1.
2 FRAM
2023-11-26
Part 1.3 - GARCH and EGARCH models
Company - VIPCLOTHING Time Frame - DAILY
require(quantmod)
## Loading required package: quantmod
## Loading required package: xts
## Loading required package: zoo
##
## Attaching package: ’zoo’
## The following objects are masked from ’package:base’:
##
## as.Date, as.Date.numeric
## Loading required package: TTR
## Registered S3 method overwritten by ’quantmod’:
## method from
## as.zoo.data.frame zoo
library(rugarch)
## Loading required package: parallel
##
## Attaching package: ’rugarch’
## The following object is masked from ’package:stats’:
##
## sigma
#### GARCH & EGARCH Models for VIPCLOTHNG.NS ####
# Data Collection
VIPCLOTHNG <- getSymbols("VIPCLOTHNG.NS", from = "2020-11-02", to = "2023-10-26", auto.assign = FALSE)
## Warning: VIPCLOTHNG.NS contains missing values. Some functions will not work if
## objects contain missing values in the middle of the series. Consider using
## na.omit(), na.approx(), na.fill(), etc to remove or replace them.
1
head(VIPCLOTHNG)
## VIPCLOTHNG.NS.Open VIPCLOTHNG.NS.High VIPCLOTHNG.NS.Low
## 2020-11-02 8.95 9.10 8.70
## 2020-11-03 8.95 8.95 8.65
## 2020-11-04 8.65 8.85 8.50
## 2020-11-05 8.65 8.75 8.50
## 2020-11-06 8.50 8.90 8.50
## 2020-11-09 8.60 8.75 8.50
## VIPCLOTHNG.NS.Close VIPCLOTHNG.NS.Volume VIPCLOTHNG.NS.Adjusted
## 2020-11-02 8.75 35156 8.75
## 2020-11-03 8.75 22822 8.75
## 2020-11-04 8.70 39265 8.70
## 2020-11-05 8.60 25793 8.60
## 2020-11-06 8.60 42164 8.60
## 2020-11-09 8.55 21833 8.55
# Extracting closing prices
VIPCLOTHNG_Close <- Cl(VIPCLOTHNG)
# Return Calculation
returns_vipclothng <- dailyReturn(VIPCLOTHNG_Close)
## Warning in to_period(xx, period = on.opts[[period]], ...): missing values
## removed from data
# Implementing Univariate GARCH
ug_spec = ugarchspec()
ug_spec
##
## *---------------------------------*
## * GARCH Model Spec *
## *---------------------------------*
##
## Conditional Variance Dynamics
## ------------------------------------
## GARCH Model : sGARCH(1,1)
## Variance Targeting : FALSE
##
## Conditional Mean Dynamics
## ------------------------------------
## Mean Model : ARFIMA(1,0,1)
## Include Mean : TRUE
## GARCH-in-Mean : FALSE
##
## Conditional Distribution
## ------------------------------------
## Distribution : norm
## Includes Skew : FALSE
## Includes Shape : FALSE
## Includes Lambda : FALSE
2
# Implementing EGARCH
eg_spec = ugarchspec(variance.model = list(model="eGARCH"))
eg_spec
##
## *---------------------------------*
## * GARCH Model Spec *
## *---------------------------------*
##
## Conditional Variance Dynamics
## ------------------------------------
## GARCH Model : eGARCH(1,1)
## Variance Targeting : FALSE
##
## Conditional Mean Dynamics
## ------------------------------------
## Mean Model : ARFIMA(1,0,1)
## Include Mean : TRUE
## GARCH-in-Mean : FALSE
##
## Conditional Distribution
## ------------------------------------
## Distribution : norm
## Includes Skew : FALSE
## Includes Shape : FALSE
## Includes Lambda : FALSE
# Estimating the models
ugfit_vipclothng = ugarchfit(spec = ug_spec, data = returns_vipclothng)
ugfit_vipclothng
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : sGARCH(1,1)
## Mean Model : ARFIMA(1,0,1)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.002192 0.001165 1.88199 0.059837
## ar1 0.248934 0.156039 1.59533 0.110637
## ma1 -0.064090 0.160416 -0.39952 0.689510
## omega 0.000051 0.000024 2.08485 0.037083
## alpha1 0.153596 0.037074 4.14293 0.000034
## beta1 0.793257 0.054150 14.64933 0.000000
##
## Robust Standard Errors:
3
## Estimate Std. Error t value Pr(>|t|)
## mu 0.002192 0.001236 1.77326 0.076185
## ar1 0.248934 0.120816 2.06044 0.039357
## ma1 -0.064090 0.124940 -0.51296 0.607977
## omega 0.000051 0.000030 1.68796 0.091418
## alpha1 0.153596 0.032717 4.69470 0.000003
## beta1 0.793257 0.058899 13.46807 0.000000
##
## LogLikelihood : 1591.986
##
## Information Criteria
## ------------------------------------
##
## Akaike -4.2981
## Bayes -4.2606
## Shibata -4.2982
## Hannan-Quinn -4.2836
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.7439 0.3884
## Lag[2*(p+q)+(p+q)-1][5] 3.6247 0.1597
## Lag[4*(p+q)+(p+q)-1][9] 6.0433 0.2495
## d.o.f=2
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.4478 0.5034
