Data analysis
Group 2 (Conquerors)
STEPHEN WAFULA BUS-244-061/2021
GILBERT GIKWA BUS-244-020/2021
SMITH SILVENUS BUS-244-050/2021
BRUCE MENGICH BUS-244-062/2021
CLINTON KARUGU BUS-244-007/2021
2025-05-06
#survival
library(survival)
library(survminer)## Loading required package: ggplot2## Loading required package: ggpubr##
## Attaching package: 'survminer'## The following object is masked from 'package:survival':
##
## myelomadatapath="inflation rates.csv"
data1=read.csv("inflation rates.CSV")
data1## Year Month Annual.Average.Inflation X12.Month.Inflation
## 1 2025 April 3.74 4.11
## 2 2025 March 3.81 3.62
## 3 2025 February 3.98 3.45
## 4 2025 January 4.21 3.28
## 5 2024 December 4.50 2.99
## 6 2024 November 4.81 2.75
## 7 2024 October 5.14 2.72
## 8 2024 September 5.50 3.56
## 9 2024 August 5.77 4.36
## 10 2024 July 5.97 4.31
## 11 2024 June 4.64 6.22
## 12 2024 May 6.49 5.10
## 13 2024 April 6.73 5.00
## 14 2024 March 6.97 5.70
## 15 2024 February 7.26 6.31
## 16 2024 January 7.50 6.85
## 17 2023 December 7.67 6.63
## 18 2023 November 7.87 6.80
## 19 2023 October 8.10 6.92
## 20 2023 September 8.32 6.78
## 21 2023 August 8.52 6.73
## 22 2023 July 8.68 7.28
## 23 2023 June 8.77 7.88
## 24 2023 May 8.78 8.03
## 25 2023 April 8.71 7.90
## 26 2023 March 8.59 9.19
## 27 2023 February 8.30 9.23
## 28 2023 January 7.95 8.98
## 29 2022 December 7.66 9.06
## 30 2022 November 7.38 9.48
## 31 2022 October 7.48 9.59
## 32 2022 September 6.81 9.18
## 33 2022 August 6.61 8.53
## 34 2022 July 6.45 8.32
## 35 2022 June 6.29 7.91
## 36 2022 May 6.16 7.08
## 37 2022 April 6.05 6.47
## 38 2022 March 6.29 5.56
## 39 2022 February 6.23 5.08
## 40 2022 January 6.08 5.39
## 41 2021 December 5.62 5.73
## 42 2021 November 6.10 5.80
## 43 2021 October 6.07 6.45
## 44 2021 September 5.35 6.91
## 45 2021 August 5.71 6.57
## 46 2021 July 5.53 6.55
## 47 2021 June 5.35 6.32
## 48 2021 May 5.20 5.87
## 49 2021 April 4.66 5.76
## 50 2021 March 5.17 5.90
## 51 2021 February 5.16 5.78
## 52 2021 January 5.74 5.69
## 53 2020 December 5.41 5.62
## 54 2020 November 5.53 5.33
## 55 2020 October 5.67 4.84
## 56 2020 September 5.79 4.20
## 57 2020 August 5.87 4.36
## 58 2020 July 6.01 4.36
## 59 2020 June 6.16 4.59
## 60 2020 May 6.18 5.33
## 61 2020 April 6.03 6.01
## 62 2020 March 5.84 5.84
## 63 2020 February 5.72 7.17
## 64 2020 January 5.29 5.78
## 65 2019 December 5.20 5.82
## 66 2019 November 5.19 5.56
## 67 2019 October 