Load Required Libraries
Load and Prepare Data
data_path <- "financial_Data.csv"
import <- read.csv(data_path)
h <- import$High
log.h <- na.omit(diff(h))
log.h_ts <- ts(log.h)
Exploratory Data Analysis
par(mfrow = c(2, 2))
plot(h, type = "l", main = "Raw High Prices", ylab = "Price")
plot(log.h, type = "l", main = "Log Returns", ylab = "Return")
acf(log.h, main = "ACF of Log Returns")
pacf(log.h, main = "PACF of Log Returns")
par(mfrow = c(1,1))
GARCH(1,1), GARCH(1,2), GARCH(2,1), GARCH(2,2) using
fGarch
garch11_model <- garchFit(~ garch(1, 1), data = log.h, trace = FALSE)
## Warning in sqrt(diag(fit$cvar)): NaNs produced
garch12_model <- garchFit(~ garch(1, 2), data = log.h, trace = FALSE)
## Warning in sqrt(diag(fit$cvar)): NaNs produced
garch21_model <- garchFit(~ garch(2, 1), data = log.h, trace = FALSE)
## Warning in sqrt(diag(fit$cvar)): NaNs produced
garch22_model <- garchFit(~ garch(2, 2), data = log.h, trace = FALSE)
## Warning in sqrt(diag(fit$cvar)): NaNs produced
summary(garch11_model)
##
## Title:
## GARCH Modelling
##
## Call:
## garchFit(formula = ~garch(1, 1), data = log.h, trace = FALSE)
##
## Mean and Variance Equation:
## data ~ garch(1, 1)
## <environment: 0x0000026c72e23ea8>
## [data = log.h]
##
## Conditional Distribution:
## norm
##
## Coefficient(s):
## mu omega alpha1 beta1
## -0.10302076 0.41140792 0.00000001 0.99999999
##
## Std. Errors:
## based on Hessian
##
## Error Analysis:
## Estimate Std. Error t value Pr(>|t|)
## mu -1.030e-01 9.894e-01 -0.104 0.917
## omega 4.114e-01 1.110e+00 0.371 0.711
## alpha1 1.000e-08 NaN NaN NaN
## beta1 1.000e+00 4.215e-03 237.257 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Log Likelihood:
## -1030.33 normalized: -4.171378
##
## Description:
## Tue May 6 09:42:55 2025 by user: victo
##
##
## Standardised Residuals Tests:
## Statistic p-Value
## Jarque-Bera Test R Chi^2 1.812496e+05 0.0000000
## Shapiro-Wilk Test R W 2.702137e-01 0.0000000
## Ljung-Box Test R Q(10) 1.407700e+00 0.9991952
## Ljung-Box Test R Q(15) 2.281588e+00 0.9999295
## Ljung-Box Test R Q(20) 2.822732e+00 0.9999976
## Ljung-Box Test R^2 Q(10) 1.188498e-01 1.0000000
## Ljung-Box Test R^2 Q(15) 1.799509e-01 1.0000000
## Ljung-Box Test R^2 Q(20) 2.529911e-01 1.0000000
## LM Arch Test R TR^2 1.515726e-01 1.0000000
##
## Information Criterion Statistics:
## AIC BIC SIC HQIC
## 8.375146 8.431978 8.374632 8.398027
summary(garch12_model)
##
## Title:
## GARCH Modelling
##
## Call:
## garchFit(formula = ~garch(1, 2), data = log.h, trace = FALSE)
##
## Mean and Variance Equation:
## data ~ garch(1, 2)
## <environment: 0x0000026c7437cbd0>
## [data = log.h]
##
## Conditional Distribution:
## norm
##
## Coefficient(s):
## mu omega alpha1 beta1 beta2
## -0.09197634 0.00025330 0.00000001 0.99999999 0.00153416
##
## Std. Errors:
## based on Hessian
##
## Error Analysis:
## Estimate Std. Error t value Pr(>|t|)
## mu -9.198e-02 9.881e-01 -0.093 0.925840
## omega 2.533e-04 1.510e+00 0.000 0.999866
## alpha1 1.000e-08 NaN NaN NaN
## beta1 1.000e+00 2.611e-01 3.830 0.000128 ***
## beta2 1.534e-03 2.657e-01 0.006 0.995393
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Log Likelihood:
## -1030.135 normalized: -4.170587
##
## Description:
## Tue May 6 09:42:55 2025 by user: victo
##
##
## Standardised Residuals Tests:
## Statistic p-Value
## Jarque-Bera Test R Chi^2 1.783573e+05 0.0000000
## Shapiro-Wilk Test R W 2.715645e-01 0.0000000
## Ljung-Box Test R Q(10) 1.420902e+00 0.9991613
## Ljung-Box Test R Q(15) 2.296993e+00 0.9999264
## Ljung-Box Test R Q(20) 2.842354e+00 0.9999974
## Ljung-Box Test R^2 Q(10) 1.204329e-01 1.0000000
## Ljung-Box Test R^2 Q(15) 1.824890e-01 1.0000000
## Ljung-Box Test R^2 Q(20) 2.566449e-01 1.0000000
## LM Arch Test R TR^2 1.537039e-01 1.0000000
##
## Information Criterion Statistics:
## AIC BIC SIC HQIC
## 8.381660 8.452700 8.380862 8.410261
summary(garch21_model)
##
## Title:
## GARCH Modelling
##
## Call:
## garchFit(formula = ~garch(2, 1), data = log.h, trace = FALSE)
##
## Mean and Variance Equation:
## data ~ garch(2, 1)
## <environment: 0x0000026c764400b0>
## [data = log.h]
##
## Conditional Distribution:
## norm
##
## Coefficient(s):
## mu omega alpha1 alpha2 beta1
## -0.10189597 0.41736275 0.00000001 0.00000001 0.99999999
##
## Std. Errors:
## based on Hessian
##
## Error Analysis:
## Estimate Std. Error t value Pr(>|t|)
## mu -1.019e-01 9.891e-01 -0.103 0.918
## omega 4.174e-01 1.116e+00 0.374 0.709
## alpha1 1.000e-08 NaN NaN NaN
## alpha2 1.000e-08 NaN NaN NaN
## beta1 1.000e+00 4.233e-03 236.257 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Log Likelihood:
## -1030.29 normalized: -4.171213
##
## Description:
## Tue May 6 09:42:55 2025 by user: victo
##
##
## Standardised Residuals Tests:
## Statistic p-Value
## Jarque-Bera Test R Chi^2 1.809666e+05 0.0000000
## Shapiro-Wilk Test R W 2.703369e-01 0.0000000
## Ljung-Box Test R Q(10) 1.408933e+00 0.9991920
## Ljung-Box Test R Q(15) 2.282837e+00 0.9999293
## Ljung-Box Test R Q(20) 2.824183e+00 0.9999976
## Ljung-Box Test R^2 Q(10) 1.190041e-01 1.0000000
## Ljung-Box Test R^2 Q(15) 1.802002e-01 1.0000000
## Ljung-Box Test R^2 Q(20) 2.533500e-01 1.0000000
## LM Arch Test R TR^2 1.517803e-01 1.0000000
##
## Information Criterion Statistics:
## AIC BIC SIC HQIC
## 8.382912 8.453952 8.382114 8.411513
summary(garch22_model)
##
## Title:
## GARCH Modelling
##
## Call:
## garchFit(formula = ~garch(2, 2), data = log.h, trace = FALSE)
##
## Mean and Variance Equation:
## data ~ garch(2, 2)
## <environment: 0x0000026c77791d20>
## [data = log.h]
##
## Conditional Distribution:
## norm
##
## Coefficient(s):
## mu omega alpha1 alpha2 beta1 beta2
## -0.09198733 0.00025330 0.00000001 0.00000001 0.99999999 0.00153417
##
## Std. Errors:
## based on Hessian
##
## Error Analysis:
## Estimate Std. Error t value Pr(>|t|)
## mu -9.199e-02 9.881e-01 -0.093 0.925831
## omega 2.533e-04 1.502e+00 0.000 0.999865
## alpha1 1.000e-08 NaN NaN NaN
## alpha2 1.000e-08 NaN NaN NaN
## beta1 1.000e+00 2.608e-01 3.834 0.000126 ***
## beta2 1.534e-03 2.655e-01 0.006 0.995389
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Log Likelihood:
## -1030.135 normalized: -4.170587
##
## Description:
## Tue May 6 09:42:55 2025 by user: victo
##
##
## Standardised Residuals Tests:
## Statistic p-Value
## Jarque-Bera Test R Chi^2 1.783571e+05 0.0000000
## Shapiro-Wilk Test R W 2.715645e-01 0.0000000
## Ljung-Box Test R Q(10) 1.420903e+00 0.9991612
## Ljung-Box Test R Q(15) 2.296994e+00 0.9999264
## Ljung-Box Test R Q(20) 2.842354e+00 0.9999974
## Ljung-Box Test R^2 Q(10) 1.204331e-01 1.0000000
## Ljung-Box Test R^2 Q(15) 1.824893e-01 1.0000000
## Ljung-Box Test R^2 Q(20) 2.566453e-01 1.0000000
## LM Arch Test R TR^2 1.537041e-01 1.0000000
##
## Information Criterion Statistics:
## AIC BIC SIC HQIC
## 8.389758 8.475006 8.388614 8.424079
predict(garch11_model, n.ahead = 120, plot = TRUE)
## meanForecast meanError standardDeviation lowerInterval upperInterval
## 1 -0.1030208 18.82311 18.82311 -36.99564 36.78959
## 2 -0.1030208 18.83403 18.83403 -37.01705 36.81101
## 3 -0.1030208 18.84495 18.84495 -37.03845 36.83241
## 4 -0.1030208 18.85586 18.85586 -37.05984 36.85380
## 5 -0.1030208 18.86677 18.86677 -37.08121 36.87517
## 6 -0.1030208 18.87767 18.87767 -37.10258 36.89653
## 7 -0.1030208 18.88856 18.88856 -37.12393 36.91789
## 8 -0.1030208 18.89945 18.89945 -37.14527 36.93922
## 9 -0.1030208 18.91033 18.91033 -37.16659 36.96055
## 10 -0.1030208 18.92121 18.92121 -37.18791 36.98186
## 11 -0.1030208 18.93208 18.93208 -37.20921 37.00317
## 12 -0.1030208 18.94294 18.94294 -37.23050 37.02446
## 13 -0.1030208 18.95379 18.95379 -37.25177 37.04573
## 14 -0.1030208 18.96464 18.96464 -37.27304 37.06700
## 15 -0.1030208 18.97549 18.97549 -37.29429 37.08825
## 16 -0.1030208 18.98632 18.98632 -37.31553 37.10949
## 17 -0.1030208 18.99716 18.99716 -37.33676 37.13072
## 18 -0.1030208 19.00798 19.00798 -37.35798 37.15194
## 19 -0.1030208 19.01880 19.01880 -37.37918 37.17314
## 20 -0.1030208 19.02961 19.02961 -37.40038 37.19434
## 21 -0.1030208 19.04042 19.04042 -37.42156 37.21552
## 22 -0.1030208 19.05122 19.05122 -37.44273 37.23668
## 23 -0.1030208 19.06201 19.06201 -37.46388 37.25784
## 24 -0.1030208 19.07280 19.07280 -37.48503 37.27899
## 25 -0.1030208 19.08358 19.08358 -37.50616 37.30012
## 26 -0.1030208 19.09436 19.09436 -37.52728 37.32124
## 27 -0.1030208 19.10513 19.10513 -37.54839 37.34235
## 28 -0.1030208 19.11589 19.11589 -37.56949 37.36344
## 29 -0.1030208 19.12665 19.12665 -37.59057 37.38453
## 30 -0.1030208 19.13740 19.13740 -37.61164 37.40560
## 31 -0.1030208 19.14815 19.14815 -37.63271 37.42666
## 32 -0.1030208 19.15889 19.15889 -37.65375 37.44771
## 33 -0.1030208 19.16962 19.16962 -37.67479 37.46875
## 34 -0.1030208 19.18035 19.18035 -37.69582 37.48978
## 35 -0.1030208 19.19107 19.19107 -37.71683 37.51079
## 36 -0.1030208 19.20179 19.20179 -37.73784 37.53179
## 37 -0.1030208 19.21250 19.21250 -37.75883 37.55278
## 38 -0.1030208 19.22320 19.22320 -37.77981 37.57376
## 39 -0.1030208 19.23390 19.23390 -37.80077 37.59473
## 40 -0.1030208 19.24459 19.24459 -37.82173 37.61569
## 41 -0.1030208 19.25528 19.25528 -37.84267 37.63663
## 42 -0.1030208 19.26596 19.26596 -37.86360 37.65756
## 43 -0.1030208 19.27663 19.27663 -37.88453 37.67848
## 44 -0.1030208 19.28730 19.28730 -37.90543 37.69939
## 45 -0.1030208 19.29796 19.29796 -37.92633 37.72029
## 46 -0.1030208 19.30862 19.30862 -37.94722 37.74118
## 47 -0.1030208 19.31927 19.31927 -37.96809 37.76205
## 48 -0.1030208 19.32991 19.32991 -37.98896 37.78292
## 49 -0.1030208 19.34055 19.34055 -38.00981 37.80377
## 50 -0.1030208 19.35119 19.35119 -38.03065 37.82461
## 51 -0.1030208 19.36181 19.36181 -38.05148 37.84544
## 52 -0.1030208 19.37243 