library(rugarch)
## Warning: package 'rugarch' was built under R version 4.4.3
## Loading required package: parallel
##
## Attaching package: 'rugarch'
## The following object is masked from 'package:stats':
##
## sigma
library(timeSeries)
## Warning: package 'timeSeries' was built under R version 4.4.3
## Loading required package: timeDate
## Warning: package 'timeDate' was built under R version 4.4.3
##
## Attaching package: 'timeSeries'
## The following object is masked from 'package:rugarch':
##
## quantile
## The following objects are masked from 'package:graphics':
##
## lines, points
library(fGarch)
## Warning: package 'fGarch' was built under R version 4.4.3
## NOTE: Packages 'fBasics', 'timeDate', and 'timeSeries' are no longer
## attached to the search() path when 'fGarch' is attached.
##
## If needed attach them yourself in your R script by e.g.,
## require("timeSeries")
data <- read.csv("DATA25.csv")
head(data)
## Year Month STOCK GDP CPI PENSION INFLATION CLAIMS INTEREST
## 1 2025 April 3.74 4.11 6.12 13.50 5.58 4.59 4.12
## 2 2025 March 3.81 3.62 6.33 13.59 5.53 4.53 3.97
## 3 2025 February 3.98 3.45 6.47 13.49 5.70 4.53 4.07
## 4 2025 January 4.21 3.28 6.48 13.47 4.04 4.63 4.20
## 5 2024 December 4.50 2.99 6.51 13.70 4.35 4.95 4.44
## 6 2024 November 4.81 2.75 6.56 13.73 4.28 5.20 4.62
D1 <- data$STOCK
D1
## [1] 3.74 3.81 3.98 4.21 4.50 4.81 5.14 5.50 5.77 5.97 4.64 6.49 6.73 6.97 7.26
## [16] 7.50 7.67 7.87 8.10 8.32 8.52 8.68 8.77 8.78 8.71 8.59 8.30 7.95 7.66 7.38
## [31] 7.48 6.81 6.61 6.45 6.29 6.16 6.05 6.29 6.23 6.08 5.62 6.10 6.07 5.35 5.71
## [46] 5.53 5.35 5.20 4.66 5.17 5.16 5.74 5.41 5.53 5.67 5.79 5.87 6.01 6.16 6.18
## [61] 6.03 5.84 5.72 5.29 5.20 5.19 5.19 5.24 5.40 5.32 5.16 5.04 4.91 4.91 4.67
## [76] 4.65 4.68 4.69 4.59 4.53 4.53 4.63 4.95 5.20 5.61 6.24 6.89 7.40 7.79 7.98
## [91] 8.15 8.33 8.40 8.36 8.21 8.13 7.84 7.20 6.76 6.43 6.26 6.30 6.43 6.48 6.50
## [106] 6.47 6.44 6.46 6.59 6.72 6.88 6.87 6.77 6.58 6.42 6.31 6.29 6.34 6.54
plot(D1, main = "Raw Log Returns", ylab = "Log Returns", col = "blue")
ts.plot(D1, main = "Time Series of Log Returns", ylab = "Log Returns")
M1 <- garchFit(formula = ~garch(1,2), data = D1, cond.dist = "snorm")
##
## Series Initialization:
## ARMA Model: arma
## Formula Mean: ~ arma(0, 0)
## GARCH Model: garch
## Formula Variance: ~ garch(1, 2)
## ARMA Order: 0 0
## Max ARMA Order: 0
## GARCH Order: 1 2
## Max GARCH Order: 2
## Maximum Order: 2
## Conditional Dist: snorm
## h.start: 3
## llh.start: 1
## Length of Series: 119
## Recursion Init: mci
## Series Scale: 1.239203
##
## Parameter Initialization:
## Initial Parameters: $params
## Limits of Transformations: $U, $V
## Which Parameters are Fixed? $includes
## Parameter Matrix:
## U V params includes
## mu -50.45123778 50.45124 5.045124 TRUE
## omega 0.00000100 100.00000 0.100000 TRUE
## alpha1 0.00000001 1.00000 0.100000 TRUE
## gamma1 -0.99999999 1.00000 0.100000 FALSE
## beta1 0.00000001 1.00000 0.400000 TRUE
## beta2 0.00000001 1.00000 0.400000 TRUE
## delta 0.00000000 2.00000 2.000000 FALSE
## skew 0.10000000 10.00000 1.000000 TRUE
## shape 1.00000000 10.00000 4.000000 FALSE
## Index List of Parameters to be Optimized:
## mu omega alpha1 beta1 beta2 skew
## 1 2 3 5 6 8
## Persistence: 0.9
##
##
## --- START OF TRACE ---
## Selected Algorithm: nlminb
##
## R coded nlminb Solver:
##
## 0: 159.15632: 5.04512 0.100000 0.100000 0.400000 0.400000 1.00000
## 1: 154.96272: 4.98105 0.0795523 0.0970025 0.379120 0.377975 1.00139
## 2: 145.29726: 4.63034 0.0387274 0.219075 0.347994 0.336366 1.01042
## 3: 143.77976: 4.74054 0.0134761 0.226519 0.331240 0.315731 1.00675
## 4: 141.53780: 4.76701 0.0417582 0.255220 0.323517 0.303153 1.00215
## 5: 133.69533: 4.94410 0.0181346 0.429541 0.246389 0.179869 0.960476
## 6: 133.50531: 4.98232 0.0704934 0.435647 0.230336 0.153306 0.941103
## 7: 131.72265: 4.88518 0.0496979 0.440950 0.226620 0.142772 0.931741
## 8: 131.28133: 4.85010 0.0302994 0.460043 0.223834 0.133610 0.918981
## 9: 130.43826: 4.82684 0.0436768 0.473522 0.232860 0.138055 0.895305
## 10: 121.85339: 4.66564 0.0352493 0.514441 0.237341 0.0964051 0.596775
## 11: 120.54503: 4.64756 0.0382866 0.520446 0.212082 0.105740 0.540769
## 12: 119.09007: 4.49829 0.0667699 0.558318 0.225412 0.116121 0.530353
## 13: 116.64726: 4.56949 0.0395345 0.576797 0.208926 0.103286 0.487975
## 14: 115.74709: 4.49852 0.0690692 0.618864 0.212452 0.107128 0.462521
## 15: 114.93566: 4.47834 0.0440602 0.627573 0.186266 0.0946344 0.418297
## 16: 114.86322: 4.62883 0.0738977 0.651082 0.165184 0.0727406 0.402222
## 17: 112.88807: 4.53560 0.0667130 0.656119 0.168660 0.0616501 0.420254
## 18: 112.87831: 4.45035 0.0711361 0.676014 0.161911 0.0571075 0.409690
## 19: 112.26814: 4.51813 0.0761797 0.679580 0.161745 0.0566190 0.410548
## 20: 112.05904: 4.49713 0.0703083 0.686370 0.158548 0.0473171 0.415549
## 21: 111.88938: 4.53934 0.0724036 0.692093 0.160213 0.0416226 0.424344
## 22: 111.66557: 4.51111 0.0732520 0.697332 0.153546 0.0395645 0.413784
## 23: 111.50435: 4.54359 0.0796713 0.705889 0.148215 0.0363240 0.408796
## 24: 111.26317: 4.51885 0.0761330 0.711066 0.147511 0.0278785 0.417987
## 25: 111.10233: 4.55255 0.0809214 0.720895 0.143365 0.0222535 0.415400
## 26: 110.86668: 4.51781 0.0817139 0.723809 