## Lag[2*(p+q)+(p+q)-1][5] 1.6607 0.7004
## Lag[4*(p+q)+(p+q)-1][9] 3.8437 0.6154
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 1.435 0.500 2.000 0.2309
## ARCH Lag[5] 1.724 1.440 1.667 0.5354
## ARCH Lag[7] 3.232 2.315 1.543 0.4709
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 1.2291
## Individual Statistics:
## mu 0.26393
## ar1 0.09305
## ma1 0.10640
## omega 0.36595
## alpha1 0.11201
## beta1 0.18128
##
## Asymptotic Critical Values (10% 5% 1%)
4
## 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 0.63219 0.5275
## Negative Sign Bias 0.07133 0.9432
## Positive Sign Bias 1.46263 0.1440
## Joint Effect 2.35943 0.5012
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 44.01 0.0009427
## 2 30 60.05 0.0006091
## 3 40 66.44 0.0039821
## 4 50 80.70 0.0029128
##
##
## Elapsed time : 0.08433294
egfit_vipclothng = ugarchfit(spec = eg_spec, data = returns_vipclothng)
egfit_vipclothng
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : eGARCH(1,1)
## Mean Model : ARFIMA(1,0,1)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.002774 0.001737 1.59715 0.110231
## ar1 0.250542 0.122626 2.04314 0.041039
## ma1 -0.062802 0.126853 -0.49508 0.620546
## omega -0.480214 0.188755 -2.54411 0.010956
## alpha1 0.064347 0.030767 2.09141 0.036492
## beta1 0.933259 0.026289 35.49985 0.000000
## gamma1 0.222122 0.057755 3.84594 0.000120
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.002774 0.002355 1.17765 0.238938
## ar1 0.250542 0.084279 2.97278 0.002951
## ma1 -0.062802 0.083386 -0.75315 0.451359
## omega -0.480214 0.221908 -2.16402 0.030463
5
## alpha1 0.064347 0.028428 2.26347 0.023607
## beta1 0.933259 0.031095 30.01300 0.000000
## gamma1 0.222122 0.057673 3.85143 0.000117
##
## LogLikelihood : 1597.562
##
## Information Criteria
## ------------------------------------
##
## Akaike -4.3105
## Bayes -4.2668
## Shibata -4.3106
## Hannan-Quinn -4.2936
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.2182 0.6404
## Lag[2*(p+q)+(p+q)-1][5] 3.3367 0.2798
## Lag[4*(p+q)+(p+q)-1][9] 5.7843 0.2934
## d.o.f=2
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.489 0.4844
## Lag[2*(p+q)+(p+q)-1][5] 2.224 0.5665
## Lag[4*(p+q)+(p+q)-1][9] 4.769 0.4642
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 2.349 0.500 2.000 0.1254
## ARCH Lag[5] 2.780 1.440 1.667 0.3233
## ARCH Lag[7] 4.438 2.315 1.543 0.2877
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 1.0615
## Individual Statistics:
## mu 0.28199
## ar1 0.07627
## ma1 0.09068
## omega 0.07745
## alpha1 0.25647
## beta1 0.08800
## gamma1 0.18207
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.69 1.9 2.35
## Individual Statistic: 0.35 0.47 0.75
##
6
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 0.3675 0.7134
## Negative Sign Bias 0.5216 0.6021
## Positive Sign Bias 0.9553 0.3397
## Joint Effect 1.1999 0.7530
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 28.02 0.08312
## 2 30 38.91 0.10339
## 3 40 52.68 0.07063
## 4 50 71.35 0.02022
##
##
## Elapsed time : 0.2032249
# Forecasting
ugforecast_vipclothng = ugarchforecast(ugfit_vipclothng, n.ahead=10)
ugforecast_vipclothng
##
## *------------------------------------*
## * GARCH Model Forecast *
## *------------------------------------*
## Model: sGARCH
## Horizon: 10
## Roll Steps: 0
## Out of Sample: 0
##
## 0-roll forecast [T0=2023-10-25]:
## Series Sigma
## T+1 -0.0030145 0.04418
## T+2 0.0008958 0.04357
## T+3 0.0018692 0.04299
## T+4 0.0021115 0.04243
## T+5 0.0021718 0.04190
## T+6 0.0021868 0.04138
## T+7 0.0021906 0.04089
## T+8 0.0021915 0.04042
## T+9 0.0021917 0.03997
## T+10 0.0021918 0.03954
egforecast_vipclothng = ugarchforecast(egfit_vipclothng, n.ahead=10)
egforecast_vipclothng
##
## *------------------------------------*
## * GARCH Model Forecast *
## *------------------------------------*
7
## Model: eGARCH
## Horizon: 10
## Roll Steps: 0
## Out of Sample: 0
##
## 0-roll forecast [T0=2023-10-25]:
## Series Sigma
## T+1 -0.002605 0.03139
## T+2 0.001426 0.03111
## T+3 0.002436 0.03085
## T+4 0.002689 0.03060
## T+5 0.002752 0.03038
## T+6 0.002768 0.03017
## T+7 0.002772 0.02997
## T+8 0.002773 0.02979
## T+9 0.002773 0.02963
## T+10 0.002773 0.02947