19.37243 -38.07229 37.86625
## 53 -0.1030208 19.38305 19.38305 -38.09310 37.88706
## 54 -0.1030208 19.39366 19.39366 -38.11390 37.90785
## 55 -0.1030208 19.40426 19.40426 -38.13468 37.92864
## 56 -0.1030208 19.41486 19.41486 -38.15545 37.94941
## 57 -0.1030208 19.42545 19.42545 -38.17621 37.97017
## 58 -0.1030208 19.43604 19.43604 -38.19696 37.99092
## 59 -0.1030208 19.44662 19.44662 -38.21770 38.01166
## 60 -0.1030208 19.45720 19.45720 -38.23842 38.03238
## 61 -0.1030208 19.46777 19.46777 -38.25914 38.05310
## 62 -0.1030208 19.47833 19.47833 -38.27984 38.07380
## 63 -0.1030208 19.48889 19.48889 -38.30054 38.09450
## 64 -0.1030208 19.49944 19.49944 -38.32122 38.11518
## 65 -0.1030208 19.50999 19.50999 -38.34189 38.13585
## 66 -0.1030208 19.52053 19.52053 -38.36255 38.15651
## 67 -0.1030208 19.53106 19.53106 -38.38320 38.17716
## 68 -0.1030208 19.54159 19.54159 -38.40383 38.19779
## 69 -0.1030208 19.55211 19.55211 -38.42446 38.21842
## 70 -0.1030208 19.56263 19.56263 -38.44507 38.23903
## 71 -0.1030208 19.57314 19.57314 -38.46568 38.25964
## 72 -0.1030208 19.58365 19.58365 -38.48627 38.28023
## 73 -0.1030208 19.59415 19.59415 -38.50685 38.30081
## 74 -0.1030208 19.60465 19.60465 -38.52742 38.32138
## 75 -0.1030208 19.61514 19.61514 -38.54798 38.34194
## 76 -0.1030208 19.62562 19.62562 -38.56853 38.36249
## 77 -0.1030208 19.63610 19.63610 -38.58907 38.38303
## 78 -0.1030208 19.64657 19.64657 -38.60960 38.40355
## 79 -0.1030208 19.65704 19.65704 -38.63011 38.42407
## 80 -0.1030208 19.66750 19.66750 -38.65062 38.44458
## 81 -0.1030208 19.67796 19.67796 -38.67111 38.46507
## 82 -0.1030208 19.68841 19.68841 -38.69159 38.48555
## 83 -0.1030208 19.69885 19.69885 -38.71207 38.50602
## 84 -0.1030208 19.70929 19.70929 -38.73253 38.52649
## 85 -0.1030208 19.71973 19.71973 -38.75298 38.54694
## 86 -0.1030208 19.73016 19.73016 -38.77342 38.56738
## 87 -0.1030208 19.74058 19.74058 -38.79385 38.58781
## 88 -0.1030208 19.75100 19.75100 -38.81426 38.60822
## 89 -0.1030208 19.76141 19.76141 -38.83467 38.62863
## 90 -0.1030208 19.77182 19.77182 -38.85507 38.64903
## 91 -0.1030208 19.78222 19.78222 -38.87545 38.66941
## 92 -0.1030208 19.79261 19.79261 -38.89583 38.68979
## 93 -0.1030208 19.80300 19.80300 -38.91619 38.71015
## 94 -0.1030208 19.81339 19.81339 -38.93655 38.73051
## 95 -0.1030208 19.82377 19.82377 -38.95689 38.75085
## 96 -0.1030208 19.83414 19.83414 -38.97722 38.77118
## 97 -0.1030208 19.84451 19.84451 -38.99755 38.79150
## 98 -0.1030208 19.85487 19.85487 -39.01786 38.81182
## 99 -0.1030208 19.86523 19.86523 -39.03816 38.83212
## 100 -0.1030208 19.87558 19.87558 -39.05845 38.85241
## 101 -0.1030208 19.88593 19.88593 -39.07873 38.87269
## 102 -0.1030208 19.89627 19.89627 -39.09900 38.89295
## 103 -0.1030208 19.90661 19.90661 -39.11925 38.91321
## 104 -0.1030208 19.91694 19.91694 -39.13950 38.93346
## 105 -0.1030208 19.92726 19.92726 -39.15974 38.95370
## 106 -0.1030208 19.93758 19.93758 -39.17997 38.97393
## 107 -0.1030208 19.94790 19.94790 -39.20018 38.99414
## 108 -0.1030208 19.95821 19.95821 -39.22039 39.01435
## 109 -0.1030208 19.96851 19.96851 -39.24059 39.03454
## 110 -0.1030208 19.97881 19.97881 -39.26077 39.05473
## 111 -0.1030208 19.98910 19.98910 -39.28095 39.07490
## 112 -0.1030208 19.99939 19.99939 -39.30111 39.09507
## 113 -0.1030208 20.00968 20.00968 -39.32126 39.11522
## 114 -0.1030208 20.01995 20.01995 -39.34141 39.13537
## 115 -0.1030208 20.03023 20.03023 -39.36154 39.15550
## 116 -0.1030208 20.04049 20.04049 -39.38166 39.17562
## 117 -0.1030208 20.05075 20.05075 -39.40178 39.19573
## 118 -0.1030208 20.06101 20.06101 -39.42188 39.21584
## 119 -0.1030208 20.07126 20.07126 -39.44197 39.23593
## 120 -0.1030208 20.08151 20.08151 -39.46205 39.25601
predict(garch12_model, n.ahead = 120, plot = TRUE)
## meanForecast meanError standardDeviation lowerInterval upperInterval
## 1 -0.09197634 19.19048 19.19048 -37.70463 37.52067
## 2 -0.09197634 19.20518 19.20518 -37.73343 37.54948
## 3 -0.09197634 19.21989 19.21989 -37.76227 37.57831
## 4 -0.09197634 19.23461 19.23461 -37.79112 37.60717
## 5 -0.09197634 19.24934 19.24934 -37.82000 37.63604
## 6 -0.09197634 19.26409 19.26409 -37.84889 37.66494
## 7 -0.09197634 19.27884 19.27884 -37.87781 37.69386
## 8 -0.09197634 19.29361 19.29361 -37.90676 37.72280
## 9 -0.09197634 19.30839 19.30839 -37.93572 37.75177
## 10 -0.09197634 19.32318 19.32318 -37.96471 37.78075
## 11 -0.09197634 19.33798 19.33798 -37.99372 37.80976
## 12 -0.09197634 19.35279 19.35279 -38.02275 37.83879
## 13 -0.09197634 19.36761 19.36761 -38.05180 37.86785
## 14 -0.09197634 19.38245 19.38245 -38.08088 37.89692
## 15 -0.09197634 19.39729 19.39729 -38.10997 37.92602
## 16 -0.09197634 19.41215 19.41215 -38.13909 37.95514
## 17 -0.09197634 19.42702 19.42702 -38.16824 37.98428
## 18 -0.09197634 19.44190 19.44190 -38.19740 38.01345
## 19 -0.09197634 19.45679 19.45679 -38.22659 38.04263
## 20 -0.09197634 19.47169 19.47169 -38.25580 38.07184
## 21 -0.09197634 19.48661 19.48661 -38.28503 38.10107
## 22 -0.09197634 19.50153 19.50153 -38.31428 38.13033
## 23 -0.09197634 19.51647 19.51647 -38.34356 38.15960
## 24 -0.09197634 19.53142 19.53142 -38.37286 38.18890
## 25 -0.09197634 19.54638 19.54638 -38.40218 38.21822
## 26 -0.09197634 19.56135 19.56135 -38.43152 38.24757
## 27 -0.09197634 19.57633 19.57633 -38.46089 38.27693
## 28 -0.09197634 19.59133 19.59133 -38.49027 38.30632
## 29 -0.09197634 19.60633 19.60633 -38.51969 38.33573
## 30 -0.09197634 19.62135 19.62135 -38.54912 38.36517
## 31 -0.09197634 19.63638 19.63638 -38.57857 38.39462
## 32 -0.09197634 19.65142 19.65142 -38.60805 38.42410
## 33 -0.09197634 19.66647 19.66647 -38.63755 38.45360
## 34 -0.09197634 19.68154 19.68154 -38.66708 38.48313
## 35 -0.09197634 19.69661 19.69661 -38.69662 38.51267
## 36 -0.09197634 19.71170 19.71170 -38.72619 38.54224
## 37 -0.09197634 19.72680 19.72680 -38.75578 38.57183
## 38 -0.09197634 19.74190 19.74190 -38.78540 38.60145
## 39 -0.09197634 19.75703 19.75703 -38.81504 38.63108
## 40 -0.09197634 19.77216 19.77216 -38.84469 38.66074
## 41 -0.09197634 19.78730 19.78730 -38.87438 38.69042
## 42 -0.09197634 19.80246 19.80246 -38.90408 38.72013
## 43 -0.09197634 19.81763 19.81763 -38.93381 38.74986
## 44 -0.09197634 19.83281 19.83281 -38.96356 38.77961
## 45 -0.09197634 19.84800 19.84800 -38.99333 38.80938
## 46 -0.09197634 19.86320 19.86320 -39.02313 38.83918
## 47 -0.09197634 19.87841 19.87841 -39.05295 38.86899
## 48 -0.09197634 19.89364 19.89364 -39.08279 38.89884
## 49 -0.09197634 19.90887 19.90887 -39.11265 38.92870
## 50 -0.09197634 19.92412 19.92412 -39.14254 38.95859
## 51 -0.09197634 19.93938 19.93938 -39.17245 38.98850
## 52 -0.09197634 19.95466 19.95466 -39.20238 39.01843
## 53 -0.09197634 19.96994 19.96994 -39.23234 39.04839
## 54 -0.09197634 19.98524 19.98524 -39.26232 39.07837
## 55 -0.09197634 20.00054 20.00054 -39.29232 39.10837
## 56 -0.09197634 20.01586 20.01586 -39.32234 39.13839
## 57 -0.09197634 20.03119 20.03119 -39.35239 39.16844
## 58 -0.09197634 20.04654 20.04654 -39.38246 39.19851
## 59 -0.09197634 20.06189 20.06189 -39.41256 39.22860
## 60 -0.09197634 20.07726 20.07726 -39.44267 39.25872
## 61 -0.09197634 20.09263 20.09263 -39.47281 39.28886
## 62 -0.09197634 20.10802 20.10802 -39.50298 39.31902
## 63 -0.09197634 20.12342 20.12342 -39.53316 39.34921
## 64 -0.09197634 20.13884 20.13884 -39.56337 39.37942
## 65 -0.09197634 20.15426 20.15426 -39.59360 39.40965
## 66 -0.09197634 20.16970 20.16970 -39.62386 39.43991
## 67 -0.09197634 20.18515 20.18515 -39.65414 39.47018
## 68 -0.09197634 20.20061 20.20061 -39.68444 39.50049
## 69 -0.09197634 20.21608 20.21608 -39.71476 39.53081
## 70 -0.09197634 20.23156 20.23156 -39.74511 39.56116
## 71 -0.09197634 20.24706 20.24706 -39.77548 39.59153
## 72 -0.09197634 20.26257 20.26257 -39.80588 39.62192
## 73 -0.09197634 20.27809 20.27809 -39.83630 39.65234
## 74 -0.09197634 20.29362 20.29362 -39.86674 39.68278
## 75 -0.09197634 20.30916 20.30916 -39.89720 39.71325
## 76 -0.09197634 20.32472 20.32472 -39.92769 39.74374
## 77 -0.09197634 20.34028 20.34028 -39.95820 39.77425
## 78 -0.09197634 20.35586 20.35586 -39.98873 39.80478
## 79 -0.09197634 20.37145 20.37145 -40.01929 39.83534
## 80 -0.09197634 20.38706 20.38706 -40.04987 39.86592
## 81 -0.09197634 20.40267 20.40267 -40.08048 39.89652
## 82 -0.09197634 20.41830 20.41830 -40.11110 39.92715
## 83 -0.09197634 20.43394 20.43394 -40.14176 39.95780
## 84 -0.09197634 20.44959 20.44959 -40.17243 39.98848
## 85 -0.09197634 20.46525 20.46525 -40.20313 40.01918
## 86 -0.09197634 20.48092 20.48092 -40.23385 40.04990
## 87 -0.09197634 20.49661 20.49661 -40.26460 40.08064
## 88 -0.09197634 20.51231 20.51231 -40.29536 40.11141
## 89 -0.09197634 20.52802 20.52802 -40.32616 40.14220
## 90 -0.09197634 20.54374 20.54374 -40.35697 40.17302
## 91 -0.09197634 20.55948 20.55948 -40.38781 40.20386
## 92 -0.09197634 20.57522 20.57522 -40.41868 40.23472
## 93 -0.09197634 20.59098 20.59098 -40.44956 40.26561
## 94 -0.09197634 20.60675 20.60675 -40.48047 40.29652
## 95 -0.09197634 20.62254 20.62254 -40.51141 40.32745
## 96 -0.09197634 20.63833 20.63833 -40.54236 40.35841
## 97 -0.09197634 20.65414 20.65414 -40.57335 40.38939
## 98 -0.09197634 20.66996 20.66996 -40.60435 40.42040
## 99 -0.09197634 20.68579 20.68579 -40.63538 40.45143
## 100 -0.09197634 20.70163 20.70163 -40.66643 40.48248
## 101 -0.09197634 20.71749 20.71749 -40.69751 40.51356
## 102 -0.09197634 20.73336 20.73336 -40.72861 40.54466
## 103 -0.09197634 20.74924 20.74924 -40.75973 40.57578
## 104 -0.09197634 20.76513 20.76513 -40.79088 40.60693
## 105 -0.09197634 20.78103 20.78103 -40.82205 40.63810
## 106 -0.09197634 20.79695 20.79695 -40.85325 40.66929
## 107 -0.09197634 20.81288 20.81288 -40.88447 40.70051
## 108 -0.09197634 20.82882 20.82882 -40.91571 40.73176
## 109 -0.09197634 20.84477 20.84477 -40.94698 40.76302
## 110 -0.09197634 20.86074 20.86074 -40.97827 40.79432
## 111 -0.09197634 20.87671 20.87671 -41.00958 40.82563
## 112 -0.09197634 20.89270 20.89270 -41.04092 40.85697
## 113 -0.09197634 20.90870 20.90870 -41.07228 40.88833
## 114 -0.09197634 20.92472 20.92472 -41.10367 40.91972
## 115 -0.09197634 20.94075 20.94075 -41.13508 40.95113
## 116 -0.09197634 20.95678 20.95678 -41.16652 40.98257
## 117 -0.09197634 20.97283 20.97283 -41.19798 41.01402
## 118 -0.09197634 20.98890 20.98890 -41.22946 41.04551
## 119 -0.09197634 21.00497 21.00497 -41.26097 41.07701
## 120 -0.09197634 21.02106 21.02106 -41.29250 41.10855
predict(garch22_model, n.ahead = 120, plot = TRUE)