0.136015 0.0215723 0.404977
## 27: 110.64654: 4.54396 0.0866924 0.732214 0.129776 0.0144392 0.407730
## 28: 110.43833: 4.52176 0.0851346 0.737968 0.125037 0.00520194 0.415279
## 29: 110.23597: 4.54026 0.0910233 0.743198 0.118188 0.00407577 0.405481
## 30: 110.10299: 4.50936 0.0925877 0.747645 0.110045 0.00131918 0.396205
## 31: 109.87975: 4.54078 0.0994268 0.753305 0.100604 1.00000e-08 0.394370
## 32: 109.65682: 4.52027 0.0998938 0.759605 0.0879943 1.00000e-08 0.396429
## 33: 109.48203: 4.53711 0.105041 0.766279 0.0779378 1.00000e-08 0.390400
## 34: 109.30219: 4.51548 0.107267 0.770518 0.0670727 1.00000e-08 0.382633
## 35: 108.39293: 4.53836 0.117359 0.822909 1.00000e-08 1.00000e-08 0.406651
## 36: 108.04285: 4.51276 0.119590 0.848459 1.00000e-08 1.00000e-08 0.383358
## 37: 108.03885: 4.54440 0.119655 0.848841 1.00000e-08 1.00000e-08 0.381788
## 38: 107.98549: 4.53050 0.118036 0.849003 1.00000e-08 1.00000e-08 0.381290
## 39: 107.96994: 4.53400 0.115699 0.849828 1.00000e-08 1.00000e-08 0.379324
## 40: 107.96334: 4.53731 0.115749 0.852615 1.00000e-08 1.00000e-08 0.377814
## 41: 107.95833: 4.53552 0.114816 0.855676 1.00000e-08 1.00000e-08 0.378163
## 42: 107.95505: 4.54068 0.113022 0.857485 1.00000e-08 1.00000e-08 0.379880
## 43: 107.95136: 4.54351 0.112023 0.864075 1.00000e-08 1.00000e-08 0.380209
## 44: 107.95084: 4.54334 0.110830 0.865235 1.00000e-08 1.00000e-08 0.381000
## 45: 107.95059: 4.54464 0.110764 0.865188 1.00000e-08 1.00000e-08 0.380598
## 46: 107.95058: 4.54450 0.110813 0.865252 1.00000e-08 1.00000e-08 0.380731
## 47: 107.95058: 4.54447 0.110816 0.865229 1.00000e-08 1.00000e-08 0.380697
## 48: 107.95058: 4.54448 0.110813 0.865233 1.00000e-08 1.00000e-08 0.380701
##
## Final Estimate of the Negative LLH:
## LLH: 133.4723 norm LLH: 1.121616
## mu omega alpha1 beta1 beta2 skew
## 5.63153825 0.17016682 0.86523311 0.00000001 0.00000001 0.38070103
##
## R-optimhess Difference Approximated Hessian Matrix:
## mu omega alpha1 beta1 beta2 skew
## mu -244.05355 -337.8425 13.07284 -101.44793 -156.14286 -11.06279
## omega -337.84250 -1040.4837 -150.07729 -379.41079 -560.92880 -319.41019
## alpha1 13.07284 -150.0773 -212.82810 -166.33298 -141.20029 36.78071
## beta1 -101.44793 -379.4108 -166.33298 -238.90843 -251.99424 28.72531
## beta2 -156.14286 -560.9288 -141.20029 -251.99424 -323.51758 -43.53064
## skew -11.06279 -319.4102 36.78071 28.72531 -43.53064 -666.98227
## attr(,"time")
## Time difference of 0.0167501 secs
##
## --- END OF TRACE ---
## Warning in sqrt(diag(fit$cvar)): NaNs produced
##
## Time to Estimate Parameters:
## Time difference of 0.08739901 secs
summary(M1)