5.19 4.95
## 68 2019 September 5.24 3.83
## 69 2019 August 5.40 5.00
## 70 2019 July 5.32 6.27
## 71 2019 June 5.16 5.70
## 72 2019 May 5.04 4.49
## 73 2019 April 4.91 6.58
## 74 2019 April 4.91 6.58
## 75 2019 March 4.67 4.35
## 76 2019 February 4.65 4.14
## 77 2019 January 4.68 4.70
## 78 2018 December 4.69 5.71
## 79 2018 November 4.59 5.58
## 80 2018 October 4.53 5.53
## 81 2018 September 4.53 5.70
## 82 2018 August 4.63 4.04
## 83 2018 July 4.95 4.35
## 84 2018 June 5.20 4.28
## 85 2018 May 5.61 3.95
## 86 2018 April 6.24 3.73
## 87 2018 March 6.89 4.18
## 88 2018 February 7.40 4.46
## 89 2018 January 7.79 4.83
## 90 2017 December 7.98 4.50
## 91 2017 November 8.15 4.73
## 92 2017 October 8.33 5.72
## 93 2017 September 8.40 7.06
## 94 2017 August 8.36 8.04
## 95 2017 July 8.21 7.47
## 96 2017 June 8.13 9.21
## 97 2017 May 7.84 11.70
## 98 2017 April 7.20 11.48
## 99 2017 March 6.76 10.28
## 100 2017 February 6.43 9.04
## 101 2017 January 6.26 6.99
## 102 2016 December 6.30 6.35
## 103 2016 November 6.43 6.68
## 104 2016 October 6.48 6.47
## 105 2016 September 6.50 6.34
## 106 2016 August 6.47 6.26
## 107 2016 July 6.44 6.40
## 108 2016 June 6.46 5.80
## 109 2016 May 6.59 5.00
## 110 2016 April 6.72 5.27
## 111 2016 March 6.88 6.45
## 112 2016 February 6.87 6.84
## 113 2016 January 6.77 7.78
## 114 2015 December 6.58 8.01
## 115 2015 November 6.42 7.32
## 116 2015 October 6.31 6.72
## 117 2015 September 6.29 5.97
## 118 2015 August 6.34 5.84
## 119 2015 July 6.54 6.62D1=data1$Annual.Average.Inflation;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 6.54hist(D1)
barplot(D1,col='blue',xlab = 'time',ylab = 'rates', main = 'inflation rates in kenya')
parmfrow=c(2,1)#fGARCH
library(fGarch)## 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")library(timeSeries)## Loading required package: timeDate##
## Attaching package: 'timeSeries'## The following objects are masked from 'package:graphics':
##
## lines, pointsimport= read.csv("inflation rates.csv");import## Year Month Annual.Average.Inflation X12.Month.Inflation
## 1 2025 April 3.74 4.11
## 2 2025 March 3.81 3.62
## 3 2025 February 3.98 3.45
## 4 2025 January 4.21 3.28
## 5 2024 December 4.50 2.99
## 6 2024 November 4.81 2.75
## 7 2024 October 5.14 2.72
## 8 2024 September 5.50 3.56
## 9 2024 August 5.77 4.36
## 10 2024 July 5.97 4.31
## 11 2024 June 4.64 6.22
## 12 2024 May 6.49 5.10
## 13 2024 April 6.73 5.00
## 14 2024 March 