 0.01016830853
## [195,] 0.00593391525
## [196,] 0.01327623823
## [197,] -0.00104188492
## [198,] 0.01235526440
## [199,] -0.00301480602
## [200,] 0.00401325534
## [201,] -0.00828620310
## [202,] 0.00903867814
## [203,] -0.00721579114
## [204,] 0.00190953562
## [205,] 0.00809662542
## [206,] 0.00697800523
## [207,] 0.01000304859
## [208,] -0.00591956183
## [209,] 0.00327256043
## [210,] -0.00140032300
## [211,] 0.01127674136
## [212,] 0.00556492701
## [213,] 0.00017542133
## [214,] -0.00285537303
## [215,] 0.00283638494
## [216,] 0.00482442701
## [217,] -0.00130219193
## [218,] 0.00257334594
## [219,] -0.00047031949
## [220,] -0.00036319278
## [221,] 0.00726338013
## [222,] 0.00106611377
## [223,] 0.00242044501
## [224,] -0.00513877055
## [225,] -0.00240950974
## [226,] 0.00160576211
## [227,] 0.01313077647
## [228,] 0.00178693089
## [229,] 0.00659826507
## [230,] -0.00457208354
## [231,] -0.01131293807
## [232,] -0.00554177924
## [233,] 0.00538766915
## [234,] 0.00047034907
## [235,] 0.00996454867
## [236,] -0.00401661280
## [237,] -0.00065557338
## [238,] 0.00438560214
## [239,] 0.00728449021
## [240,] 0.00201230512
## [241,] 0.00904332188
## [242,] 0.00103527561
## [243,] 0.00049627297
## [244,] 0.00671519627
## [245,] 0.00423758250
## [246,] 0.00231558283
## [247,] 0.00080783084
## [248,] 0.00773397154
## [249,] -0.00174935121
## [250,] -0.00675446214
## [251,] 0.00297003222
media (mu)
Indica que la media se aproxima a cero y es significativamente acercandose a la media general.
## [1] 0.001183922
varianza (s2)
la varianza muestra una confirmacion significativa diferente a la media.
## ^IXIC.close
## ^IXIC.close 0.0000978898
Desviacion estandad (s)
La desviacion estandar muestra un volatilidad de 0.009893928, esto quiere decir que el precio puede moverse hacia arriba o abajo.
## [1] 0.009893928
El histrograma muestra una dispersionmenor de lo esperado. tambien presenta una probable una asimetria, en cuanto a los valores atipicos no se obserba. No presenta datos multimodales y su distribucion ajustada en forma de linea siguen la altura de las barras. y por ultimo su dispersion no es amplia esto indica que las barras esta llenas de forma consistente.
x<-seq(-0.1,0.1,by=0.01)
hist(
l_NASDAQ,prob=TRUE,ylim=c(0,80),xlim = c(-0.1,0.1),breaks = 50,col = "grey94",
main = c("Histograma de los retornos"),
xlab = expression(r==ln(P[t]/P[t-1])),
ylab=c("Densidad"),
)
lines(density(l_NASDAQ),lwd=1.5,lty=2)
curve(dnorm(x,mean=mu,sd=s),lwd=2,lty=2,col="red",add = T)
5.1) Jarque-Bera,
5.2) Kolmogorov,
5.3) Spahiro-Wilk, ¿Cual es la hipotesis nula de cada uno de estos test? Interprete sus resultados.(3pts)
##
## Shapiro-Wilk normality test
##
## data: l_NASDAQ
## W = 0.95853, p-value = 0.000001278
##
## One-sample Kolmogorov-Smirnov test
##
## data: l_NASDAQ
## D = 0.076839, p-value = 0.1032
## alternative hypothesis: two-sided
##
## Jarque Bera Test
##
## data: l_NASDAQ
## X-squared = 74.388, df = 2, p-value < 0.00000000000000022
## [1] -0.03030498
El Value at Risk es de -3030.498 dolares
## [1] -0.01512554
El Value at Risk es de -1512.554 dolares
## [1] -0.01105111
El Value at Risk es de -1105.111 dolares
###alpha1 = 0.01
set.seed(100000)
simulacion <- rnorm(100000,mean = mu,sd = s)
VARsim<-quantile(simulacion,0.01);VARsim## 1%
## -0.02180821
El Value at Risk es:
## 1%
## -2157.213
set.seed(100000)
simulacion <- rnorm(100000,mean = mu,sd = s)
VARsim<-quantile(simulacion,0.05);VARsim## 5%
## -0.01503324
El Value at Risk es:
## 5%
## -1492.08
set.seed(100000)
simulacion <- rnorm(100000,mean = mu,sd = s)
VARsim<-quantile(simulacion,0.1);VARsim## 10%
## -0.01153218
El Value at Risk es:
## 10%
## -1146.593
Realice 10 000 simulaciones de un proceso browniano con media y varianza (A partir de los retornos continuos de la pregunta 2)
Calcule el VaR de cada simulacion y guarde su resultado en un vector de datos.