##
## Title:
## GARCH Modelling
##
## Call:
## garchFit(formula = ~garch(1, 2), data = D1, cond.dist = "snorm")
##
## Mean and Variance Equation:
## data ~ garch(1, 2)
## <environment: 0x000001efac6777a0>
## [data = D1]
##
## Conditional Distribution:
## snorm
##
## Coefficient(s):
## mu omega alpha1 beta1 beta2 skew
## 5.63153825 0.17016682 0.86523311 0.00000001 0.00000001 0.38070103
##
## Std. Errors:
## based on Hessian
##
## Error Analysis:
## Estimate Std. Error t value Pr(>|t|)
## mu 5.632e+00 8.563e-02 65.765 < 2e-16 ***
## omega 1.702e-01 NaN NaN NaN
## alpha1 8.652e-01 1.303e-01 6.638 3.18e-11 ***
## beta1 1.000e-08 2.234e-01 0.000 1
## beta2 1.000e-08 NaN NaN NaN
## skew 3.807e-01 2.235e-02 17.036 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Log Likelihood:
## -133.4723 normalized: -1.121616
##
## Description:
## Fri May 30 11:45:20 2025 by user: Brian Juma
##
##
## Standardised Residuals Tests:
## Statistic p-Value
## Jarque-Bera Test R Chi^2 13.3817145 1.242217e-03
## Shapiro-Wilk Test R W 0.8651981 5.225923e-09
## Ljung-Box Test R Q(10) 335.9525493 0.000000e+00
## Ljung-Box Test R Q(15) 336.3501854 0.000000e+00
## Ljung-Box Test R Q(20) 339.8315722 0.000000e+00
## Ljung-Box Test R^2 Q(10) 39.7333261 1.887816e-05
## Ljung-Box Test R^2 Q(15) 44.9315362 7.850087e-05
## Ljung-Box Test R^2 Q(20) 48.1981224 3.989977e-04
## LM Arch Test R TR^2 36.7745879 2.430013e-04
##
## Information Criterion Statistics:
## AIC BIC SIC HQIC
## 2.344073 2.484197 2.339306 2.400973
spec <- ugarchspec(
variance.model = list(model = "eGARCH", garchOrder = c(1,2)),
mean.model = list(armaOrder = c(1,2), include.mean = FALSE),
distribution.model = "std"
)
spec
##
## *---------------------------------*
## * GARCH Model Spec *
## *---------------------------------*
##
## Conditional Variance Dynamics
## ------------------------------------
## GARCH Model : eGARCH(1,2)
## Variance Targeting : FALSE
##
## Conditional Mean Dynamics
## ------------------------------------
## Mean Model : ARFIMA(1,0,2)
## Include Mean : FALSE
## GARCH-in-Mean : FALSE
##
## Conditional Distribution
## ------------------------------------
## Distribution : std
## Includes Skew : FALSE
## Includes Shape : TRUE
## Includes Lambda : FALSE
fit <- ugarchfit(spec = spec, data = D1)
## Warning in .egarchfit(spec = spec, data = data, out.sample = out.sample, :
## ugarchfit-->warning: solver failer to converge.
fit
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : eGARCH(1,2)
## Mean Model : ARFIMA(1,0,2)
## Distribution : std
##
## Convergence Problem:
## Solver Message:
Load Libraries and Data
library(survival)
data(package = "survival")
str(aml)