6.97 5.70
## 15 2024 February 7.26 6.31
## 16 2024 January 7.50 6.85
## 17 2023 December 7.67 6.63
## 18 2023 November 7.87 6.80
## 19 2023 October 8.10 6.92
## 20 2023 September 8.32 6.78
## 21 2023 August 8.52 6.73
## 22 2023 July 8.68 7.28
## 23 2023 June 8.77 7.88
## 24 2023 May 8.78 8.03
## 25 2023 April 8.71 7.90
## 26 2023 March 8.59 9.19
## 27 2023 February 8.30 9.23
## 28 2023 January 7.95 8.98
## 29 2022 December 7.66 9.06
## 30 2022 November 7.38 9.48
## 31 2022 October 7.48 9.59
## 32 2022 September 6.81 9.18
## 33 2022 August 6.61 8.53
## 34 2022 July 6.45 8.32
## 35 2022 June 6.29 7.91
## 36 2022 May 6.16 7.08
## 37 2022 April 6.05 6.47
## 38 2022 March 6.29 5.56
## 39 2022 February 6.23 5.08
## 40 2022 January 6.08 5.39
## 41 2021 December 5.62 5.73
## 42 2021 November 6.10 5.80
## 43 2021 October 6.07 6.45
## 44 2021 September 5.35 6.91
## 45 2021 August 5.71 6.57
## 46 2021 July 5.53 6.55
## 47 2021 June 5.35 6.32
## 48 2021 May 5.20 5.87
## 49 2021 April 4.66 5.76
## 50 2021 March 5.17 5.90
## 51 2021 February 5.16 5.78
## 52 2021 January 5.74 5.69
## 53 2020 December 5.41 5.62
## 54 2020 November 5.53 5.33
## 55 2020 October 5.67 4.84
## 56 2020 September 5.79 4.20
## 57 2020 August 5.87 4.36
## 58 2020 July 6.01 4.36
## 59 2020 June 6.16 4.59
## 60 2020 May 6.18 5.33
## 61 2020 April 6.03 6.01
## 62 2020 March 5.84 5.84
## 63 2020 February 5.72 7.17
## 64 2020 January 5.29 5.78
## 65 2019 December 5.20 5.82
## 66 2019 November 5.19 5.56
## 67 2019 October 5.19 4.95
## 68 2019 September 5.24 3.83
## 69 2019 August 5.40 5.00
## 70 2019 July 5.32 6.27
## 71 2019 June 5.16 5.70
## 72 2019 May 5.04 4.49
## 73 2019 April 4.91 6.58
## 74 2019 April 4.91 6.58
## 75 2019 March 4.67 4.35
## 76 2019 February 4.65 4.14
## 77 2019 January 4.68 4.70
## 78 2018 December 4.69 5.71
## 79 2018 November 4.59 5.58
## 80 2018 October 4.53 5.53
## 81 2018 September 4.53 5.70
## 82 2018 August 4.63 4.04
## 83 2018 July 4.95 4.35
## 84 2018 June 5.20 4.28
## 85 2018 May 5.61 3.95
## 86 2018 April 6.24 3.73
## 87 2018 March 6.89 4.18
## 88 2018 February 7.40 4.46
## 89 2018 January 7.79 4.83
## 90 2017 December 7.98 4.50
## 91 2017 November 8.15 4.73
## 92 2017 October 8.33 5.72
## 93 2017 September 8.40 7.06
## 94 2017 August 8.36 8.04
## 95 2017 July 8.21 7.47
## 96 2017 June 8.13 9.21
## 97 2017 May 7.84 11.70
## 98 2017 April 7.20 11.48
## 99 2017 March 6.76 10.28
## 100 2017 February 6.43 