## meanForecast meanError standardDeviation lowerInterval upperInterval
## 1 -0.09198733 19.19051 19.19051 -37.70470 37.52073
## 2 -0.09198733 19.20521 19.20521 -37.73351 37.54954
## 3 -0.09198733 19.21992 19.21992 -37.76234 37.57837
## 4 -0.09198733 19.23464 19.23464 -37.79120 37.60722
## 5 -0.09198733 19.24938 19.24938 -37.82007 37.63610
## 6 -0.09198733 19.26412 19.26412 -37.84897 37.66500
## 7 -0.09198733 19.27888 19.27888 -37.87789 37.69392
## 8 -0.09198733 19.29364 19.29364 -37.90683 37.72286
## 9 -0.09198733 19.30842 19.30842 -37.93580 37.75182
## 10 -0.09198733 19.32321 19.32321 -37.96479 37.78081
## 11 -0.09198733 19.33801 19.33801 -37.99380 37.80982
## 12 -0.09198733 19.35282 19.35282 -38.02283 37.83885
## 13 -0.09198733 19.36765 19.36765 -38.05188 37.86791
## 14 -0.09198733 19.38248 19.38248 -38.08096 37.89698
## 15 -0.09198733 19.39733 19.39733 -38.11005 37.92608
## 16 -0.09198733 19.41219 19.41219 -38.13917 37.95520
## 17 -0.09198733 19.42706 19.42706 -38.16832 37.98434
## 18 -0.09198733 19.44194 19.44194 -38.19748 38.01351
## 19 -0.09198733 19.45683 19.45683 -38.22667 38.04269
## 20 -0.09198733 19.47173 19.47173 -38.25588 38.07190
## 21 -0.09198733 19.48664 19.48664 -38.28511 38.10113
## 22 -0.09198733 19.50157 19.50157 -38.31436 38.13039
## 23 -0.09198733 19.51651 19.51651 -38.34364 38.15967
## 24 -0.09198733 19.53146 19.53146 -38.37294 38.18896
## 25 -0.09198733 19.54642 19.54642 -38.40226 38.21829
## 26 -0.09198733 19.56139 19.56139 -38.43160 38.24763
## 27 -0.09198733 19.57637 19.57637 -38.46097 38.27700
## 28 -0.09198733 19.59137 19.59137 -38.49036 38.30639
## 29 -0.09198733 19.60637 19.60637 -38.51977 38.33580
## 30 -0.09198733 19.62139 19.62139 -38.54920 38.36523
## 31 -0.09198733 19.63642 19.63642 -38.57866 38.39469
## 32 -0.09198733 19.65146 19.65146 -38.60814 38.42417
## 33 -0.09198733 19.66651 19.66651 -38.63764 38.45367
## 34 -0.09198733 19.68157 19.68157 -38.66717 38.48319
## 35 -0.09198733 19.69665 19.69665 -38.69671 38.51274
## 36 -0.09198733 19.71174 19.71174 -38.72628 38.54231
## 37 -0.09198733 19.72683 19.72683 -38.75587 38.57190
## 38 -0.09198733 19.74194 19.74194 -38.78549 38.60151
## 39 -0.09198733 19.75707 19.75707 -38.81512 38.63115
## 40 -0.09198733 19.77220 19.77220 -38.84478 38.66081
## 41 -0.09198733 19.78734 19.78734 -38.87447 38.69049
## 42 -0.09198733 19.80250 19.80250 -38.90417 38.72020
## 43 -0.09198733 19.81767 19.81767 -38.93390 38.74993
## 44 -0.09198733 19.83285 19.83285 -38.96365 38.77968
## 45 -0.09198733 19.84804 19.84804 -38.99342 38.80945
## 46 -0.09198733 19.86324 19.86324 -39.02322 38.83925
## 47 -0.09198733 19.87845 19.87845 -39.05304 38.86907
## 48 -0.09198733 19.89368 19.89368 -39.08288 38.89891
## 49 -0.09198733 19.90892 19.90892 -39.11275 38.92877
## 50 -0.09198733 19.92417 19.92417 -39.14263 38.95866
## 51 -0.09198733 19.93943 19.93943 -39.17254 38.98857
## 52 -0.09198733 19.95470 19.95470 -39.20248 39.01850
## 53 -0.09198733 19.96998 19.96998 -39.23243 39.04846
## 54 -0.09198733 19.98528 19.98528 -39.26241 39.07844
## 55 -0.09198733 20.00059 20.00059 -39.29242 39.10844
## 56 -0.09198733 20.01591 20.01591 -39.32244 39.13847
## 57 -0.09198733 20.03124 20.03124 -39.35249 39.16851
## 58 -0.09198733 20.04658 20.04658 -39.38256 39.19858
## 59 -0.09198733 20.06193 20.06193 -39.41265 39.22868
## 60 -0.09198733 20.07730 20.07730 -39.44277 39.25880
## 61 -0.09198733 20.09268 20.09268 -39.47291 39.28894
## 62 -0.09198733 20.10807 20.10807 -39.50307 39.31910
## 63 -0.09198733 20.12347 20.12347 -39.53326 39.34929
## 64 -0.09198733 20.13888 20.13888 -39.56347 39.37950
## 65 -0.09198733 20.15431 20.15431 -39.59370 39.40973
## 66 -0.09198733 20.16974 20.16974 -39.62396 39.43998
## 67 -0.09198733 20.18519 20.18519 -39.65424 39.47026
## 68 -0.09198733 20.20065 20.20065 -39.68454 39.50056
## 69 -0.09198733 20.21612 20.21612 -39.71486 39.53089
## 70 -0.09198733 20.23161 20.23161 -39.74521 39.56124
## 71 -0.09198733 20.24711 20.24711 -39.77558 39.59161
## 72 -0.09198733 20.26261 20.26261 -39.80598 39.62200
## 73 -0.09198733 20.27813 20.27813 -39.83640 39.65242
## 74 -0.09198733 20.29366 20.29366 -39.86684 39.68286
## 75 -0.09198733 20.30921 20.30921 -39.89730 39.71333
## 76 -0.09198733 20.32476 20.32476 -39.92779 39.74382
## 77 -0.09198733 20.34033 20.34033 -39.95830 39.77433
## 78 -0.09198733 20.35591 20.35591 -39.98884 39.80486
## 79 -0.09198733 20.37150 20.37150 -40.01940 39.83542
## 80 -0.09198733 20.38710 20.38710 -40.04998 39.86600
## 81 -0.09198733 20.40272 20.40272 -40.08058 39.89661
## 82 -0.09198733 20.41835 20.41835 -40.11121 39.92724
## 83 -0.09198733 20.43398 20.43398 -40.14186 39.95789
## 84 -0.09198733 20.44964 20.44964 -40.17254 39.98856
## 85 -0.09198733 20.46530 20.46530 -40.20324 40.01926
## 86 -0.09198733 20.48097 20.48097 -40.23396 40.04998
## 87 -0.09198733 20.49666 20.49666 -40.26470 40.08073
## 88 -0.09198733 20.51236 20.51236 -40.29547 40.11150
## 89 -0.09198733 20.52807 20.52807 -40.32627 40.14229
## 90 -0.09198733 20.54379 20.54379 -40.35708 40.17311
## 91 -0.09198733 20.55953 20.55953 -40.38792 40.20395
## 92 -0.09198733 20.57527 20.57527 -40.41879 40.23481
## 93 -0.09198733 20.59103 20.59103 -40.44967 40.26570
## 94 -0.09198733 20.60680 20.60680 -40.48058 40.29661
## 95 -0.09198733 20.62259 20.62259 -40.51152 40.32754
## 96 -0.09198733 20.63838 20.63838 -40.54248 40.35850
## 97 -0.09198733 20.65419 20.65419 -40.57346 40.38948
## 98 -0.09198733 20.67001 20.67001 -40.60446 40.42049
## 99 -0.09198733 20.68584 20.68584 -40.63549 40.45152
## 100 -0.09198733 20.70169 20.70169 -40.66654 40.48257
## 101 -0.09198733 20.71754 20.71754 -40.69762 40.51365
## 102 -0.09198733 20.73341 20.73341 -40.72872 40.54475
## 103 -0.09198733 20.74929 20.74929 -40.75985 40.57587
## 104 -0.09198733 20.76518 20.76518 -40.79099 40.60702
## 105 -0.09198733 20.78109 20.78109 -40.82217 40.63819
## 106 -0.09198733 20.79700 20.79700 -40.85336 40.66939
## 107 -0.09198733 20.81293 20.81293 -40.88458 40.70061
## 108 -0.09198733 20.82887 20.82887 -40.91583 40.73185
## 109 -0.09198733 20.84482 20.84482 -40.94709 40.76312
## 110 -0.09198733 20.86079 20.86079 -40.97838 40.79441
## 111 -0.09198733 20.87677 20.87677 -41.00970 40.82573
## 112 -0.09198733 20.89276 20.89276 -41.04104 40.85706
## 113 -0.09198733 20.90876 20.90876 -41.07240 40.88843
## 114 -0.09198733 20.92477 20.92477 -41.10379 40.91982
## 115 -0.09198733 20.94080 20.94080 -41.13520 40.95123
## 116 -0.09198733 20.95684 20.95684 -41.16664 40.98266
## 117 -0.09198733 20.97289 20.97289 -41.19810 41.01412
## 118 -0.09198733 20.98895 20.98895 -41.22958 41.04561
## 119 -0.09198733 21.00503 21.00503 -41.26109 41.07711
## 120 -0.09198733 21.02112 21.02112 -41.29262 41.10864
eGARCH Models using rugarch
# eGARCH Models using `rugarch`
# Define eGARCH model specifications
egarch_models <- list(
egarch11 = ugarchspec(
variance.model = list(model = "eGARCH", garchOrder = c(1, 1)),
mean.model = list(armaOrder = c(0, 0), include.mean = TRUE),
distribution.model = "norm"
),
egarch12 = ugarchspec(
variance.model = list(model = "eGARCH", garchOrder = c(1, 2)),
mean.model = list(armaOrder = c(0, 0), include.mean = TRUE),
distribution.model = "norm"
),
egarch21 = ugarchspec(
variance.model = list(model = "eGARCH", garchOrder = c(2, 1)),
mean.model = list(armaOrder = c(0, 0), include.mean = TRUE),
distribution.model = "norm"
),
egarch22 = ugarchspec(
variance.model = list(model = "eGARCH", garchOrder = c(2, 2)),
mean.model = list(armaOrder = c(0, 0), include.mean = TRUE),
distribution.model = "norm"
)
)
# Fit models to the data (ensure `log.h` is defined and numeric)
fit_egarch <- lapply(egarch_models, function(spec) {
ugarchfit(spec = spec, data = log.h, solver = "hybrid")
})
# Extract model coefficients
egarch_coefs <- lapply(fit_egarch, coef)
print(egarch_coefs)
## $egarch11
## mu omega alpha1 beta1 gamma1
## 0.27778059 3.47117756 1.00788084 0.01926387 1.06366206
##
## $egarch12
## mu omega alpha1 beta1 beta2 gamma1
## -1.4500122 6.4319537 2.4091016 0.3962988 -0.3797081 2.9621385
##
## $egarch21
## mu omega alpha1 alpha2 beta1 gamma1
## 0.08387409 -0.08023885 0.11971505 0.04468266 0.99999999 -0.54928852
## gamma2
## 0.42233103
##
## $egarch22
## mu omega alpha1 alpha2 beta1 beta2 gamma1
## 0.1654386 -0.2142866 0.9316198 -0.2810897 0.6377920 0.4064154 0.5958231
## gamma2
## -0.4636316
# Optional: Forecast using the fitted models
egarch_forecasts <- lapply(fit_egarch, function(fit) ugarchforecast(fit, n.ahead = 10))
# You can inspect a specific forecast like this:
print(egarch_forecasts$egarch11)
##
## *------------------------------------*
## * GARCH Model Forecast *
## *------------------------------------*
## Model: eGARCH
## Horizon: 10
## Roll Steps: 0
## Out of Sample: 0
##
## 0-roll forecast [T0=1970-09-05]:
## Series Sigma
## T+1 0.2778 3.813
## T+2 0.2778 5.820
## T+3 0.2778 5.868
## T+4 0.2778 5.869
## T+5 0.2778 5.869
## T+6 0.2778 5.869
## T+7 0.2778 5.869
## T+8 0.2778 5.869
## T+9 0.2778 5.869
## T+10 0.2778 5.869
# Optional: Plot diagnostics
#lapply(fit_egarch, plot)