Grafique la distribucion de los VaR simulados.
Calcule el promedio, y su intervalo de confianza con los percentiles 0.025 y 0.975 de los datos simulados.
# Creando tabla de datos
id.VaR <- data.frame(
Nomb.VaR= c("VAR1c","VAR2c","VAR3c"),
ALPHA = c(0.01,0.05,0.1),
percentil_2.5 = c(-0.02551162,-0.01747768,-0.01355481),
percentil_97.5 = c(-0.01733742,-0.01245654,-0.009383086),
VaR = c(-1899.853,-1756.778,-1009.18),
stringsAsFactors = FALSE
)
# Print the data frame.
print(id.VaR) ## Nomb.VaR ALPHA percentil_2.5 percentil_97.5 VaR
## 1 VAR1c 0.01 -0.02551162 -0.017337420 -1899.853
## 2 VAR2c 0.05 -0.01747768 -0.012456540 -1756.778
## 3 VAR3c 0.10 -0.01355481 -0.009383086 -1009.180
VAR.mc <- numeric()
for (i in 1:10000) {
changes <- rnorm(length(l_NASDAQ),mean=1+mu,sd=s)
sim.ts <- cumprod(c(as.numeric(tsNASDAQ[1]),changes))
sim.R <- diff(log(sim.ts))
sim.q1 <- quantile(sim.R,0.01,na.rm = T)
sim.VAR1 <- exp(sim.q1)-1
VAR.mc[i] <- sim.VAR1
}
mean(VAR.mc)## [1] -0.02114664
## [1] 0.002070564
El Value at Risk es:
## 1%
## -1899.853
Grafica de la distribucion de los VaR simulados
percentiles 0.025
## 2.5%
## -0.02551162
percentiles 0.975
## 97.5%
## -0.01733742
VAR.mc <- numeric()
for (i in 1:10000) {
changes <- rnorm(length(l_NASDAQ),mean=1+mu,sd=s)
sim.ts <- cumprod(c(as.numeric(tsNASDAQ[1]),changes))
sim.R <- diff(log(sim.ts))
sim.q2 <- quantile(sim.R,0.05,na.rm = T)
sim.VAR2 <- exp(sim.q2)-1
VAR.mc[i] <- sim.VAR2
}
mean(VAR.mc)## [1] -0.01489754
## [1] 0.001286669
El Value at Risk es:
## 5%
## -1756.778
Grafica de la distribucion de los VaR simulados
percentiles 0.025
## 2.5%
## -0.01747768
percentiles 0.975
## 97.5%
## -0.01245654
VAR.mc <- numeric()
for (i in 1:10000) {
changes <- rnorm(length(l_NASDAQ),mean=1+mu,sd=s)
sim.ts <- cumprod(c(as.numeric(tsNASDAQ[1]),changes))
sim.R <- diff(log(sim.ts))
sim.q3 <- quantile(sim.R,0.1,na.rm = T)
sim.VAR3 <- exp(sim.q3)-1
VAR.mc[i] <- sim.VAR3
}
mean(VAR.mc)## [1] -0.01141814
## [1] 0.001069744
El Value at Risk es:
## 10%
## -1009.18
Grafica de la distribucion de los VaR simulados
percentiles 0.025
## 2.5%
## -0.01355481
percentiles 0.975
## 97.5%
## -0.009383086
En la ecuacion de los parametros podemos observar que los tres son estadisticamente significativo.
La varianza incondicional es constante y son las betas de los errores igual a 0.925105482, < 1.
La prevalecencia es 0.000007323.