9.04
## 101 2017 January 6.26 6.99
## 102 2016 December 6.30 6.35
## 103 2016 November 6.43 6.68
## 104 2016 October 6.48 6.47
## 105 2016 September 6.50 6.34
## 106 2016 August 6.47 6.26
## 107 2016 July 6.44 6.40
## 108 2016 June 6.46 5.80
## 109 2016 May 6.59 5.00
## 110 2016 April 6.72 5.27
## 111 2016 March 6.88 6.45
## 112 2016 February 6.87 6.84
## 113 2016 January 6.77 7.78
## 114 2015 December 6.58 8.01
## 115 2015 November 6.42 7.32
## 116 2015 October 6.31 6.72
## 117 2015 September 6.29 5.97
## 118 2015 August 6.34 5.84
## 119 2015 July 6.54 6.62D2=import$Annual.Average.Inflation;D2## [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 6.54plot(D2)
ts.plot(D2)
log.D2=diff(D2);log.D2## [1] 0.07 0.17 0.23 0.29 0.31 0.33 0.36 0.27 0.20 -1.33 1.85 0.24
## [13] 0.24 0.29 0.24 0.17 0.20 0.23 0.22 0.20 0.16 0.09 0.01 -0.07
## [25] -0.12 -0.29 -0.35 -0.29 -0.28 0.10 -0.67 -0.20 -0.16 -0.16 -0.13 -0.11
## [37] 0.24 -0.06 -0.15 -0.46 0.48 -0.03 -0.72 0.36 -0.18 -0.18 -0.15 -0.54
## [49] 0.51 -0.01 0.58 -0.33 0.12 0.14 0.12 0.08 0.14 0.15 0.02 -0.15
## [61] -0.19 -0.12 -0.43 -0.09 -0.01 0.00 0.05 0.16 -0.08 -0.16 -0.12 -0.13
## [73] 0.00 -0.24 -0.02 0.03 0.01 -0.10 -0.06 0.00 0.10 0.32 0.25 0.41
## [85] 0.63 0.65 0.51 0.39 0.19 0.17 0.18 0.07 -0.04 -0.15 -0.08 -0.29
## [97] -0.64 -0.44 -0.33 -0.17 0.04 0.13 0.05 0.02 -0.03 -0.03 0.02 0.13
## [109] 0.13 0.16 -0.01 -0.10 -0.19 -0.16 -0.11 -0.02 0.05 0.20plot(log.D2)
ts.plot(log.D2)
acf(log.D2)
pacf(log.D2)
s=log.D2^2;s## [1] 0.0049 0.0289 0.0529 0.0841 0.0961 0.1089 0.1296 0.0729 0.0400 1.7689
## [11] 3.4225 0.0576 0.0576 0.0841 0.0576 0.0289 0.0400 0.0529 0.0484 0.0400
## [21] 0.0256 0.0081 0.0001 0.0049 0.0144 0.0841 0.1225 0.0841 0.0784 0.0100
## [31] 0.4489 0.0400 0.0256 0.0256 0.0169 0.0121 0.0576 0.0036 0.0225 0.2116
## [41] 0.2304 0.0009 0.5184 0.1296 0.0324 0.0324 0.0225 0.2916 0.2601 0.0001
## [51] 0.3364 0.1089 0.0144 0.0196 0.0144 0.0064 0.0196 0.0225 0.0004 0.0225
## [61] 0.0361 0.0144 0.1849 0.0081 0.0001 0.0000 0.0025 0.0256 0.0064 0.0256
## [71] 0.0144 0.0169 0.0000 0.0576 0.0004 0.0009 0.0001 0.0100 0.0036 0.0000
## [81] 0.0100 0.1024 0.0625 0.1681 0.3969 0.4225 0.2601 0.1521 0.0361 0.0289
## [91] 0.0324 0.0049 0.0016 0.0225 0.0064 0.0841 0.4096 0.1936 0.1089 0.0289
## [101] 0.0016 0.0169 0.0025 0.0004 0.0009 0.0009 0.0004 0.0169 0.0169 0.0256
## [111] 0.0001 0.0100 0.0361 0.0256 0.0121 0.0004 0.0025 0.0400plot(s)
ts.plot(s)