## 'data.frame': 23 obs. of 3 variables:
## $ time : num 9 13 13 18 23 28 31 34 45 48 ...
## $ status: num 1 1 0 1 1 0 1 1 0 1 ...
## $ x : Factor w/ 2 levels "Maintained","Nonmaintained": 1 1 1 1 1 1 1 1 1 1 ...
head(aml)
## time status x
## 1 9 1 Maintained
## 2 13 1 Maintained
## 3 13 0 Maintained
## 4 18 1 Maintained
## 5 23 1 Maintained
## 6 28 0 Maintained
surv_object <- Surv(time = aml$time, event = aml$status)
km_fit <- survfit(surv_object ~ x, data = aml)
print(km_fit)
## Call: survfit(formula = surv_object ~ x, data = aml)
##
## n events median 0.95LCL 0.95UCL
## x=Maintained 11 7 31 18 NA
## x=Nonmaintained 12 11 23 8 NA
summary(km_fit)
## Call: survfit(formula = surv_object ~ x, data = aml)
##
## x=Maintained
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 9 11 1 0.909 0.0867 0.7541 1.000
## 13 10 1 0.818 0.1163 0.6192 1.000
## 18 8 1 0.716 0.1397 0.4884 1.000
## 23 7 1 0.614 0.1526 0.3769 0.999
## 31 5 1 0.491 0.1642 0.2549 0.946
## 34 4 1 0.368 0.1627 0.1549 0.875
## 48 2 1 0.184 0.1535 0.0359 0.944
##
## x=Nonmaintained
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 5 12 2 0.8333 0.1076 0.6470 1.000
## 8 10 2 0.6667 0.1361 0.4468 0.995
## 12 8 1 0.5833 0.1423 0.3616 0.941
## 23 6 1 0.4861 0.1481 0.2675 0.883
## 27 5 1 0.3889 0.1470 0.1854 0.816
## 30 4 1 0.2917 0.1387 0.1148 0.741
## 33 3 1 0.1944 0.1219 0.0569 0.664
## 43 2 1 0.0972 0.0919 0.0153 0.620
## 45 1 1 0.0000 NaN NA NA
plot(km_fit,
xlab = "Time (Weeks)",
ylab = "Survival Probability",
col = c("blue", "red"),
lty = c(1, 2),
main = "Kaplan-Meier Survival Curves for AML Patients by Treatment",
mark.time = TRUE)
legend("topright",
legend = levels(aml$x),
col = c("blue", "red"),
lty = c(1, 2))
plot(km_fit,
xlab = "Time (Weeks)",
ylab = "Survival Probability",
col = c("blue", "red"),
lty = c(1, 2),
main = "Kaplan-Meier Survival Curves with Confidence Intervals",
mark.time = TRUE,
conf.int = TRUE)
legend("topright",
legend = levels(aml$x),
col = c("blue", "red"),
lty = c(1, 2))
surv_diff <- survdiff(surv_object ~ x, data = aml)
print(surv_diff)
## Call:
## survdiff(formula = surv_object ~ x, data = aml)
##
## N Observed Expected (O-E)^2/E (O-E)^2/V
## x=Maintained 11 7 10.69 1.27 3.4
## x=Nonmaintained 12 11 7.31 1.86 3.4
##
## Chisq= 3.4 on 1 degrees of freedom, p= 0.07
## Load Required Libraries
library(goftest)
data <- read.csv("DATA25.csv")
claims <- data$CLAIMS
D1 <- diff(claims)
D1
## [1] -0.06 0.00 0.10 0.32 0.25 0.41 0.63 0.65 0.51 0.39 0.19 0.17
## [13] 0.18 0.07 -0.04 -0.15 -0.08 -0.29 -0.64 -0.44 -0.33 -0.17 0.04 0.13
## [25] 0.05 0.02 -0.03 -0.03 0.02 0.13 0.13 0.16 -0.01 -0.10 -0.19 -0.16
## [37] -0.11 -0.02 0.05 0.20 0.09 0.02 0.04 -0.06 0.00 0.11 0.14 0.09
## [49] 0.11 0.11 0.14 -0.14 -0.14 -0.20 -0.27 -0.19 -0.18 -0.20 -0.29 -0.33
## [61] -0.34 -0.30 -0.25 -0.06 0.12 0.40 0.65 0.72 0.91 0.96 1.18 1.29
## [73] 1.37 1.25 1.04 0.94 0.70 0.43 0.10 -0.05 -0.52 -0.83 -1.08 -1.20
## [85] -1.33 -1.31 -1.18 -1.12 -1.00 -0.92 -0.76 -0.71 -0.44 -0.12 0.03 0.06
## [97] 0.10 0.28 0.29 0.34 0.40 0.42 0.47 0.71 0.85 0.76 0.60 1.00
## [109] 1.18 0.99 1.01 0.93 0.76 0.82 0.79 0.35 -0.20 -0.31
D1_positive <- D1[D1 > 0]