GJR-GARCH Models using rugarch
gjr_models <- list(
gjr11 = ugarchspec(variance.model = list(model="gjrGARCH", garchOrder=c(1,1)), mean.model=list(armaOrder=c(0,0)), distribution.model="norm"),
gjr12 = ugarchspec(variance.model = list(model="gjrGARCH", garchOrder=c(1,2)), mean.model=list(armaOrder=c(0,0)), distribution.model="norm"),
gjr21 = ugarchspec(variance.model = list(model="gjrGARCH", garchOrder=c(2,1)), mean.model=list(armaOrder=c(0,0)), distribution.model="norm"),
gjr22 = ugarchspec(variance.model = list(model="gjrGARCH", garchOrder=c(2,2)), mean.model=list(armaOrder=c(0,0)), distribution.model="norm")
)
fit_gjr_models <- lapply(gjr_models, function(spec) ugarchfit(data=log.h, spec=spec, solver="hybrid"))
lapply(fit_gjr_models, coef)
## $gjr11
## mu omega alpha1 beta1 gamma1
## -0.93841343 0.41903772 0.01262167 0.99557055 -0.01928445
##
## $gjr12
## mu omega alpha1 beta1 beta2
## 7.382630e-02 1.069272e-01 1.036676e-20 3.928563e-01 6.144344e-01
## gamma1
## -1.985695e-02
##
## $gjr21
## mu omega alpha1 alpha2 beta1
## 1.811668e-01 1.664226e-06 1.065664e-10 3.628408e-18 9.885479e-01
## gamma1 gamma2
## -9.252576e-01 9.139672e-01
##
## $gjr22
## mu omega alpha1 alpha2 beta1 beta2
## 0.698430545 1.707849016 0.006329759 0.636465648 0.013075105 0.664617463
## gamma1 gamma2
## -0.006151383 -0.636824562
lapply(fit_gjr_models, summary)
## $gjr11
## Length Class Mode
## 1 uGARCHfit S4
##
## $gjr12
## Length Class Mode
## 1 uGARCHfit S4
##
## $gjr21
## Length Class Mode
## 1 uGARCHfit S4
##
## $gjr22
## Length Class Mode
## 1 uGARCHfit S4
# lapply(fit_gjr_models, plot)
Compare GJR-GARCH Models
model_names <- names(fit_gjr_models)
gjr_ic <- sapply(fit_gjr_models, function(fit) infocriteria(fit))
colnames(gjr_ic) <- model_names
gjr_llh <- sapply(fit_gjr_models, function(fit) likelihood(fit))
names(gjr_llh) <- model_names
print("Information Criteria (lower is better):")
## [1] "Information Criteria (lower is better):"
print(round(gjr_ic, 4))
## gjr11 gjr12 gjr21 gjr22
## [1,] 7.7157 7.4058 6.9727 6.8647
## [2,] 7.7867 7.4910 7.0722 6.9784
## [3,] 7.7149 7.4046 6.9712 6.8627
## [4,] 7.7443 7.4401 7.0128 6.9105
print("Log-Likelihoods (higher is better):")
## [1] "Log-Likelihoods (higher is better):"
print(round(gjr_llh, 4))
## gjr11 gjr12 gjr21 gjr22
## -947.8897 -908.6129 -854.1328 -839.7955
GJR-GARCH(2,2) with Different Distributions
fit_gjr_by_dist <- function(distribution) {
spec <- ugarchspec(
variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)),
mean.model = list(armaOrder = c(0, 0)),
distribution.model = distribution
)
ugarchfit(spec = spec, data = log.h, solver = "hybrid")
}
model_norm <- fit_gjr_by_dist("norm")
model_std <- fit_gjr_by_dist("std")
model_ged <- fit_gjr_by_dist("ged")
ic_table <- cbind(
norm = infocriteria(model_norm),
std = infocriteria(model_std),
ged = infocriteria(model_ged)
)
colnames(ic_table) <- c("Normal", "Student-t", "GED")
print(round(ic_table, 4))
## Normal Student-t GED
## Akaike 7.0434 5.7560 15.4882
## Bayes 7.1571 5.8839 15.6161
## Shibata 7.0414 5.7535 15.4857
## Hannan-Quinn 7.0892 5.8075 15.5397
llh <- c(
Normal = likelihood(model_norm),
Student_t = likelihood(model_std),
GED = likelihood(model_ged)
)
print(round(llh, 4))
## Normal Student_t GED
## -861.8604 -701.8682 -1903.7953
Extra: Built-in Data Extraction and Correlation/Regression
Analysis
# EXTRACT IN BUILT DATA
data2 = read.csv("financial_Data.csv"); data2
## Date Open High Low Close Adj.Close Volume
## 1 2/7/2023 150.640 155.230 150.640 154.650 154.4142 83322600
## 2 2/8/2023 153.880 154.580 151.170 151.920 151.6884 64120100
## 3 2/9/2023 153.780 154.330 150.420 150.870 150.6400 56007100
## 4 2/10/2023 149.460 151.340 149.220 151.010 151.0100 57450700
## 5 2/13/2023 150.950 154.260 150.920 153.850 153.8500 62199000
## 6 2/14/2023 152.120 153.770 150.860 153.200 153.2000 61707600
## 7 2/15/2023 153.110 155.500 152.880 155.330 155.3300 65573800
## 8 2/16/2023 153.510 156.330 153.350 153.710 153.7100 68167900
## 9 2/17/2023 152.350 153.000 150.850 152.550 152.5500 59144100
## 10 2/21/2023 150.200 151.300 148.410 148.480 148.4800 58867200
## 11 2/22/2023 148.870 149.950 147.160 148.910 148.9100 51011300
## 12 2/23/2023 150.090 150.340 147.240 149.400 149.4000 48394200
## 13 2/24/2023 147.110 147.190 145.720 146.710 146.7100 55469600
## 14 2/27/2023 147.710 149.170 147.450 147.920 147.9200 44998500
## 15 2/28/2023 147.050 149.080 146.830 147.410 147.4100 50547000
## 16 3/1/2023 146.830 147.230 145.010 145.310 145.3100 55479000
## 17 3/2/2023 144.380 146.710 143.900 145.910 145.9100 52238100
## 18 3/3/2023 148.040 151.110 147.330 151.030 151.0300 70732300
## 19 3/6/2023 153.790 156.300 153.460 153.830 153.8300 87558000
## 20 3/7/2023 153.700 154.030 151.130 151.600 151.6000 56182000
## 21 3/8/2023 152.810 153.470 151.830 152.870 152.8700 47204800
## 22 3/9/2023 153.560 154.540 150.230 150.590 150.5900 53833600
## 23 3/10/2023 150.210 150.940 147.610 148.500 148.5000 68572400
## 24 3/13/2023 147.810 153.140 147.700 150.470 150.4700 84457100
## 25 3/14/2023 151.280 153.400 150.100 152.590 152.5900 73695900
## 26 3/15/2023 151.190 153.250 149.920 152.990 152.9900 77167900
## 27 3/16/2023 152.160 156.460 151.640 155.850 155.8500 76161100
## 28 3/17/2023 156.080 156.740 154.280 155.000 155.0000 98944600
## 29 3/20/2023 155.070 157.820 154.150 157.400 157.4000 73641400
## 30 3/21/2023 157.320 159.400 156.540 159.280 159.2800 73938300
## 31 3/22/2023 159.300 162.140 157.810 157.830 157.8300 75701800
## 32 3/23/2023 158.830 161.550 157.680 158.930 158.9300 67622100
## 33 3/24/2023 158.860 160.340 157.850 160.250 160.2500 59196500
## 34 3/27/2023 159.940 160.770 157.870 158.280 158.2800 52390300
## 35 3/28/2023 157.970 158.490 155.980 157.650 157.6500 45992200
## 36 3/29/2023 159.370 161.050 159.350 160.770 160.7700 51305700
## 37 3/30/2023 161.530 162.470 161.270 162.360 162.3600 49501700
## 38 3/31/2023 162.440 165.000 161.910 164.900 164.9000 68749800
## 39 4/3/2023 164.270 166.290 164.220 166.170 166.1700 56976200
## 40 4/4/2023 166.600 166.840 165.110 165.630 165.6300 46278300
## 41 4/5/2023 164.740 165.050 161.800 163.760 163.7600 51511700
## 42 4/6/2023 162.430 164.960 162.000 164.660 164.6600 45390100
## 43 4/10/2023 161.420 162.030 160.080 162.030 162.0300 47716900
## 44 4/11/2023 162.350 162.360 160.510 160.800 160.8000 47644200
## 45 4/12/2023 161.220 162.060 159.780 160.100 160.1000 50133100
## 46 4/13/2023 161.630 165.800 161.420 165.560 165.5600 68445600
## 47 4/14/2023 164.590 166.320 163.820 165.210 165.2100 49386500
## 48 4/17/2023 165.090 165.390 164.030 165.230 165.2300 41516200
## 49 4/18/2023 166.100 167.410 165.650 166.470 166.4700 49923000
## 50 4/19/2023 165.800 168.160 165.540 167.630 167.6300 47720200
## 51 4/20/2023 166.090 167.870 165.560 166.650 166.6500 52456400
## 52 4/21/2023 165.050 166.450 164.490 165.020 165.0200 58337300
## 53 4/24/2023 165.000 165.600 163.890 165.330 165.3300 41949600
## 54 4/25/2023 165.190 166.310 163.730 163.770 163.7700 48714100
## 55 4/26/2023 163.060 165.280 162.800 163.760 163.7600 45498800
## 56 4/27/2023 165.190 168.560 165.190 168.410 168.4100 64902300
## 57 4/28/2023 168.490 169.850 167.880 169.680 169.6800 55209200
## 58 5/1/2023 169.280 170.450 168.640 169.590 169.5900 52472900
## 59 5/2/2023 170.090 170.350 167.540 168.540 168.5400 48425700
## 60 5/3/2023 169.500 170.920 167.160 167.450 167.4500 65136000
## 61 5/4/2023 164.890 167.040 164.310 165.790 165.7900 81235400
## 62 5/5/2023 170.980 174.300 170.760 173.570 173.5700 113316400
## 63 2/7/2023 260.530 268.770 260.080 267.560 266.8915 50841400
## 64 2/8/2023 273.200 276.760 266.210 266.730 266.0636 54686000
## 65 2/9/2023 273.800 273.980 262.800 263.620 262.9614 42375100
## 66 2/10/2023 261.530 264.090 260.660 263.100 262.4427 25818500
## 67 2/13/2023 267.640 274.600 267.150 271.320 270.6421 44630900
## 68 2/14/2023 272.670 274.970 269.280 272.170 271.4900 37047900
## 69 2/15/2023 268.320 270.730 266.180 269.320 269.3200 28922400
## 70 2/16/2023 264.020 266.740 261.900 262.150 262.1500 29603600
## 71 2/17/2023 259.390 260.090 256.000 258.060 258.0600 30000100
## 72 2/21/2023 254.480 255.490 251.590 252.670 252.6700 28397400
## 73 2/22/2023 254.090 254.340 250.340 251.510 251.5100 22491100
## 74 2/23/2023 255.560 256.840 250.480 254.770 254.7700 29219100
## 75 2/24/2023 249.960 251.000 248.100 249.220 249.2200 24990900
## 76 2/27/2023 252.460 252.820 249.390 250.160 250.1600 21190000
## 77 2/28/2023 249.070 251.490 248.730 249.420 249.4200 22491000
## 78 3/1/2023 250.760 250.930 245.790 246.270 246.2700 27565300
## 79 3/2/2023 246.550 251.400 245.610 251.110 251.1100 24808200
## 80 3/3/2023 252.190 255.620 251.390 255.290 255.2900 30760100
## 81 3/6/2023 256.430 260.120 255.980 256.870 256.8700 24109800
## 82 3/7/2023 256.300 257.690 253.390 254.150 254.1500 21473200
## 83 3/8/2023 254.040 254.540 250.810 253.700 253.7000 17340200
## 84 3/9/2023 255.820 259.560 251.580 252.320 252.3200 26653400
## 85 3/10/2023 251.080 252.790 247.600 248.590 248.5900 28333900
## 86 3/13/2023 247.400 257.910 245.730 253.920 253.9200 33339700
## 87 3/14/2023 256.750 261.070 255.860 260.790 260.7900 33620300
## 88 3/15/2023 259.980 266.480 259.210 265.440 265.4400 46028000
## 89 3/16/2023 265.210 276.560 263.280 276.200 276.2000 54768800
## 90 3/17/2023 278.260 283.330 276.320 279.430 279.4300 69527400
## 91 3/20/2023 276.980 277.480 269.850 272.230 272.2300 43466600
## 92 3/21/2023 274.880 275.000 269.520 273.780 273.7800 34558700
## 93 3/22/2023 273.400 281.040 272.180 272.290 272.2900 34873300
## 94 3/23/2023 277.940 281.060 275.200 277.660 277.6600 36610900
## 95 3/24/2023 277.240 