M2=garchFit(~garch(1,1),data = log.D2,trace = F);M2##
## Title:
## GARCH Modelling
##
## Call:
## garchFit(formula = ~garch(1, 1), data = log.D2, trace = F)
##
## Mean and Variance Equation:
## data ~ garch(1, 1)
## <environment: 0x00000203be7b4ee8>
## [data = log.D2]
##
## Conditional Distribution:
## norm
##
## Coefficient(s):
## mu omega alpha1 beta1
## -0.0224632 0.0096866 0.8708402 0.3139453
##
## Std. Errors:
## based on Hessian
##
## Error Analysis:
## Estimate Std. Error t value Pr(>|t|)
## mu -0.022463 0.023956 -0.938 0.34840
## omega 0.009687 0.005584 1.735 0.08279 .
## alpha1 0.870840 0.321604 2.708 0.00677 **
## beta1 0.313945 0.116863 2.686 0.00722 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Log Likelihood:
## -11.23655 normalized: -0.09522499
##
## Description:
## Tue May 6 18:26:37 2025 by user: SILVENUSsummary(M2)##
## Title:
## GARCH Modelling
##
## Call:
## garchFit(formula = ~garch(1, 1), data = log.D2, trace = F)
##
## Mean and Variance Equation:
## data ~ garch(1, 1)
## <environment: 0x00000203be7b4ee8>
## [data = log.D2]
##
## Conditional Distribution:
## norm
##
## Coefficient(s):
## mu omega alpha1 beta1
## -0.0224632 0.0096866 0.8708402 0.3139453
##
## Std. Errors:
## based on Hessian
##
## Error Analysis:
## Estimate Std. Error t value Pr(>|t|)
## mu -0.022463 0.023956 -0.938 0.34840
## omega 0.009687 0.005584 1.735 0.08279 .
## alpha1 0.870840 0.321604 2.708 0.00677 **
## beta1 0.313945 0.116863 2.686 0.00722 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Log Likelihood:
## -11.23655 normalized: -0.09522499
##
## Description:
## Tue May 6 18:26:37 2025 by user: SILVENUS
##
##
## Standardised Residuals Tests:
## Statistic p-Value
## Jarque-Bera Test R Chi^2 52.2611358 4.483747e-12
## Shapiro-Wilk Test R W 0.9321416 1.534461e-05
## Ljung-Box Test R Q(10) 23.4110865 9.326786e-03
## Ljung-Box Test R Q(15) 31.8778266 6.689206e-03
## Ljung-Box Test R Q(20) 38.5065827 7.674429e-03
## Ljung-Box Test R^2 Q(10) 3.2880888 9.738088e-01
## Ljung-Box Test R^2 Q(15) 4.5347064 9.953867e-01
## Ljung-Box Test R^2 Q(20) 6.7619136 9.973959e-01
## LM Arch Test R TR^2 6.4689585 8.906240e-01
##
## Information Criterion Statistics:
## AIC BIC SIC HQIC
## 0.2582466 0.3521681 0.2560473 0.2963815plot(M2, which=1)
plot(M2, which=6)
plot(M2,which=13)
#gjrGARCH
D1=read.csv("inflation rates.csv");D1## Year Month Annual.Average.Inflation X12.Month.Inflation
## 1 2025 April 3.74 4.11
## 2 2025 March 3.81 3.62
## 3 2025 February 3.98 3.45
## 4 2025 January 4.21 3.28
## 5 2024 December 4.50 2.99
## 6 2024 November 4.81 2.75
## 7 2024 October 5.14 2.72
## 8 2024 September 5.50 3.56
## 9 2024 August 5.77 4.36
## 10 2024 July 5.97 4.31
## 11 2024 June 4.64 6.22
## 12 2024 May 6.49 5.10
## 13 2024 April 6.73 5.00
## 14 2024 March 6.97 5.70
## 15 2024 February 7.26 6.31
## 16 2024 January 7.50 6.85
## 17 2023 December 7.67 6.63
## 18 2023 November 7.87 6.80
## 19 2023 October 8.10 6.92
## 20 2023 September 8.32 6.78
## 21 2023 August 8.52 6.73
## 22 2023 July 8.68 7.28
## 23 2023 June 8.77 7.88
## 24 2023 May 8.78 8.03
## 25 2023 April 8.71 7.90
## 26 2023 March 8.59 9.19
## 27 2023 February 8.30 9.23
## 28 2023 January 7.95 8.98
## 29 2022 December 7.66 9.06
## 30 2022 November 7.38 9.48
## 31 2022 October 7.48 9.59
## 32 2022 September 6.81 9.18
## 33 2022 August 6.61 8.53
## 34 2022 July 6.45 8.32
## 35 2022 June 6.29 7.91
## 36 2022 May 6.16 7.08
## 37 2022 April 6.05 6.47
## 38 2022 March 6.29 5.56
## 39 2022 February 6.23 5.08
## 40 2022 January 6.08 5.39
## 41 2021 December 