DATA ANALYSIS
SMITH SILVENUS BUS-244-050/2021
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$X12.Month.Inflation;D1## [1] 4.11 3.62 3.45 3.28 2.99 2.75 2.72 3.56 4.36 4.31 6.22 5.10
## [13] 5.00 5.70 6.31 6.85 6.63 6.80 6.92 6.78 6.73 7.28 7.88 8.03
## [25] 7.90 9.19 9.23 8.98 9.06 9.48 9.59 9.18 8.53 8.32 7.91 7.08
## [37] 6.47 5.56 5.08 5.39 5.73 5.80 6.45 6.91 6.57 6.55 6.32 5.87
## [49] 5.76 5.90 5.78 5.69 5.62 5.33 4.84 4.20 4.36 4.36 4.59 5.33
## [61] 6.01 5.84 7.17 5.78 5.82 5.56 4.95 3.83 5.00 6.27 5.70 4.49
## [73] 6.58 6.58 4.35 4.14 4.70 5.71 5.58 5.53 5.70 4.04 4.35 4.28
## [85] 3.95 3.73 4.18 4.46 4.83 4.50 4.73 5.72 7.06 8.04 7.47 9.21
## [97] 11.70 11.48 10.28 9.04 6.99 6.35 6.68 6.47 6.34 6.26 6.40 5.80
## [109] 5.00 5.27 6.45 6.84 7.78 8.01 7.32 6.72 5.97 5.84 6.62hist(D1)
barplot(D1,col='RED',xlab = 'time',ylab = 'rates', main = 'inflation rates in kenya')
parmfrow=c(1,1)#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$X12.Month.Inflation;D2## [1] 4.11 3.62 3.45 3.28 2.99 2.75 2.72 3.56 4.36 4.31 6.22 5.10
## [13] 5.00 5.70 6.31 6.85 6.63 6.80 6.92 6.78 6.73 7.28 7.88 8.03
## [25] 7.90 9.19 9.23 8.98 9.06 9.48 9.59 9.18 8.53 8.32 7.91 7.08
## [37] 6.47 5.56 5.08 5.39 5.73 5.80 6.45 6.91 6.57 6.55 6.32 5.87
## [49] 5.76 5.90 5.78 5.69 5.62 5.33 4.84 4.20 4.36 4.36 4.59 5.33
## [61] 6.01 5.84 7.17 5.78 5.82 5.56 4.95 3.83 5.00 6.27 5.70 4.49
## [73] 6.58 6.58 4.35 4.14 4.70 5.71 5.58 5.53 5.70 4.04 4.35 4.28
## [85] 3.95 3.73 4.18 4.46 4.83 4.50 4.73 5.72 7.06 8.04 7.47 9.21
## [97] 11.70 11.48 10.28 9.04 6.99 6.35 6.68 6.47 6.34 6.26 6.40 5.80
## [109] 5.00 5.27 6.45 6.84 7.78 8.01 7.32 6.72 5.97 5.84 6.62plot(D2)
ts.plot(D2)
log.D2=diff(D2);log.D2## [1] -0.49 -0.17 -0.17 -0.29 -0.24 -0.03 0.84 0.80 -0.05 1.91 -1.12 -0.10
## [13] 0.70 0.61 0.54 -0.22 0.17 0.12 -0.14 -0.05 0.55 0.60 0.15 -0.13
## [25] 1.29 0.04 -0.25 0.08 0.42 0.11 -0.41 -0.65 -0.21 -0.41 -0.83 -0.61
## [37] -0.91 -0.48 0.31 0.34 0.07 0.65 0.46 -0.34 -0.02 -0.23 -0.45 -0.11
## [49] 0.14 -0.12 -0.09 -0.07 -0.29 -0.49 -0.64 0.16 0.00 0.23 0.74 0.68
## [61] -0.17 1.33 -1.39 0.04 -0.26 -0.61 -1.12 1.17 1.27 -0.57 -1.21 2.09
## [73] 0.00 -2.23 -0.21 0.56 1.01 -0.13 -0.05 0.17 -1.66 0.31 -0.07 -0.33
## [85] -0.22 0.45 0.28 0.37 -0.33 0.23 0.99 1.34 0.98 -0.57 1.74 2.49
## [97] -0.22 -1.20 -1.24 -2.05 -0.64 0.33 -0.21 -0.13 -0.08 0.14 -0.60 -0.80
## [109] 0.27 1.18 0.39 0.94 0.23 -0.69 -0.60 -0.75 -0.13 0.78plot(log.D2)
ts.plot(log.D2)
acf(log.D2)
pacf(log.D2)
s=log.D2^2;s## [1] 0.2401 0.0289 0.0289 0.0841 0.0576 0.0009 0.7056 0.6400 0.0025 3.6481
## [11] 1.2544 0.0100 0.4900 0.3721 0.2916 0.0484 0.0289 0.0144 0.0196 0.0025
## [21] 0.3025 0.3600 0.0225 0.0169 1.6641 0.0016 0.0625 0.0064 0.1764 0.0121
## [31] 0.1681 0.4225 0.0441 0.1681 0.6889 0.3721 0.8281 0.2304 0.0961 0.1156
## [41] 0.0049 0.4225 0.2116 0.1156 0.0004 0.0529 0.2025 0.0121 0.0196 0.0144
## [51] 0.0081 0.0049 0.0841 0.2401 0.4096 0.0256 0.0000 0.0529 0.5476 0.4624
## [61] 0.0289 1.7689 1.9321 0.0016 0.0676 0.3721 1.2544 1.3689 1.6129 0.3249
## [71] 1.4641 4.3681 0.0000 4.9729 0.0441 0.3136 1.0201 0.0169 0.0025 0.0289
## [81] 2.7556 0.0961 0.0049 0.1089 0.0484 0.2025 0.0784 0.1369 0.1089 0.0529