280.630 275.280 280.570 280.5700 28172000
## 96 3/27/2023 280.500 281.460 275.520 276.380 276.3800 26840200
## 97 3/28/2023 275.790 276.140 272.050 275.230 275.2300 21878600
## 98 3/29/2023 278.960 281.140 278.410 280.510 280.5100 25087000
## 99 3/30/2023 284.230 284.460 281.480 284.050 284.0500 25053400
## 100 3/31/2023 283.730 289.270 283.000 288.300 288.3000 32766000
## 101 4/3/2023 286.520 288.270 283.950 287.230 287.2300 24883300
## 102 4/4/2023 287.230 290.450 285.670 287.180 287.1800 25824300
## 103 4/5/2023 285.850 287.150 282.920 284.340 284.3400 22064800
## 104 4/6/2023 283.210 292.080 282.030 291.600 291.6000 29770300
## 105 4/10/2023 289.210 289.600 284.710 289.390 289.3900 23103000
## 106 4/11/2023 285.750 285.980 281.640 282.830 282.8300 27276600
## 107 4/12/2023 284.790 287.010 281.960 283.490 283.4900 27403400
## 108 4/13/2023 283.590 289.900 283.170 289.840 289.8400 24222700
## 109 4/14/2023 287.000 288.480 283.690 286.140 286.1400 20987900
## 110 4/17/2023 289.930 291.600 286.160 288.800 288.8000 23836200
## 111 4/18/2023 291.570 291.760 287.010 288.370 288.3700 20161800
## 112 4/19/2023 285.990 289.050 284.540 288.450 288.4500 17150300
## 113 4/20/2023 285.250 289.030 285.080 286.110 286.1100 23244400
## 114 4/21/2023 285.010 286.270 283.060 285.760 285.7600 21676400
## 115 4/24/2023 282.090 284.950 278.720 281.770 281.7700 26611000
## 116 4/25/2023 279.510 281.600 275.370 275.420 275.4200 45772200
## 117 4/26/2023 296.700 299.570 292.730 295.370 295.3700 64599200
## 118 4/27/2023 295.970 305.200 295.250 304.830 304.8300 46462600
## 119 4/28/2023 304.010 308.930 303.310 307.260 307.2600 36446700
## 120 5/1/2023 306.970 308.600 305.150 305.560 305.5600 21294100
## 121 5/2/2023 307.760 309.180 303.910 305.410 305.4100 26404400
## 122 5/3/2023 306.620 308.610 304.090 304.400 304.4000 22360800
## 123 5/4/2023 306.240 307.760 303.400 305.410 305.4100 22519900
## 124 5/5/2023 305.720 311.970 304.270 310.650 310.6500 28181200
## 125 2/7/2023 358.510 364.180 354.180 362.950 362.9500 6289400
## 126 2/8/2023 360.020 368.190 358.310 366.830 366.8300 6253200
## 127 2/9/2023 372.410 373.830 361.740 362.500 362.5000 6901100
## 128 2/10/2023 359.160 362.140 347.140 347.360 347.3600 7291100
## 129 2/13/2023 349.500 359.700 344.250 358.570 358.5700 7134400
## 130 2/14/2023 357.550 363.750 353.400 359.960 359.9600 4624800
## 131 2/15/2023 356.630 362.880 354.240 361.420 361.4200 3966000
## 132 2/16/2023 355.000 361.500 350.310 350.710 350.7100 5215700
## 133 2/17/2023 347.910 349.000 342.440 347.960 347.9600 5294700
## 134 2/21/2023 342.850 344.130 336.420 337.500 337.5000 5710300
## 135 2/22/2023 337.500 341.910 332.820 334.880 334.8800 4546200
## 136 2/23/2023 331.230 331.280 314.300 323.650 323.6500 13238700
## 137 2/24/2023 319.300 321.500 314.520 317.150 317.1500 6830700
## 138 2/27/2023 323.870 330.000 322.120 323.030 323.0300 6142600
## 139 2/28/2023 323.700 327.620 321.170 322.130 322.1300 3676100
## 140 3/1/2023 321.550 326.600 312.360 313.480 313.4800 4911300
## 141 3/2/2023 310.960 315.570 310.380 311.880 311.8800 4911000
## 142 3/3/2023 315.450 317.490 310.820 315.180 315.1800 5953300
## 143 3/6/2023 317.000 323.300 311.840 312.030 312.0300 5660700
## 144 3/7/2023 312.680 314.300 306.620 308.470 308.4700 4553100
## 145 3/8/2023 309.290 311.830 305.750 311.790 311.7900 3479500
## 146 3/9/2023 312.080 312.510 294.880 297.780 297.7800 7443400
## 147 3/10/2023 297.900 298.790 289.000 292.760 292.7600 5759300
## 148 3/13/2023 287.340 299.240 285.330 293.510 293.5100 6292400
## 149 3/14/2023 295.970 297.450 290.310 294.940 294.9400 5956700
## 150 3/15/2023 292.510 306.310 292.280 303.790 303.7900 9215300
## 151 3/16/2023 304.750 316.600 301.710 310.060 310.0600 7903700
## 152 3/17/2023 310.060 310.760 300.000 303.500 303.5000 6918800
## 153 3/20/2023 299.790 307.500 296.000 305.130 305.1300 5113400
## 154 3/21/2023 306.320 307.920 300.430 305.790 305.7900 4886300
## 155 3/22/2023 306.310 306.450 293.540 293.900 293.9000 5808000
## 156 3/23/2023 304.680 322.780 304.140 320.370 320.3700 15653300
## 157 3/24/2023 320.630 331.830 320.630 328.390 328.3900 12991700
## 158 3/27/2023 327.550 336.440 324.410 327.660 327.6600 8625800
## 159 3/28/2023 326.060 333.320 321.280 323.520 323.5200 6489400
## 160 3/29/2023 326.290 332.850 325.730 332.030 332.0300 6287300
## 161 3/30/2023 340.270 343.290 335.300 338.430 338.4300 7131500
## 162 3/31/2023 340.050 345.840 337.200 345.480 345.4800 5610200
## 163 4/3/2023 341.830 348.580 340.400 348.280 348.2800 4413700
## 164 4/4/2023 348.490 349.800 343.950 346.750 346.7500 3298100
## 165 4/5/2023 345.300 345.430 336.250 342.350 342.3500 4205500
## 166 4/6/2023 339.340 340.480 332.630 339.330 339.3300 4660500
## 167 4/10/2023 335.270 339.880 333.360 338.990 338.9900 2657900
## 168 4/11/2023 343.450 347.140 337.640 338.210 338.2100 4044800
## 169 4/12/2023 340.810 342.800 330.040 331.030 331.0300 3965400
## 170 4/13/2023 339.990 346.430 338.750 346.190 346.1900 7406400
## 171 4/14/2023 342.940 344.850 336.410 338.630 338.6300 5350500
## 172 4/17/2023 338.000 338.390 327.500 332.720 332.7200 6136000
## 173 4/18/2023 335.000 337.190 330.500 333.700 333.7000 17944500
## 174 4/19/2023 324.210 325.750 316.100 323.120 323.1200 22128300
## 175 4/20/2023 320.390 331.430 318.330 325.350 325.3500 9947800
## 176 4/21/2023 323.000 328.290 319.500 327.980 327.9800 6348000
## 177 4/24/2023 330.200 334.660 326.750 329.020 329.0200 5586600
## 178 4/25/2023 328.500 328.660 321.100 322.550 322.5500 5426600
## 179 4/26/2023 321.360 325.900 320.470 321.150 321.1500 4623200
## 180 4/27/2023 324.300 327.450 317.440 325.850 325.8500 5618800
## 181 4/28/2023 325.240 330.810 324.000 329.930 329.9300 4221900
## 182 5/1/2023 329.440 331.230 318.090 324.120 324.1200 5341500
## 183 5/2/2023 325.000 326.070 315.620 317.550 317.5500 4318600
## 184 5/3/2023 317.550 324.620 315.850 319.300 319.3000 5064100
## 185 5/4/2023 319.010 323.610 317.950 320.780 320.7800 3879700
## 186 5/5/2023 323.610 324.150 319.440 322.760 322.7600 3988600
## 187 2/7/2023 103.630 108.670 103.548 108.040 108.0400 33738800
## 188 2/8/2023 102.690 103.580 98.455 100.000 100.0000 73546000
## 189 2/9/2023 100.540 100.610 93.860 95.460 95.4600 97798600
## 190 2/10/2023 95.740 97.020 94.530 94.860 94.8600 49325300
## 191 2/13/2023 95.010 95.350 94.050 95.000 95.0000 43116600
## 192 2/14/2023 94.660 95.175 92.650 94.950 94.9500 42513100
## 193 2/15/2023 94.740 97.340 94.360 97.100 97.1000 36964500
## 194 2/16/2023 95.540 97.880 94.970 95.780 95.7800 35642100
## 195 2/17/2023 95.070 95.750 93.450 94.590 94.5900 31095100
## 196 2/21/2023 93.240 93.415 92.000 92.050 92.0500 28367200
## 197 2/22/2023 91.934 92.360 90.870 91.800 91.8000 29891100
## 198 2/23/2023 92.130 92.130 90.010 91.070 91.0700 32423700
## 199 2/24/2023 89.630 90.130 88.860 89.350 89.3500 31295600
## 200 2/27/2023 90.090 90.450 89.610 90.100 90.1000 22724300
## 201 2/28/2023 89.540 91.450 89.520 90.300 90.3000 30546900
## 202 3/1/2023 90.160 91.200 89.850 90.510 90.5100 26323900
## 203 3/2/2023 89.860 92.480 89.770 92.310 92.3100 23328600
## 204 3/3/2023 92.740 94.110 92.660 94.020 94.0200 30242500
## 205 3/6/2023 94.360 96.300 94.300 95.580 95.5800 28288200
## 206 3/7/2023 95.420 96.090 93.844 94.170 94.1700 24101500
## 207 3/8/2023 94.405 96.240 94.405 94.650 94.6500 25395200
## 208 3/9/2023 94.490 95.920 92.355 92.660 92.6600 24438900
## 209 3/10/2023 92.500 93.180 90.800 91.010 91.0100 32850100
## 210 3/13/2023 90.565 93.080 89.940 91.660 91.6600 31508600
## 211 3/14/2023 93.070 94.830 92.780 94.250 94.2500 32303900
## 212 3/15/2023 93.540 97.250 93.040 96.550 96.5500 38367300
## 213 3/16/2023 96.570 101.970 95.870 101.070 101.0700 54499500
## 214 3/17/2023 100.840 103.490 100.750 102.460 102.4600 76140300
## 215 3/20/2023 101.060 102.580 100.790 101.930 101.9300 26033900
## 216 3/21/2023 101.980 105.960 101.860 105.840 105.8400 33122800
## 217 3/22/2023 105.140 107.510 104.210 104.220 104.2200 32336900
## 218 3/23/2023 105.890 107.101 105.410 106.260 106.2600 31385800
## 219 3/24/2023 105.740 106.160 104.740 106.060 106.0600 25245000
## 220 3/27/2023 105.320 105.400 102.630 103.060 103.0600 25393400
## 221 3/28/2023 103.000 103.000 100.280 101.360 101.3600 24913500
## 222 3/29/2023 102.720 102.820 101.030 101.900 101.9000 26148300
## 223 3/30/2023 101.440 101.610 100.290 101.320 101.3200 25009800
## 224 3/31/2023 101.710 104.190 101.440 104.000 104.0000 28086500
## 225 4/3/2023 102.670 104.950 102.380 104.910 104.9100 20719900
## 226 4/4/2023 104.840 106.100 104.600 105.120 105.1200 20377200
## 227 4/5/2023 106.120 106.540 104.102 104.950 104.9500 21864200
## 228 4/6/2023 105.770 109.630 104.815 108.900 108.9000 34684200
## 229 4/10/2023 107.390 107.970 105.600 106.950 106.9500 19741500
## 230 4/11/2023 106.920 107.220 105.280 106.120 106.1200 18721300
## 231 4/12/2023 107.390 107.587 104.970 105.220 105.2200 22761600
## 232 4/13/2023 106.470 108.265 106.440 108.190 108.1900 21650700
## 233 4/14/2023 107.690 109.580 107.590 109.460 109.4600 20745400
## 234 4/17/2023 105.430 106.710 105.320 106.420 106.4200 29043400
## 235 4/18/2023 107.000 107.050 104.780 105.120 105.1200 17641400
## 236 4/19/2023 104.215 105.725 103.800 105.020 105.0200 16732000
## 237 4/20/2023 104.650 106.888 104.640 105.900 105.9000 22515300
## 238 4/21/2023 106.090 106.640 105.485 105.910 105.9100 22369800
## 239 4/24/2023 106.050 107.320 105.360 106.780 106.7800 21410900
## 240 4/25/2023 106.610 107.440 104.560 104.610 104.6100 31408100
## 241 4/26/2023 105.560 107.020 103.270 104.450 104.4500 37068200
## 242 4/27/2023 105.230 109.150 104.420 108.370 108.3700 38235200
## 243 4/28/2023 107.800 108.290 106.040 108.220 108.2200 23957900
## 244 5/1/2023 107.720 108.680 107.500 107.710 107.7100 20926300
## 245 5/2/2023 107.660 107.730 104.500 105.980 105.9800 20343100
## 246 5/3/2023 106.220 108.130 105.620 106.120 106.1200 17116300
## 247 5/4/2023 106.160 106.300 104.700 105.210 105.2100 19780600
## 248 5/5/2023 105.320 106.440 104.739 106.215 106.2150 20705300
data3 = data2$Adj.Close; data3