5.62 5.73
## 42 2021 November 6.10 5.80
## 43 2021 October 6.07 6.45
## 44 2021 September 5.35 6.91
## 45 2021 August 5.71 6.57
## 46 2021 July 5.53 6.55
## 47 2021 June 5.35 6.32
## 48 2021 May 5.20 5.87
## 49 2021 April 4.66 5.76
## 50 2021 March 5.17 5.90
## 51 2021 February 5.16 5.78
## 52 2021 January 5.74 5.69
## 53 2020 December 5.41 5.62
## 54 2020 November 5.53 5.33
## 55 2020 October 5.67 4.84
## 56 2020 September 5.79 4.20
## 57 2020 August 5.87 4.36
## 58 2020 July 6.01 4.36
## 59 2020 June 6.16 4.59
## 60 2020 May 6.18 5.33
## 61 2020 April 6.03 6.01
## 62 2020 March 5.84 5.84
## 63 2020 February 5.72 7.17
## 64 2020 January 5.29 5.78
## 65 2019 December 5.20 5.82
## 66 2019 November 5.19 5.56
## 67 2019 October 5.19 4.95
## 68 2019 September 5.24 3.83
## 69 2019 August 5.40 5.00
## 70 2019 July 5.32 6.27
## 71 2019 June 5.16 5.70
## 72 2019 May 5.04 4.49
## 73 2019 April 4.91 6.58
## 74 2019 April 4.91 6.58
## 75 2019 March 4.67 4.35
## 76 2019 February 4.65 4.14
## 77 2019 January 4.68 4.70
## 78 2018 December 4.69 5.71
## 79 2018 November 4.59 5.58
## 80 2018 October 4.53 5.53
## 81 2018 September 4.53 5.70
## 82 2018 August 4.63 4.04
## 83 2018 July 4.95 4.35
## 84 2018 June 5.20 4.28
## 85 2018 May 5.61 3.95
## 86 2018 April 6.24 3.73
## 87 2018 March 6.89 4.18
## 88 2018 February 7.40 4.46
## 89 2018 January 7.79 4.83
## 90 2017 December 7.98 4.50
## 91 2017 November 8.15 4.73
## 92 2017 October 8.33 5.72
## 93 2017 September 8.40 7.06
## 94 2017 August 8.36 8.04
## 95 2017 July 8.21 7.47
## 96 2017 June 8.13 9.21
## 97 2017 May 7.84 11.70
## 98 2017 April 7.20 11.48
## 99 2017 March 6.76 10.28
## 100 2017 February 6.43 9.04
## 101 2017 January 6.26 6.99
## 102 2016 December 6.30 6.35
## 103 2016 November 6.43 6.68
## 104 2016 October 6.48 6.47
## 105 2016 September 6.50 6.34
## 106 2016 August 6.47 6.26
## 107 2016 July 6.44 6.40
## 108 2016 June 6.46 5.80
## 109 2016 May 6.59 5.00
## 110 2016 April 6.72 5.27
## 111 2016 March 6.88 6.45
## 112 2016 February 6.87 6.84
## 113 2016 January 6.77 7.78
## 114 2015 December 6.58 8.01
## 115 2015 November 6.42 7.32
## 116 2015 October 6.31 6.72
## 117 2015 September 6.29 5.97
## 118 2015 August 6.34 5.84
## 119 2015 July 6.54 6.62D2=D1$Annual.Average.Inflation;D2## [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 6.54D3=diff(D2);D3## [1] 0.07 0.17 0.23 0.29 0.31 0.33 0.36 0.27 0.20 -1.33 1.85 0.24
## [13] 0.24 0.29 0.24 0.17 0.20 0.23 0.22 0.20 0.16 0.09 0.01 -0.07
## [25] -0.12 -0.29 -0.35 -0.29 -0.28 0.10 -0.67 -0.20 -0.16 -0.16 -0.13 -0.11
## [37] 0.24 -0.06 -0.15 -0.46 0.48 -0.03 -0.72 0.36 -0.18 -0.18 -0.15 -0.54
## [49] 0.51 -0.01 0.58 -0.33 0.12 0.14 0.12 0.08 0.14 0.15 0.02 -0.15
## [61] -0.19 -0.12 -0.43 -0.09 -0.01 0.00 0.05 0.16 -0.08 -0.16 -0.12 -0.13
## [73] 0.00 -0.24 -0.02 0.03 0.01 -0.10 -0.06 0.00 0.10 0.32 0.25 0.41
## [85] 0.63 0.65 0.51 0.39 0.19 0.17 0.18 0.07 -0.04 -0.15 -0.08 -0.29
## [97] -0.64 -0.44 -0.33 -0.17 0.04 0.13 0.05 0.02 -0.03 -0.03 0.02 0.13
## [109] 0.13 0.16 -0.01 -0.10 -0.19 -0.16 -0.11 -0.02 0.05 0.20library(rugarch)## Loading required package: parallel##
## Attaching package: 'rugarch'## The following object is masked from 'package:stats':
##
## sigmalibrary(forecast)## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo##
## Attaching package: 'forecast'## The following object is masked from 'package:ggpubr':
##
## gghistogramM2=ugarchspec(variance.model=list(model="gjrGARCH",garchOrder=c(1,1)),mean.model=list(armaOrder=c(0,0),include.mean=F),distribution.model="norm");M2##