## [91] 0.9801 1.7956 0.9604 0.3249 3.0276 6.2001 0.0484 1.4400 1.5376 4.2025
## [101] 0.4096 0.1089 0.0441 0.0169 0.0064 0.0196 0.3600 0.6400 0.0729 1.3924
## [111] 0.1521 0.8836 0.0529 0.4761 0.3600 0.5625 0.0169 0.6084plot(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: 0x00000294a396a968>
## [data = log.D2]
##
## Conditional Distribution:
## norm
##
## Coefficient(s):
## mu omega alpha1 beta1
## 0.0098779 0.1003311 0.3098247 0.5376797
##
## Std. Errors:
## based on Hessian
##
## Error Analysis:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.009878 0.064824 0.152 0.87889
## omega 0.100331 0.065814 1.524 0.12739
## alpha1 0.309825 0.130679 2.371 0.01775 *
## beta1 0.537680 0.173927 3.091 0.00199 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Log Likelihood:
## -125.9211 normalized: -1.067128
##
## Description:
## Tue May 6 19:44:36 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: 0x00000294a396a968>
## [data = log.D2]
##
## Conditional Distribution:
## norm
##
## Coefficient(s):
## mu omega alpha1 beta1
## 0.0098779 0.1003311 0.3098247 0.5376797
##
## Std. Errors:
## based on Hessian
##
## Error Analysis:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.009878 0.064824 0.152 0.87889
## omega 0.100331 0.065814 1.524 0.12739
## alpha1 0.309825 0.130679 2.371 0.01775 *
## beta1 0.537680 0.173927 3.091 0.00199 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Log Likelihood:
## -125.9211 normalized: -1.067128
##
## Description:
## Tue May 6 19:44:36 2025 by user: SILVENUS
##
##
## Standardised Residuals Tests:
## Statistic p-Value
## Jarque-Bera Test R Chi^2 3.7865334 0.15057911
## Shapiro-Wilk Test R W 0.9814011 0.10184708
## Ljung-Box Test R Q(10) 13.8932515 0.17791666
## Ljung-Box Test R Q(15) 23.9652562 0.06568585
## Ljung-Box Test R Q(20) 30.9612364 0.05570428
## Ljung-Box Test R^2 Q(10) 6.6272829 0.76010062
## Ljung-Box Test R^2 Q(15) 17.2107609 0.30642205
## Ljung-Box Test R^2 Q(20) 26.7987106 0.14102270
## LM Arch Test R TR^2 7.3020377 0.83702530
##
## Information Criterion Statistics:
## AIC BIC SIC HQIC
## 2.202053 2.295975 2.199854 2.240188plot(M2, which=2)
plot(M2, which=8)
plot(M2,which=10)
#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$X12.Month.Inflation;D2## [1] 4.11 3.62 3.45 3.28 2.99 2.75 2.72 3.56 4.36 4.31 6.22 5.10
## [13] 5.00 5.70 6.31 6.85 6.63 6.80 6.92 6.78 6.73 7.28 7.88 8.03
## [25] 7.90 9.19 9.23 8.98 9.06 9.48 9.59 9.18 8.53 8.32 7.91 7.08
## [37] 6.47 5.56 5.08 5.39 5.73 5.80 6.45 6.91 6.57 6.55 6.32 5.87
## [49] 5.76 5.90 5.78 5.69 5.62 5.33 4.84 4.20 4.36 4.36 4.59 5.33
## [61] 6.01 5.84 7.17 5.78 5.82 5.56 4.95 3.83 5.00 6.27 5.70 4.49
## [73] 6.58 6.58 4.35 4.14 4.70 5.71 5.58 5.53 5.70 4.04 4.35 4.28
## [85] 3.95 3.73 4.18 4.46 4.83 4.50 4.73 5.72 7.06 8.04 7.47 9.21
## [97] 11.70 11.48 10.28 9.04 6.99 6.35 6.68 6.47 6.34 6.26 6.40 5.80
## [109] 5.00 5.27 6.45 6.84 7.78 8.01 7.32 6.72 5.97 5.84 6.62D3=diff(D2);D3## [1] -0.49 -0.17 -0.17 -0.29 -0.24 -0.03 0.84 0.80 -0.05 1.91 -1.12 -0.10
## [13] 0.70 0.61 0.54 -0.22 0.17 0.12 -0.14 -0.05 0.55 0.60 0.15 -0.13
## [25] 1.29 0.04 -0.25 0.08 0.42 0.11 -0.41 -0.65 -0.21 -0.41 -0.83 -0.61
## [37] -0.91 -0.48 0.31 0.34 0.07 0.65 0.46 -0.34 -0.02 -0.23 -0.45 -0.11
## [49] 0.14 -0.12 -0.09 -0.07 -0.29 -0.49 -0.64 0.16 0.00 0.23 0.74 0.68
## [61] -0.17 1.33 -1.39 0.04 -0.26 -0.61 -1.12 1.17 1.27 -0.57 -1.21 2.09
## [73] 0.00 -2.23 -0.21 0.56 1.01 -0.13 -0.05 0.17 -1.66 0.31 -0.07 -0.33
## [85] -0.22 0.45 0.28 0.37 -0.33 0.23 0.99 1.34 0.98 -0.57 1.74 2.49
## [97] -0.22 -1.20 -1.24 -2.05 -0.64 0.33 -0.21 -0.13 -0.08 0.14 -0.60 -0.80
## [109] 0.27 1.18 0.39 0.94 0.23 -0.69 -0.60 -0.75 -0.13 0.78library(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(1,2)),mean.model=list(armaOrder=c(0,0),include.mean=T),distribution.model="norm");M2##
## *---------------------------------*
## * GARCH Model Spec *
## *---------------------------------*
##
## Conditional Variance Dynamics
## ------------------------------------
## GARCH Model : gjrGARCH(1,2)
## Variance Targeting : FALSE
##
## Conditional Mean Dynamics
## ------------------------------------
## Mean Model : ARFIMA(0,0,0)
## Include Mean : TRUE
## 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(1,2)
## Mean Model : ARFIMA(0,0,0)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.033639 0.062744 0.53613 0.591871
## omega 0.079890 0.043309 1.84466 0.065087
## alpha1 0.423376 0.157776 2.68340 0.007288
## beta1 0.652211 0.446723 1.45999 0.144293
## beta2 0.000000 0.395932 0.00000 1.000000
## gamma1 -0.413546 0.176984 -2.33663 0.019459
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.033639 0.079899 0.42102 0.673743
## omega 0.079890 0.046496 1.71821 0.085758
## alpha1 0.423376 0.232610 1.82011 0.068742
## beta1 0.652211 0.612163 1.06542 0.286686
## beta2 0.000000 0.487702 0.00000 1.000000
## gamma1 -0.413546 0.247628 -1.67003 0.094914
##
## LogLikelihood : -123.6012
##
## Information Criteria
## ------------------------------------
##
## Akaike 2.1966
## Bayes 2.3375
## Shibata 2.1918
## Hannan-Quinn 2.2538
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 5.146 0.02330
## Lag[2*(p+q)+(p+q)-1][2] 5.257 0.03473
## Lag[4*(p+q)+(p+q)-1][5] 7.043 0.05063
## d.o.f=0
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.00107 0.9739
## Lag[2*(p+q)+(p+q)-1][8] 1.40363 0.9381
## Lag[4*(p+q)+(p+q)-1][14] 3.70391 0.9067
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 0.470 0.500 2.000 0.4930
## ARCH Lag[6] 1.742 1.461 1.711 0.5502
## ARCH Lag[8] 2.646 2.368 1.583 0.6116
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 1.6532
## Individual Statistics:
## mu 0.10759
## omega 0.11776
## alpha1 0.06855
## beta1 0.13947
## beta2 0.15586
## gamma1 0.07836
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.49 1.68 2.12
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 0.3320 0.7405
## Negative Sign Bias 0.4984 0.6192
## Positive Sign Bias 0.3367 0.7370
## Joint Effect 1.6058 0.6581
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 18.27 0.5044
## 2 30 38.61 0.1094
## 3 40 43.36 0.2909
## 4 50 46.41 0.5789
##
##
## Elapsed time : 2.837727plot(M2fit, which=8)
plot(M2fit, which=11)
plot(M2fit, which=1)
summary(M2fit, which=8)## Length Class Mode