## [1] 154.4142 151.6884 150.6400 151.0100 153.8500 153.2000 155.3300 153.7100
## [9] 152.5500 148.4800 148.9100 149.4000 146.7100 147.9200 147.4100 145.3100
## [17] 145.9100 151.0300 153.8300 151.6000 152.8700 150.5900 148.5000 150.4700
## [25] 152.5900 152.9900 155.8500 155.0000 157.4000 159.2800 157.8300 158.9300
## [33] 160.2500 158.2800 157.6500 160.7700 162.3600 164.9000 166.1700 165.6300
## [41] 163.7600 164.6600 162.0300 160.8000 160.1000 165.5600 165.2100 165.2300
## [49] 166.4700 167.6300 166.6500 165.0200 165.3300 163.7700 163.7600 168.4100
## [57] 169.6800 169.5900 168.5400 167.4500 165.7900 173.5700 266.8915 266.0636
## [65] 262.9614 262.4427 270.6421 271.4900 269.3200 262.1500 258.0600 252.6700
## [73] 251.5100 254.7700 249.2200 250.1600 249.4200 246.2700 251.1100 255.2900
## [81] 256.8700 254.1500 253.7000 252.3200 248.5900 253.9200 260.7900 265.4400
## [89] 276.2000 279.4300 272.2300 273.7800 272.2900 277.6600 280.5700 276.3800
## [97] 275.2300 280.5100 284.0500 288.3000 287.2300 287.1800 284.3400 291.6000
## [105] 289.3900 282.8300 283.4900 289.8400 286.1400 288.8000 288.3700 288.4500
## [113] 286.1100 285.7600 281.7700 275.4200 295.3700 304.8300 307.2600 305.5600
## [121] 305.4100 304.4000 305.4100 310.6500 362.9500 366.8300 362.5000 347.3600
## [129] 358.5700 359.9600 361.4200 350.7100 347.9600 337.5000 334.8800 323.6500
## [137] 317.1500 323.0300 322.1300 313.4800 311.8800 315.1800 312.0300 308.4700
## [145] 311.7900 297.7800 292.7600 293.5100 294.9400 303.7900 310.0600 303.5000
## [153] 305.1300 305.7900 293.9000 320.3700 328.3900 327.6600 323.5200 332.0300
## [161] 338.4300 345.4800 348.2800 346.7500 342.3500 339.3300 338.9900 338.2100
## [169] 331.0300 346.1900 338.6300 332.7200 333.7000 323.1200 325.3500 327.9800
## [177] 329.0200 322.5500 321.1500 325.8500 329.9300 324.1200 317.5500 319.3000
## [185] 320.7800 322.7600 108.0400 100.0000 95.4600 94.8600 95.0000 94.9500
## [193] 97.1000 95.7800 94.5900 92.0500 91.8000 91.0700 89.3500 90.1000
## [201] 90.3000 90.5100 92.3100 94.0200 95.5800 94.1700 94.6500 92.6600
## [209] 91.0100 91.6600 94.2500 96.5500 101.0700 102.4600 101.9300 105.8400
## [217] 104.2200 106.2600 106.0600 103.0600 101.3600 101.9000 101.3200 104.0000
## [225] 104.9100 105.1200 104.9500 108.9000 106.9500 106.1200 105.2200 108.1900
## [233] 109.4600 106.4200 105.1200 105.0200 105.9000 105.9100 106.7800 104.6100
## [241] 104.4500 108.3700 108.2200 107.7100 105.9800 106.1200 105.2100 106.2150
# VISUALIZATION
hist(data3)
barplot(data3)
hist(data3, col='blue')
library(survival)
# import of data and variables
data2 = read.csv("financial_Data.csv"); data2
## Date Open High Low Close Adj.Close Volume
## 1 2/7/2023 150.640 155.230 150.640 154.650 154.4142 83322600
## 2 2/8/2023 153.880 154.580 151.170 151.920 151.6884 64120100
## 3 2/9/2023 153.780 154.330 150.420 150.870 150.6400 56007100
## 4 2/10/2023 149.460 151.340 149.220 151.010 151.0100 57450700
## 5 2/13/2023 150.950 154.260 150.920 153.850 153.8500 62199000
## 6 2/14/2023 152.120 153.770 150.860 153.200 153.2000 61707600
## 7 2/15/2023 153.110 155.500 152.880 155.330 155.3300 65573800
## 8 2/16/2023 153.510 156.330 153.350 153.710 153.7100 68167900
## 9 2/17/2023 152.350 153.000 150.850 152.550 152.5500 59144100
## 10 2/21/2023 150.200 151.300 148.410 148.480 148.4800 58867200
## 11 2/22/2023 148.870 149.950 147.160 148.910 148.9100 51011300
## 12 2/23/2023 150.090 150.340 147.240 149.400 149.4000 48394200
## 13 2/24/2023 147.110 147.190 145.720 146.710 146.7100 55469600
## 14 2/27/2023 147.710 149.170 147.450 147.920 147.9200 44998500
## 15 2/28/2023 147.050 149.080 146.830 147.410 147.4100 50547000
## 16 3/1/2023 146.830 147.230 145.010 145.310 145.3100 55479000
## 17 3/2/2023 144.380 146.710 143.900 145.910 145.9100 52238100
## 18 3/3/2023 148.040 151.110 147.330 151.030 151.0300 70732300
## 19 3/6/2023 153.790 156.300 153.460 153.830 153.8300 87558000
## 20 3/7/2023 153.700 154.030 151.130 151.600 151.6000 56182000
## 21 3/8/2023 152.810 153.470 151.830 152.870 152.8700 47204800
## 22 3/9/2023 153.560 154.540 150.230 150.590 150.5900 53833600
## 23 3/10/2023 150.210 150.940 147.610 148.500 148.5000 68572400
## 24 3/13/2023 147.810 153.140 147.700 150.470 150.4700 84457100
## 25 3/14/2023 151.280 153.400 150.100 152.590 152.5900 73695900
## 26 3/15/2023 151.190 153.250 149.920 152.990 152.9900 77167900
## 27 3/16/2023 152.160 156.460 151.640 155.850 155.8500 76161100
## 28 3/17/2023 156.080 156.740 154.280 155.000 155.0000 98944600
## 29 3/20/2023 155.070 157.820 154.150 157.400 157.4000 73641400
## 30 3/21/2023 157.320 159.400 156.540 159.280 159.2800 73938300
## 31 3/22/2023 159.300 162.140 157.810 157.830 157.8300 75701800
## 32 3/23/2023 158.830 161.550 157.680 158.930 158.9300 67622100
## 33 3/24/2023 158.860 160.340 157.850 160.250 160.2500 59196500
## 34 3/27/2023 159.940 160.770 157.870 158.280 158.2800 52390300
## 35 3/28/2023 157.970 158.490 155.980 157.650 157.6500 45992200
## 36 3/29/2023 159.370 161.050 159.350 160.770 160.7700 51305700
## 37 3/30/2023 161.530 162.470 161.270 162.360 162.3600 49501700
## 38 3/31/2023 162.440 165.000 161.910 164.900 164.9000 68749800
## 39 4/3/2023 164.270 166.290 164.220 166.170 166.1700 56976200
## 40 4/4/2023 166.600 166.840 165.110 165.630 165.6300 46278300
## 41 4/5/2023 164.740 165.050 161.800 163.760 163.7600 51511700
## 42 4/6/2023 162.430 164.960 162.000 164.660 164.6600 45390100
## 43 4/10/2023 161.420 162.030 160.080 162.030 162.0300 47716900
## 44 4/11/2023 162.350 162.360 160.510 160.800 160.8000 47644200
## 45 4/12/2023 161.220 162.060 159.780 160.100 160.1000 50133100
## 46 4/13/2023 161.630 165.800 161.420 165.560 165.5600 68445600
## 47 4/14/2023 164.590 166.320 163.820 165.210 165.2100 49386500
## 48 4/17/2023 165.090 165.390 164.030 165.230 165.2300 41516200
## 49 4/18/2023 166.100 167.410 165.650 166.470 166.4700 49923000
## 50 4/19/2023 165.800 168.160 165.540 167.630 167.6300 47720200
## 51 4/20/2023 166.090 167.870 165.560 166.650 166.6500 52456400
## 52 4/21/2023 165.050 166.450 164.490 165.020 165.0200 58337300
## 53 4/24/2023 165.000 165.600 163.890 165.330 165.3300 41949600
## 54 4/25/2023 165.190 166.310 163.730 163.770 163.7700 48714100
## 55 4/26/2023 163.060 165.280 162.800 163.760 163.7600 45498800
## 56 4/27/2023 165.190 168.560 165.190 168.410 168.4100 64902300
## 57 4/28/2023 168.490 169.850 167.880 169.680 169.6800 55209200
## 58 5/1/2023 169.280 170.450 168.640 169.590 169.5900 52472900
## 59 5/2/2023 170.090 170.350 167.540 168.540 168.5400 48425700
## 60 5/3/2023 169.500 170.920 167.160 167.450 167.4500 65136000
## 61 5/4/2023 164.890 167.040 164.310 165.790 165.7900 81235400
## 62 5/5/2023 170.980 174.300 170.760 173.570 173.5700 113316400
## 63 2/7/2023 260.530 268.770 260.080 267.560 266.8915 50841400
## 64 2/8/2023 273.200 276.760 266.210 266.730 266.0636 54686000
## 65 2/9/2023 273.800 273.980 262.800 263.620 262.9614 42375100
## 66 2/10/2023 261.530 264.090 260.660 263.100 262.4427 25818500
## 67 2/13/2023 267.640 274.600 267.150 271.320 270.6421 44630900
## 68 2/14/2023 272.670 274.970 269.280 272.170 271.4900 37047900
## 69 2/15/2023 268.320 270.730 266.180 269.320 269.3200 28922400
## 70 2/16/2023 264.020 266.740 261.900 262.150 262.1500 29603600
## 71 2/17/2023 259.390 260.090 256.000 258.060 258.0600 30000100
## 72 2/21/2023 254.480 255.490 251.590 252.670 252.6700 28397400
## 73 2/22/2023 254.090 254.340 250.340 251.510 251.5100 22491100
## 74 2/23/2023 255.560 256.840 250.480 254.770 254.7700 29219100
## 75 2/24/2023 249.960 251.000 248.100 249.220 249.2200 24990900
## 76 2/27/2023 252.460 252.820 249.390 250.160 250.1600 21190000
## 77 2/28/2023 249.070 251.490 248.730 249.420 249.4200 22491000
## 78 3/1/2023 250.760 250.930 245.790 246.270 246.2700 27565300
## 79 3/2/2023 246.550 251.400 245.610 251.110 251.1100 24808200
## 80 3/3/2023 252.190 255.620 251.390 255.290 255.2900 30760100
## 81 3/6/2023 256.430 260.120 255.980 256.870 256.8700 24109800
## 82 3/7/2023 256.300 257.690 253.390 254.150 254.1500 21473200
## 83 3/8/2023 254.040 254.540 250.810 253.700 253.7000 17340200
## 84 3/9/2023 255.820 259.560 251.580 252.320 252.3200 26653400
## 85 3/10/2023 251.080 252.790 247.600 248.590 248.5900 28333900
## 86 3/13/2023 247.400 257.910 245.730 253.920 253.9200 33339700
## 87 3/14/2023 256.750 261.070 255.860 260.790 260.7900 33620300
## 88 3/15/2023 259.980 266.480 259.210 265.440 265.4400 46028000
## 89 3/16/2023 265.210 276.560 263.280 276.200 276.2000 54768800
## 90 3/17/2023 278.260 283.330 276.320 279.430 279.4300 69527400
## 91 3/20/2023 276.980 277.480 269.850 272.230 272.2300 43466600
## 92 3/21/2023 274.880 275.000 269.520 273.780 273.7800 34558700
## 93 3/22/2023 273.400 281.040 272.180 272.290 272.2900 34873300
## 94 3/23/2023 277.940 281.060 275.200 277.660 277.6600 36610900
## 95 3/24/2023 277.240 280.630 275.280 280.570 280.5700 28172000
## 96 3/27/2023 280.500 281.460 275.520 276.380 276.3800 26840200
## 97 3/28/2023 275.790 276.140 272.050 275.230 275.2300 21878600
## 98 3/29/2023 278.960 281.140 278.410 280.510 280.5100 25087000
## 99 3/30/2023 284.230 284.460 281.480 284.050 284.0500 25053400
## 100 3/31/2023 283.730 289.270 283.000 288.300 288.3000 32766000
## 101 4/3/2023 286.520 288.270 283.950 287.230 287.2300 24883300
## 102 4/4/2023 287.230 290.450 285.670 287.180 287.1800 