## *---------------------------------*
## * GARCH Model Spec *
## *---------------------------------*
##
## Conditional Variance Dynamics
## ------------------------------------
## GARCH Model : gjrGARCH(1,1)
## Variance Targeting : FALSE
##
## Conditional Mean Dynamics
## ------------------------------------
## Mean Model : ARFIMA(0,0,0)
## Include Mean : FALSE
## GARCH-in-Mean : FALSE
##
## Conditional Distribution
## ------------------------------------
## Distribution : norm
## Includes Skew : FALSE
## Includes Shape : FALSE
## Includes Lambda : FALSEM2fit=ugarchfit(D3,spec=M2);M2fit##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(0,0,0)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## omega 0.01265 0.007435 1.70134 0.088880
## alpha1 0.74355 0.256466 2.89920 0.003741
## beta1 0.34263 0.110622 3.09729 0.001953
## gamma1 -0.17435 0.283386 -0.61523 0.538406
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## omega 0.01265 0.008884 1.42386 0.154487
## alpha1 0.74355 0.329786 2.25463 0.024157
## beta1 0.34263 0.116339 2.94508 0.003229
## gamma1 -0.17435 0.336144 -0.51867 0.603994
##
## LogLikelihood : -12.22014
##
## Information Criteria
## ------------------------------------
##
## Akaike 0.27492
## Bayes 0.36884
## Shibata 0.27272
## Hannan-Quinn 0.31305
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 6.234 0.012531
## Lag[2*(p+q)+(p+q)-1][2] 10.247 0.001644
## Lag[4*(p+q)+(p+q)-1][5] 14.892 0.000475
## d.o.f=0
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.3116 0.5767
## Lag[2*(p+q)+(p+q)-1][5] 1.0306 0.8527
## Lag[4*(p+q)+(p+q)-1][9] 1.5005 0.9555
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.01228 0.500 2.000 0.9118
## ARCH Lag[5] 0.37938 1.440 1.667 0.9185
## ARCH Lag[7] 0.73405 2.315 1.543 0.9526
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 0.9008
## Individual Statistics:
## omega 0.5321
## alpha1 0.4912
## beta1 0.4402
## gamma1 0.3748
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.07 1.24 1.6
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 0.2044 0.8384
## Negative Sign Bias 0.2749 0.7839
## Positive Sign Bias 0.5225 0.6024
## Joint Effect 0.3990 0.9405
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 22.34 0.26771
## 2 30 39.63 0.09022
## 3 40 50.58 0.10142
## 4 50 60.15 0.13204
##
##
## Elapsed time : 1.775362plot(M2fit, which=9)
plot(M2fit, which=10)
plot(M2fit, which=2)##
## please wait...calculating quantiles...
summary(M2fit, which=9)## Length Class Mode
## 1 uGARCHfit S4summary(M2fit,which=10)## Length Class Mode
## 1 uGARCHfit S4summary(M2fit,which=2)## Length Class Mode
## 1 uGARCHfit S4#plotting the forecast
forc=ugarchforecast(fitORspec=M2fit,n.ahead = 12);forc##
## *------------------------------------*
## * GARCH Model Forecast *
## *------------------------------------*
## Model: gjrGARCH
## Horizon: 12
## Roll Steps: 0
## Out of Sample: 0
##
## 0-roll forecast [T0=1970-04-29]:
## Series Sigma
## T+1 0 0.2241
## T+2 0 0.2507
## T+3 0 0.2746
## T+4 0 0.2966
## T+5 0 0.3171
## T+6 0 0.3363
## T+7 0 0.3545
## T+8 0 0.3717
## T+9 0 0.3882
## T+10 0 0.4040
## T+11 0 0.4191
## T+12 0 0.4338plot(forc, which=1)
plot(forc, which=3)
#eGARCH
library(rugarch)
library(forecast)
M2=ugarchspec(variance.model=list(model="eGARCH",garchOrder=c(1,1)),mean.model=list(armaOrder=c(0,0),include.mean=F),distribution.model="norm");M2##