R1 <- diff(log(tsNASDAQ))
ts.garch <- garch(R1, c(1,1), cond.dist="norm", include.mean = FALSE, trade = FALSE)##
## ***** ESTIMATION WITH ANALYTICAL GRADIENT *****
##
##
## I INITIAL X(I) D(I)
##
## 1 8.810082e-05 1.000e+00
## 2 5.000000e-02 1.000e+00
## 3 5.000000e-02 1.000e+00
##
## IT NF F RELDF PRELDF RELDX STPPAR D*STEP NPRELDF
## 0 1 -1.036e+03
## 1 7 -1.036e+03 2.86e-04 9.48e-04 1.0e-04 9.8e+09 1.0e-05 4.66e+06
## 2 8 -1.036e+03 7.05e-05 9.59e-05 9.3e-05 2.0e+00 1.0e-05 1.55e+00
## 3 16 -1.039e+03 2.81e-03 4.85e-03 4.7e-01 2.0e+00 8.8e-02 1.56e+00
## 4 19 -1.041e+03 1.46e-03 1.04e-03 6.9e-01 9.8e-01 2.3e-01 8.25e-03
## 5 21 -1.046e+03 5.55e-03 3.44e-03 4.5e-01 2.0e+00 4.6e-01 2.81e+00
## 6 23 -1.047e+03 7.61e-04 1.61e-03 3.0e-02 1.9e+00 4.6e-02 3.65e-03
## 7 24 -1.048e+03 9.76e-04 2.14e-03 3.0e-02 1.9e+00 4.6e-02 3.28e-02
## 8 31 -1.048e+03 4.25e-07 3.30e-05 5.8e-05 2.0e+00 8.6e-05 4.09e-04
## 9 32 -1.048e+03 1.73e-05 2.05e-05 2.9e-05 2.0e+00 4.3e-05 2.47e-05
## 10 35 -1.048e+03 1.38e-07 3.17e-07 3.3e-04 1.7e+00 5.0e-04 2.38e-06
## 11 36 -1.048e+03 4.18e-07 4.55e-07 4.8e-04 7.3e-01 1.0e-03 6.84e-07
## 12 37 -1.048e+03 1.12e-07 3.31e-07 5.3e-04 8.1e-01 1.0e-03 5.60e-07
## 13 38 -1.048e+03 1.90e-07 1.98e-07 5.5e-04 5.4e-01 1.0e-03 2.43e-07
## 14 52 -1.048e+03 -4.47e-14 2.05e-14 7.0e-15 5.0e+05 1.0e-14 3.19e-08
##
## ***** FALSE CONVERGENCE *****
##
## FUNCTION -1.048322e+03 RELDX 6.983e-15
## FUNC. EVALS 52 GRAD. EVALS 14
## PRELDF 2.050e-14 NPRELDF 3.189e-08
##
## I FINAL X(I) D(I) G(I)
##
## 1 7.322641e-06 1.000e+00 -2.074e+03
## 2 1.833333e-01 1.000e+00 -1.290e-01
## 3 7.417722e-01 1.000e+00 -5.975e-02
##
## Call:
## garch(x = R1, order = c(1, 1), cond.dist = "norm", include.mean = FALSE, trade = FALSE)
##
## Model:
## GARCH(1,1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.9971 -0.3604 0.1917 0.7754 2.6166
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## a0 0.000007323 0.000003433 2.133 0.032927 *
## a1 0.183333268 0.049790401 3.682 0.000231 ***
## b1 0.741772214 0.063917969 11.605 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Diagnostic Tests:
## Jarque Bera Test
##
## data: Residuals
## X-squared = 44.569, df = 2, p-value = 0.0000000002099
##
##
## Box-Ljung test
##
## data: Squared.Residuals
## X-squared = 0.4746, df = 1, p-value = 0.4909
## Time Series:
## Start = 2019.00280701754
## End = 2019.70456140351
## Frequency = 356.25
## [1] NA 2.616614253 0.549824722 0.524332308 0.471522017
## [6] 0.252089759 -0.143473634 -0.734189441 1.398515451 0.118994189
## [11] 0.611775055 0.953201625 -1.826688120 0.061178416 0.604975549
## [16] 1.232763090 -1.023009747 -0.750273730 2.109980927 1.035953292
## [21] -0.188417005 0.987245418 0.645663538 -0.338729804 -1.217801640
## [26] 0.132812152 0.144603087 1.730047667 0.078460503 0.098897330
## [31] 0.746220136 0.240446354 0.041305540 -0.564899174 1.334353406
## [36] 0.475010632 -0.095165575 0.102108625 -0.453555938 1.321585515
## [41] -0.333916525 -0.023839077 -1.465744209 -1.547941719 -0.214033274
## [46] 2.582940262 0.388473890 0.674562425 -0.169650560 0.858064646
## [51] 0.389839043 0.152382015 0.087071405 2.024817052 -2.834268939
## [56] -0.049418233 0.586213966 -0.565006453 0.326950967 0.832155494
## [61] 1.397763782 0.252838280 0.655881096 -0.055178410 0.747051398
## [66] 0.245869125 -0.773631938 0.957470522 -0.286321906 0.660769522
## [71] -0.148199832 0.463761797 -0.081315479 0.040391750 0.362267829
## [76] 2.234363345 -0.289572866 0.274967101 0.484232677 0.278747628
## [81] -1.257791661 -0.794205575 -0.224098733 2.325746795 -0.537853218
## [86] -2.275387537 -0.220526680 -0.394993034 0.083884714 -3.997149407
## [91] 0.675139655 0.725129692 0.666702472 -0.775642249 -1.157904406
## [96] 0.835176316 -0.364527179 -1.433876326 0.094803985 -0.362026083
## [101] -0.809569205 0.284844335 -1.757541149 -1.579225826 2.254651930
## [106] 0.420416690 0.385816355 1.340697180 0.800802030 -0.006207162
## [111] -0.348111534 0.569777453 -0.554967500 0.705628773 1.632113430
## [116] 0.430385817 0.886831791 -0.274438060 -0.395972482 -1.981961598
## [121] 0.330452060 0.820876202 0.554961201 1.284357828 0.250969354
## [126] 0.925132028 -0.126678218 -1.034014427 0.685352280 0.980665233
## [131] -0.102049476 0.810936248 0.235646335 -0.629195862 -0.681035155
## [136] 0.401813379 -1.148602305 1.012797054 0.793525724 1.170446078
## [141] -1.302289978 1.326049242 -0.491723458 -0.281872498 -1.525218650
## [146] -0.888919051 -1.511292868 -3.589451270 0.784850194 0.228828762
## [151] 1.527172517 -0.627765225 -0.827119506 1.386910886 -2.077533492
## [156] -0.050920566 1.021865324 0.847802557 -0.451682949 0.661518982
## [161] -0.285858416 -2.697868455 0.792855172 -0.220486433 0.278644075
## [166] 1.205283260 -0.105039960 -1.003694138 1.169727933 1.530200536
## [171] -0.134724530 -0.172346226 -0.040341172 1.159647965 0.321683900
## [176] -0.250854497 -0.355615785 0.531121320 -0.146578696 0.099016936
## [181] -1.242292319 -0.090950898 -2.215558163 1.164212801 -0.623027290
## [186] -1.292503055 0.794835280 -1.247170603 -1.630275945 1.007301930
## [191] 1.267696196 -0.285958906 -1.622151273 0.863860813 0.522347595
## [196] 1.268697651 -0.094769918 1.253353540 -0.290921188 0.426246392
## [201] -0.950289168 1.034703780 -0.812330019 0.219911907 1.012718886
## [206] 0.854065262 1.233476569 -0.686049007 0.394049001 -0.180110012
## [211] 1.556031990 0.667070616 0.021821630 -0.384097010 0.401886373
## [216] 0.713296079 -0.193001533 0.399937936 -0.075074197 -0.060136366
## [221] 1.238337318 0.163507302 0.387249981 -0.840555755 -0.381511814
## [226] 0.260575508 2.189557974 0.220609496 0.877235035 -0.604155441
## [231] -1.544700972 -0.659678081 0.666712997 0.060181009 1.372977991
## [236] -0.499748885 -0.085935125 0.616709998 1.047499291 0.276611118
## [241] 1.314605841 0.136625286 0.070106254 1.006217746 0.607685608
## [246] 0.338900010 0.123285828 1.233839874 -0.254001231 -1.029228646
## [251] 0.430332426