25824300
## 103 4/5/2023 285.850 287.150 282.920 284.340 284.3400 22064800
## 104 4/6/2023 283.210 292.080 282.030 291.600 291.6000 29770300
## 105 4/10/2023 289.210 289.600 284.710 289.390 289.3900 23103000
## 106 4/11/2023 285.750 285.980 281.640 282.830 282.8300 27276600
## 107 4/12/2023 284.790 287.010 281.960 283.490 283.4900 27403400
## 108 4/13/2023 283.590 289.900 283.170 289.840 289.8400 24222700
## 109 4/14/2023 287.000 288.480 283.690 286.140 286.1400 20987900
## 110 4/17/2023 289.930 291.600 286.160 288.800 288.8000 23836200
## 111 4/18/2023 291.570 291.760 287.010 288.370 288.3700 20161800
## 112 4/19/2023 285.990 289.050 284.540 288.450 288.4500 17150300
## 113 4/20/2023 285.250 289.030 285.080 286.110 286.1100 23244400
## 114 4/21/2023 285.010 286.270 283.060 285.760 285.7600 21676400
## 115 4/24/2023 282.090 284.950 278.720 281.770 281.7700 26611000
## 116 4/25/2023 279.510 281.600 275.370 275.420 275.4200 45772200
## 117 4/26/2023 296.700 299.570 292.730 295.370 295.3700 64599200
## 118 4/27/2023 295.970 305.200 295.250 304.830 304.8300 46462600
## 119 4/28/2023 304.010 308.930 303.310 307.260 307.2600 36446700
## 120 5/1/2023 306.970 308.600 305.150 305.560 305.5600 21294100
## 121 5/2/2023 307.760 309.180 303.910 305.410 305.4100 26404400
## 122 5/3/2023 306.620 308.610 304.090 304.400 304.4000 22360800
## 123 5/4/2023 306.240 307.760 303.400 305.410 305.4100 22519900
## 124 5/5/2023 305.720 311.970 304.270 310.650 310.6500 28181200
## 125 2/7/2023 358.510 364.180 354.180 362.950 362.9500 6289400
## 126 2/8/2023 360.020 368.190 358.310 366.830 366.8300 6253200
## 127 2/9/2023 372.410 373.830 361.740 362.500 362.5000 6901100
## 128 2/10/2023 359.160 362.140 347.140 347.360 347.3600 7291100
## 129 2/13/2023 349.500 359.700 344.250 358.570 358.5700 7134400
## 130 2/14/2023 357.550 363.750 353.400 359.960 359.9600 4624800
## 131 2/15/2023 356.630 362.880 354.240 361.420 361.4200 3966000
## 132 2/16/2023 355.000 361.500 350.310 350.710 350.7100 5215700
## 133 2/17/2023 347.910 349.000 342.440 347.960 347.9600 5294700
## 134 2/21/2023 342.850 344.130 336.420 337.500 337.5000 5710300
## 135 2/22/2023 337.500 341.910 332.820 334.880 334.8800 4546200
## 136 2/23/2023 331.230 331.280 314.300 323.650 323.6500 13238700
## 137 2/24/2023 319.300 321.500 314.520 317.150 317.1500 6830700
## 138 2/27/2023 323.870 330.000 322.120 323.030 323.0300 6142600
## 139 2/28/2023 323.700 327.620 321.170 322.130 322.1300 3676100
## 140 3/1/2023 321.550 326.600 312.360 313.480 313.4800 4911300
## 141 3/2/2023 310.960 315.570 310.380 311.880 311.8800 4911000
## 142 3/3/2023 315.450 317.490 310.820 315.180 315.1800 5953300
## 143 3/6/2023 317.000 323.300 311.840 312.030 312.0300 5660700
## 144 3/7/2023 312.680 314.300 306.620 308.470 308.4700 4553100
## 145 3/8/2023 309.290 311.830 305.750 311.790 311.7900 3479500
## 146 3/9/2023 312.080 312.510 294.880 297.780 297.7800 7443400
## 147 3/10/2023 297.900 298.790 289.000 292.760 292.7600 5759300
## 148 3/13/2023 287.340 299.240 285.330 293.510 293.5100 6292400
## 149 3/14/2023 295.970 297.450 290.310 294.940 294.9400 5956700
## 150 3/15/2023 292.510 306.310 292.280 303.790 303.7900 9215300
## 151 3/16/2023 304.750 316.600 301.710 310.060 310.0600 7903700
## 152 3/17/2023 310.060 310.760 300.000 303.500 303.5000 6918800
## 153 3/20/2023 299.790 307.500 296.000 305.130 305.1300 5113400
## 154 3/21/2023 306.320 307.920 300.430 305.790 305.7900 4886300
## 155 3/22/2023 306.310 306.450 293.540 293.900 293.9000 5808000
## 156 3/23/2023 304.680 322.780 304.140 320.370 320.3700 15653300
## 157 3/24/2023 320.630 331.830 320.630 328.390 328.3900 12991700
## 158 3/27/2023 327.550 336.440 324.410 327.660 327.6600 8625800
## 159 3/28/2023 326.060 333.320 321.280 323.520 323.5200 6489400
## 160 3/29/2023 326.290 332.850 325.730 332.030 332.0300 6287300
## 161 3/30/2023 340.270 343.290 335.300 338.430 338.4300 7131500
## 162 3/31/2023 340.050 345.840 337.200 345.480 345.4800 5610200
## 163 4/3/2023 341.830 348.580 340.400 348.280 348.2800 4413700
## 164 4/4/2023 348.490 349.800 343.950 346.750 346.7500 3298100
## 165 4/5/2023 345.300 345.430 336.250 342.350 342.3500 4205500
## 166 4/6/2023 339.340 340.480 332.630 339.330 339.3300 4660500
## 167 4/10/2023 335.270 339.880 333.360 338.990 338.9900 2657900
## 168 4/11/2023 343.450 347.140 337.640 338.210 338.2100 4044800
## 169 4/12/2023 340.810 342.800 330.040 331.030 331.0300 3965400
## 170 4/13/2023 339.990 346.430 338.750 346.190 346.1900 7406400
## 171 4/14/2023 342.940 344.850 336.410 338.630 338.6300 5350500
## 172 4/17/2023 338.000 338.390 327.500 332.720 332.7200 6136000
## 173 4/18/2023 335.000 337.190 330.500 333.700 333.7000 17944500
## 174 4/19/2023 324.210 325.750 316.100 323.120 323.1200 22128300
## 175 4/20/2023 320.390 331.430 318.330 325.350 325.3500 9947800
## 176 4/21/2023 323.000 328.290 319.500 327.980 327.9800 6348000
## 177 4/24/2023 330.200 334.660 326.750 329.020 329.0200 5586600
## 178 4/25/2023 328.500 328.660 321.100 322.550 322.5500 5426600
## 179 4/26/2023 321.360 325.900 320.470 321.150 321.1500 4623200
## 180 4/27/2023 324.300 327.450 317.440 325.850 325.8500 5618800
## 181 4/28/2023 325.240 330.810 324.000 329.930 329.9300 4221900
## 182 5/1/2023 329.440 331.230 318.090 324.120 324.1200 5341500
## 183 5/2/2023 325.000 326.070 315.620 317.550 317.5500 4318600
## 184 5/3/2023 317.550 324.620 315.850 319.300 319.3000 5064100
## 185 5/4/2023 319.010 323.610 317.950 320.780 320.7800 3879700
## 186 5/5/2023 323.610 324.150 319.440 322.760 322.7600 3988600
## 187 2/7/2023 103.630 108.670 103.548 108.040 108.0400 33738800
## 188 2/8/2023 102.690 103.580 98.455 100.000 100.0000 73546000
## 189 2/9/2023 100.540 100.610 93.860 95.460 95.4600 97798600
## 190 2/10/2023 95.740 97.020 94.530 94.860 94.8600 49325300
## 191 2/13/2023 95.010 95.350 94.050 95.000 95.0000 43116600
## 192 2/14/2023 94.660 95.175 92.650 94.950 94.9500 42513100
## 193 2/15/2023 94.740 97.340 94.360 97.100 97.1000 36964500
## 194 2/16/2023 95.540 97.880 94.970 95.780 95.7800 35642100
## 195 2/17/2023 95.070 95.750 93.450 94.590 94.5900 31095100
## 196 2/21/2023 93.240 93.415 92.000 92.050 92.0500 28367200
## 197 2/22/2023 91.934 92.360 90.870 91.800 91.8000 29891100
## 198 2/23/2023 92.130 92.130 90.010 91.070 91.0700 32423700
## 199 2/24/2023 89.630 90.130 88.860 89.350 89.3500 31295600
## 200 2/27/2023 90.090 90.450 89.610 90.100 90.1000 22724300
## 201 2/28/2023 89.540 91.450 89.520 90.300 90.3000 30546900
## 202 3/1/2023 90.160 91.200 89.850 90.510 90.5100 26323900
## 203 3/2/2023 89.860 92.480 89.770 92.310 92.3100 23328600
## 204 3/3/2023 92.740 94.110 92.660 94.020 94.0200 30242500
## 205 3/6/2023 94.360 96.300 94.300 95.580 95.5800 28288200
## 206 3/7/2023 95.420 96.090 93.844 94.170 94.1700 24101500
## 207 3/8/2023 94.405 96.240 94.405 94.650 94.6500 25395200
## 208 3/9/2023 94.490 95.920 92.355 92.660 92.6600 24438900
## 209 3/10/2023 92.500 93.180 90.800 91.010 91.0100 32850100
## 210 3/13/2023 90.565 93.080 89.940 91.660 91.6600 31508600
## 211 3/14/2023 93.070 94.830 92.780 94.250 94.2500 32303900
## 212 3/15/2023 93.540 97.250 93.040 96.550 96.5500 38367300
## 213 3/16/2023 96.570 101.970 95.870 101.070 101.0700 54499500
## 214 3/17/2023 100.840 103.490 100.750 102.460 102.4600 76140300
## 215 3/20/2023 101.060 102.580 100.790 101.930 101.9300 26033900
## 216 3/21/2023 101.980 105.960 101.860 105.840 105.8400 33122800
## 217 3/22/2023 105.140 107.510 104.210 104.220 104.2200 32336900
## 218 3/23/2023 105.890 107.101 105.410 106.260 106.2600 31385800
## 219 3/24/2023 105.740 106.160 104.740 106.060 106.0600 25245000
## 220 3/27/2023 105.320 105.400 102.630 103.060 103.0600 25393400
## 221 3/28/2023 103.000 103.000 100.280 101.360 101.3600 24913500
## 222 3/29/2023 102.720 102.820 101.030 101.900 101.9000 26148300
## 223 3/30/2023 101.440 101.610 100.290 101.320 101.3200 25009800
## 224 3/31/2023 101.710 104.190 101.440 104.000 104.0000 28086500
## 225 4/3/2023 102.670 104.950 102.380 104.910 104.9100 20719900
## 226 4/4/2023 104.840 106.100 104.600 105.120 105.1200 20377200
## 227 4/5/2023 106.120 106.540 104.102 104.950 104.9500 21864200
## 228 4/6/2023 105.770 109.630 104.815 108.900 108.9000 34684200
## 229 4/10/2023 107.390 107.970 105.600 106.950 106.9500 19741500
## 230 4/11/2023 106.920 107.220 105.280 106.120 106.1200 18721300
## 231 4/12/2023 107.390 107.587 104.970 105.220 105.2200 22761600
## 232 4/13/2023 106.470 108.265 106.440 108.190 108.1900 21650700
## 233 4/14/2023 107.690 109.580 107.590 109.460 109.4600 20745400
## 234 4/17/2023 105.430 106.710 105.320 106.420 106.4200 29043400
## 235 4/18/2023 107.000 107.050 104.780 105.120 105.1200 17641400
## 236 4/19/2023 104.215 105.725 103.800 105.020 105.0200 16732000
## 237 4/20/2023 104.650 106.888 104.640 105.900 105.9000 22515300
## 238 4/21/2023 106.090 106.640 105.485 105.910 105.9100 22369800
## 239 4/24/2023 106.050 107.320 105.360 106.780 106.7800 21410900
## 240 4/25/2023 106.610 107.440 104.560 104.610 104.6100 31408100
## 241 4/26/2023 105.560 107.020 103.270 104.450 104.4500 37068200
## 242 4/27/2023 105.230 109.150 104.420 108.370 108.3700 38235200
## 243 4/28/2023 107.800 108.290 106.040 108.220 108.2200 23957900
## 244 5/1/2023 107.720 108.680 107.500 107.710 107.7100 20926300
## 245 5/2/2023 107.660 107.730 104.500 105.980 105.9800 20343100
## 246 5/3/2023 106.220 108.130 105.620 106.120 106.1200 17116300
## 247 5/4/2023 106.160 106.300 104.700 105.210 105.2100 19780600
## 248 5/5/2023 105.320 106.440 104.739 106.215 106.2150 20705300
d = data2$Close
h = data2$High
g = data2$Low
# creating data frame
data.frame(d, h, g)