## 1 uGARCHfit S4summary(M2fit,which=11)## 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: gjrGARCH
## Horizon: 12
## Roll Steps: 0
## Out of Sample: 0
##
## 0-roll forecast [T0=1970-04-29]:
## Series Sigma
## T+1 0.03364 0.7218
## T+2 0.03364 0.7297
## T+3 0.03364 0.7366
## T+4 0.03364 0.7425
## T+5 0.03364 0.7476
## T+6 0.03364 0.7519
## T+7 0.03364 0.7557
## T+8 0.03364 0.7590
## T+9 0.03364 0.7618
## T+10 0.03364 0.7643
## T+11 0.03364 0.7664
## T+12 0.03364 0.7683plot(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=T),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 : TRUE
## 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|)
## mu 0.034182 0.062702 0.54516 0.585645
## omega -0.086525 0.062787 -1.37806 0.168185
## alpha1 0.198839 0.087104 2.28278 0.022443
## beta1 0.861708 0.070697 12.18877 0.000000
## gamma1 0.356108 0.151604 2.34894 0.018827
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.034182 0.083456 0.40958 0.682111
## omega -0.086525 0.065826 -1.31444 0.188698
## alpha1 0.198839 0.079781 2.49231 0.012691
## beta1 0.861708 0.056702 15.19712 0.000000
## gamma1 0.356108 0.148456 2.39874 0.016451
##
## LogLikelihood : -123.7458
##
## Information Criteria
## ------------------------------------
##
## Akaike 2.1821
## Bayes 2.2995
## Shibata 2.1787
## Hannan-Quinn 2.2298
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 5.829 0.01577
## Lag[2*(p+q)+(p+q)-1][2] 5.903 0.02335
## Lag[4*(p+q)+(p+q)-1][5] 7.705 0.03486
## d.o.f=0
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.01954 0.8888
## Lag[2*(p+q)+(p+q)-1][5] 0.35040 0.9781
## Lag[4*(p+q)+(p+q)-1][9] 1.89869 0.9168
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.1150 0.500 2.000 0.7346
## ARCH Lag[5] 0.3428 1.440 1.667 0.9287
## ARCH Lag[7] 1.7925 2.315 1.543 0.7611
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 0.5286
## Individual Statistics:
## mu 0.15247
## omega 0.11697
## alpha1 0.15776
## beta1 0.06495
## gamma1 0.05869
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.28 1.47 1.88
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 0.6039 0.5471
## Negative Sign Bias 0.1936 0.8468
## Positive Sign Bias 0.1958 0.8451
## Joint Effect 1.4827 0.6863
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 19.29 0.4385
## 2 30 34.54 0.2200
## 3 40 39.29 0.4570
## 4 50 48.95 0.4752
##
##
## Elapsed time : 0.514575plot(M2fit, which=9)
plot(M2fit, which=8)
plot(M2fit, which=2)##
## please wait...calculating quantiles...
summary(M2fit, which=9)## Length Class Mode
## 1 uGARCHfit S4summary(M2fit,which=8)## 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: eGARCH
## Horizon: 12
## Roll Steps: 0
## Out of Sample: 0
##
## 0-roll forecast [T0=1970-04-29]:
## Series Sigma
## T+1 0.03418 0.7574
## T+2 0.03418 0.7538
## T+3 0.03418 0.7506
## T+4 0.03418 0.7479
## T+5 0.03418 0.7456
## T+6 0.03418 0.7436
## T+7 0.03418 0.7419
## T+8 0.03418 0.7405
## T+9 0.03418 0.7392
## T+10 0.03418 0.7381
## T+11 0.03418 0.7372
## T+12 0.03418 0.7364plot(forc, which=1)
plot(forc, which=3)
#kaplan meier
library(survival)
library(survminer)
d1=data.frame(time=c(2,11,14,18,3),event=c(1,1,0,1,0))
kmc=with(d1,Surv(time,event));
kmc## [1] 2 11 14+ 18 3+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 18 11 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 0.800 0.179 0.516 1
## 11 3 1 0.533 0.248 0.214 1
## 18 1 1 0.000 NaN NA NA