## *---------------------------------*
## * GARCH Model Spec *
## *---------------------------------*
##
## Conditional Variance Dynamics
## ------------------------------------
## GARCH Model : eGARCH(1,1)
## Variance Targeting : FALSE
##
## Conditional Mean Dynamics
## ------------------------------------
## Mean Model : ARFIMA(0,0,0)
## Include Mean : FALSE
## GARCH-in-Mean : FALSE
##
## Conditional Distribution
## ------------------------------------
## Distribution : norm
## Includes Skew : FALSE
## Includes Shape : FALSE
## Includes Lambda : FALSEM2fit=ugarchfit(D3,spec=M2);M2fit##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : eGARCH(1,1)
## Mean Model : ARFIMA(0,0,0)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## omega -0.603023 0.246867 -2.44271 0.014578
## alpha1 0.081554 0.115579 0.70561 0.480431
## beta1 0.758233 0.088915 8.52767 0.000000
## gamma1 0.949852 0.205476 4.62269 0.000004
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## omega -0.603023 0.282966 -2.13108 0.033082
## alpha1 0.081554 0.121534 0.67104 0.502196
## beta1 0.758233 0.083103 9.12398 0.000000
## gamma1 0.949852 0.185846 5.11097 0.000000
##
## LogLikelihood : -9.480091
##
## Information Criteria
## ------------------------------------
##
## Akaike 0.22848
## Bayes 0.32240
## Shibata 0.22628
## Hannan-Quinn 0.26661
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 7.919 0.0048919
## Lag[2*(p+q)+(p+q)-1][2] 12.149 0.0005174
## Lag[4*(p+q)+(p+q)-1][5] 17.006 0.0001276
## d.o.f=0
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.007734 0.9299
## Lag[2*(p+q)+(p+q)-1][5] 0.759587 0.9112
## Lag[4*(p+q)+(p+q)-1][9] 1.393928 0.9638
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.06164 0.500 2.000 0.8039
## ARCH Lag[5] 0.38749 1.440 1.667 0.9162
## ARCH Lag[7] 0.92035 2.315 1.543 0.9262
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 0.8825
## Individual Statistics:
## omega 0.32888
## alpha1 0.03955
## beta1 0.38274
## gamma1 0.51148
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.07 1.24 1.6
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 0.0933 0.9258
## Negative Sign Bias 0.1178 0.9064
## Positive Sign Bias 0.5700 0.5698
## Joint Effect 0.3557 0.9492
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 28.44 0.07531
## 2 30 39.63 0.09022
## 3 40 60.31 0.01586
## 4 50 66.75 0.04663
##
##
## Elapsed time : 0.339668plot(M2fit, which=10)
plot(M2fit, which=8)
plot(M2fit, which=1)
summary(M2fit, which=10)## Length Class Mode
## 1 uGARCHfit S4summary(M2fit,which=8)## Length Class Mode
## 1 uGARCHfit S4summary(M2fit,which=1)## Length Class Mode
## 1 uGARCHfit S4#plotting the forecast
forc=ugarchforecast(fitORspec=M2fit,n.ahead = 12);forc##
## *------------------------------------*
## * GARCH Model Forecast *
## *------------------------------------*
## Model: eGARCH
## Horizon: 12
## Roll Steps: 0
## Out of Sample: 0
##
## 0-roll forecast [T0=1970-04-29]:
## Series Sigma
## T+1 0 0.2386
## T+2 0 0.2495
## T+3 0 0.2582
## T+4 0 0.2650
## T+5 0 0.2702
## T+6 0 0.2742
## T+7 0 0.2774
## T+8 0 0.2797
## T+9 0 0.2816
## T+10 0 0.2829
## T+11 0 0.2840
## T+12 0 0.2848plot(forc, which=1)
plot(forc, which=3)
#kaplan meier
library(survival)
library(survminer)
d1=data.frame(time=c(2,10,12,18,4),event=c(1,0,1,1,0))
kmc=with(d1,Surv(time,event));
kmc## [1] 2 10+ 12 18 4+plot(kmc)
plot(kmc,fun="cumhaz")
kmc2=survfit(Surv(time,event)~1,data=d1);kmc2## Call: survfit(formula = Surv(time, event) ~ 1, data = d1)
##
## n events median 0.95LCL 0.95UCL
## [1,] 5 3 12 12 NAsummary(kmc2)## Call: survfit(formula = Surv(time, event) ~ 1, data = d1)
##
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 2 5 1 0.8 0.179 0.5161 1
## 12 2 1 0.4 0.297 0.0935 1
## 18 1 1 0.0 NaN NA NA