## d h g
## 1 154.650 155.230 150.640
## 2 151.920 154.580 151.170
## 3 150.870 154.330 150.420
## 4 151.010 151.340 149.220
## 5 153.850 154.260 150.920
## 6 153.200 153.770 150.860
## 7 155.330 155.500 152.880
## 8 153.710 156.330 153.350
## 9 152.550 153.000 150.850
## 10 148.480 151.300 148.410
## 11 148.910 149.950 147.160
## 12 149.400 150.340 147.240
## 13 146.710 147.190 145.720
## 14 147.920 149.170 147.450
## 15 147.410 149.080 146.830
## 16 145.310 147.230 145.010
## 17 145.910 146.710 143.900
## 18 151.030 151.110 147.330
## 19 153.830 156.300 153.460
## 20 151.600 154.030 151.130
## 21 152.870 153.470 151.830
## 22 150.590 154.540 150.230
## 23 148.500 150.940 147.610
## 24 150.470 153.140 147.700
## 25 152.590 153.400 150.100
## 26 152.990 153.250 149.920
## 27 155.850 156.460 151.640
## 28 155.000 156.740 154.280
## 29 157.400 157.820 154.150
## 30 159.280 159.400 156.540
## 31 157.830 162.140 157.810
## 32 158.930 161.550 157.680
## 33 160.250 160.340 157.850
## 34 158.280 160.770 157.870
## 35 157.650 158.490 155.980
## 36 160.770 161.050 159.350
## 37 162.360 162.470 161.270
## 38 164.900 165.000 161.910
## 39 166.170 166.290 164.220
## 40 165.630 166.840 165.110
## 41 163.760 165.050 161.800
## 42 164.660 164.960 162.000
## 43 162.030 162.030 160.080
## 44 160.800 162.360 160.510
## 45 160.100 162.060 159.780
## 46 165.560 165.800 161.420
## 47 165.210 166.320 163.820
## 48 165.230 165.390 164.030
## 49 166.470 167.410 165.650
## 50 167.630 168.160 165.540
## 51 166.650 167.870 165.560
## 52 165.020 166.450 164.490
## 53 165.330 165.600 163.890
## 54 163.770 166.310 163.730
## 55 163.760 165.280 162.800
## 56 168.410 168.560 165.190
## 57 169.680 169.850 167.880
## 58 169.590 170.450 168.640
## 59 168.540 170.350 167.540
## 60 167.450 170.920 167.160
## 61 165.790 167.040 164.310
## 62 173.570 174.300 170.760
## 63 267.560 268.770 260.080
## 64 266.730 276.760 266.210
## 65 263.620 273.980 262.800
## 66 263.100 264.090 260.660
## 67 271.320 274.600 267.150
## 68 272.170 274.970 269.280
## 69 269.320 270.730 266.180
## 70 262.150 266.740 261.900
## 71 258.060 260.090 256.000
## 72 252.670 255.490 251.590
## 73 251.510 254.340 250.340
## 74 254.770 256.840 250.480
## 75 249.220 251.000 248.100
## 76 250.160 252.820 249.390
## 77 249.420 251.490 248.730
## 78 246.270 250.930 245.790
## 79 251.110 251.400 245.610
## 80 255.290 255.620 251.390
## 81 256.870 260.120 255.980
## 82 254.150 257.690 253.390
## 83 253.700 254.540 250.810
## 84 252.320 259.560 251.580
## 85 248.590 252.790 247.600
## 86 253.920 257.910 245.730
## 87 260.790 261.070 255.860
## 88 265.440 266.480 259.210
## 89 276.200 276.560 263.280
## 90 279.430 283.330 276.320
## 91 272.230 277.480 269.850
## 92 273.780 275.000 269.520
## 93 272.290 281.040 272.180
## 94 277.660 281.060 275.200
## 95 280.570 280.630 275.280
## 96 276.380 281.460 275.520
## 97 275.230 276.140 272.050
## 98 280.510 281.140 278.410
## 99 284.050 284.460 281.480
## 100 288.300 289.270 283.000
## 101 287.230 288.270 283.950
## 102 287.180 290.450 285.670
## 103 284.340 287.150 282.920
## 104 291.600 292.080 282.030
## 105 289.390 289.600 284.710
## 106 282.830 285.980 281.640
## 107 283.490 287.010 281.960
## 108 289.840 289.900 283.170
## 109 286.140 288.480 283.690
## 110 288.800 291.600 286.160
## 111 288.370 291.760 287.010
## 112 288.450 289.050 284.540
## 113 286.110 289.030 285.080
## 114 285.760 286.270 283.060
## 115 281.770 284.950 278.720
## 116 275.420 281.600 275.370
## 117 295.370 299.570 292.730
## 118 304.830 305.200 295.250
## 119 307.260 308.930 303.310
## 120 305.560 308.600 305.150
## 121 305.410 309.180 303.910
## 122 304.400 308.610 304.090
## 123 305.410 307.760 303.400
## 124 310.650 311.970 304.270
## 125 362.950 364.180 354.180
## 126 366.830 368.190 358.310
## 127 362.500 373.830 361.740
## 128 347.360 362.140 347.140
## 129 358.570 359.700 344.250
## 130 359.960 363.750 353.400
## 131 361.420 362.880 354.240
## 132 350.710 361.500 350.310
## 133 347.960 349.000 342.440
## 134 337.500 344.130 336.420
## 135 334.880 341.910 332.820
## 136 323.650 331.280 314.300
## 137 317.150 321.500 314.520
## 138 323.030 330.000 322.120
## 139 322.130 327.620 321.170
## 140 313.480 326.600 312.360
## 141 311.880 315.570 310.380
## 142 315.180 317.490 310.820
## 143 312.030 323.300 311.840
## 144 308.470 314.300 306.620
## 145 311.790 311.830 305.750
## 146 297.780 312.510 294.880
## 147 292.760 298.790 289.000
## 148 293.510 299.240 285.330
## 149 294.940 297.450 290.310
## 150 303.790 306.310 292.280
## 151 310.060 316.600 301.710
## 152 303.500 310.760 300.000
## 153 305.130 307.500 296.000
## 154 305.790 307.920 300.430
## 155 293.900 306.450 293.540
## 156 320.370 322.780 304.140
## 157 328.390 331.830 320.630
## 158 327.660 336.440 324.410
## 159 323.520 333.320 321.280
## 160 332.030 332.850 325.730
## 161 338.430 343.290 335.300
## 162 345.480 345.840 337.200
## 163 348.280 348.580 340.400
## 164 346.750 349.800 343.950
## 165 342.350 345.430 336.250
## 166 339.330 340.480 332.630
## 167 338.990 339.880 333.360
## 168 338.210 347.140 337.640
## 169 331.030 342.800 330.040
## 170 346.190 346.430 338.750
## 171 338.630 344.850 336.410
## 172 332.720 338.390 327.500
## 173 333.700 337.190 330.500
## 174 323.120 325.750 316.100
## 175 325.350 331.430 318.330
## 176 327.980 328.290 319.500
## 177 329.020 334.660 326.750
## 178 322.550 328.660 321.100
## 179 321.150 325.900 320.470
## 180 325.850 327.450 317.440
## 181 329.930 330.810 324.000
## 182 324.120 331.230 318.090
## 183 317.550 326.070 315.620
## 184 319.300 324.620 315.850
## 185 320.780 323.610 317.950
## 186 322.760 324.150 319.440
## 187 108.040 108.670 103.548
## 188 100.000 103.580 98.455
## 189 95.460 100.610 93.860
## 190 94.860 97.020 94.530
## 191 95.000 95.350 94.050
## 192 94.950 95.175 92.650
## 193 97.100 97.340 94.360
## 194 95.780 97.880 94.970
## 195 94.590 95.750 93.450
## 196 92.050 93.415 92.000
## 197 91.800 92.360 90.870
## 198 91.070 92.130 90.010
## 199 89.350 90.130 88.860
## 200 90.100 90.450 89.610
## 201 90.300 91.450 89.520
## 202 90.510 91.200 89.850
## 203 92.310 92.480 89.770
## 204 94.020 94.110 92.660
## 205 95.580 96.300 94.300
## 206 94.170 96.090 93.844
## 207 94.650 96.240 94.405
## 208 92.660 95.920 92.355
## 209 91.010 93.180 90.800
## 210 91.660 93.080 89.940
## 211 94.250 94.830 92.780
## 212 96.550 97.250 93.040
## 213 101.070 101.970 95.870
## 214 102.460 103.490 100.750
## 215 101.930 102.580 100.790
## 216 105.840 105.960 101.860
## 217 104.220 107.510 104.210
## 218 106.260 107.101 105.410
## 219 106.060 106.160 104.740
## 220 103.060 105.400 102.630
## 221 101.360 103.000 100.280
## 222 101.900 102.820 101.030
## 223 101.320 101.610 100.290
## 224 104.000 104.190 101.440
## 225 104.910 104.950 102.380
## 226 105.120 106.100 104.600
## 227 104.950 106.540 104.102
## 228 108.900 109.630 104.815
## 229 106.950 107.970 105.600
## 230 106.120 107.220 105.280
## 231 105.220 107.587 104.970
## 232 108.190 108.265 106.440
## 233 109.460 109.580 107.590
## 234 106.420 106.710 105.320
## 235 105.120 107.050 104.780
## 236 105.020 105.725 103.800
## 237 105.900 106.888 104.640
## 238 105.910 106.640 105.485
## 239 106.780 107.320 105.360
## 240 104.610 107.440 104.560
## 241 104.450 107.020 103.270
## 242 108.370 109.150 104.420
## 243 108.220 108.290 106.040
## 244 107.710 108.680 107.500
## 245 105.980 107.730 104.500
## 246 106.120 108.130 105.620
## 247 105.210 106.300 104.700
## 248 106.215 106.440 104.739
# correlation
cor(d, h)
## [1] 0.9996436
cor(d, g)
## [1] 0.9996625
cor(h, g)
## [1] 0.999654
# regression
lm(d ~ g + h)
##
## Call:
## lm(formula = d ~ g + h)
##
## Coefficients:
## (Intercept) g h
## 0.1723 0.5349 0.4655
# analysis of variance
aov(lm(d ~ g + h))
## Call:
## aov(formula = lm(d ~ g + h))
##
## Terms:
## g h Residuals
## Sum of Squares 2064833.6 319.3 1075.1
## Deg. of Freedom 1 1 245
##
## Residual standard error: 2.094752
## Estimated effects may be unbalanced
summary(lm(d ~ g + h))
##
## Call:
## lm(formula = d ~ g + h)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.0668 -1.0546 -0.0468 1.0636 7.2652
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.17232 0.34677 0.497 0.62
## g 0.53490 0.05621 9.517 < 2e-16 ***
## h 0.46548 0.05456 8.531 1.53e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.095 on 245 degrees of freedom
## Multiple R-squared: 0.9995, Adjusted R-squared: 0.9995
## F-statistic: 2.353e+05 on 2 and 245 DF, p-value: < 2.2e-16
# plot
hist(d)
hist(h)
hist(g)
plot(lm(d ~ g + h))
library(survminer)
## Loading required package: ggpubr
##
## Attaching package: 'survminer'
## The following object is masked from 'package:survival':
##
## myeloma
d1 = data.frame(time=c(3,4,6,11,17,21,24,25,26,30),
event=c(1,1,0,2,0,1,0,0,1,0))
kmc = with(d1, Surv(time, event)); kmc
## Warning in Surv(time, event): Invalid status value, converted to NA
## [1] 3+ 4+ 6? 11 17? 21+ 24? 25? 26+ 30?
plot(kmc)
plot(kmc, fun = "cumhaz")
kmc2 = surv_fit(Surv(time, event) ~ 1, data = d1); kmc2
## Warning in Surv(time, event): Invalid status value, converted to NA
## Call: survfit(formula = Surv(time, event) ~ 1, data = structure(list(
## time = c(3, 4, 6, 11, 17, 21, 24, 25, 26, 30), event = c(1,
## 1, 0, 2, 0, 1, 0, 0, 1, 0)), class = "data.frame", row.names = c(NA,
## -10L)))
##
## 5 observations deleted due to missingness
## n events median 0.95LCL 0.95UCL
## [1,] 5 1 NA 11 NA
summary(kmc2)
## Call: survfit(formula = Surv(time, event) ~ 1, data = structure(list(
## time = c(3, 4, 6, 11, 17, 21, 24, 25, 26, 30), event = c(1,
## 1, 0, 2, 0, 1, 0, 0, 1, 0)), class = "data.frame", row.names = c(NA,
## -10L)))
##
## 5 observations deleted due to missingness
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 11 3 1 0.667 0.272 0.3 1