GARCH Uber
Jay Khedekar
27/03/2021
Packages
library(tidyverse)
library(rugarch)
library(rmgarch)
library(quantmod)
library(xts)Loading Data
Creating a clean data frame from the given data
df <- read.csv("uber_data.csv")
df$Date <- as.Date(df$Date, format = "%d-%m-%Y")
glimpse(df)## Rows: 463
## Columns: 7
## $ Date <date> 2019-05-10, 2019-05-13, 2019-05-14, 2019-05-15, 2019-05-16,...
## $ Open <dbl> 42.000, 38.790, 38.310, 39.370, 41.480, 41.980, 41.190, 42.0...
## $ High <dbl> 45.000, 39.240, 39.960, 41.880, 44.060, 43.290, 41.680, 42.2...
## $ Low <dbl> 41.060, 36.080, 36.850, 38.950, 41.250, 41.270, 39.460, 41.2...
## $ Close <dbl> 41.57, 37.10, 39.96, 41.29, 43.00, 41.91, 41.59, 41.50, 41.2...
## $ Volume <int> 186322500, 79442400, 46661100, 36086100, 38115500, 20225700,...
## $ Adj <dbl> 41.57, 37.10, 39.96, 41.29, 43.00, 41.91, 41.59, 41.50, 41.2...head(df)## Date Open High Low Close Volume Adj
## 1 2019-05-10 42.00 45.00 41.06 41.57 186322500 41.57
## 2 2019-05-13 38.79 39.24 36.08 37.10 79442400 37.10
## 3 2019-05-14 38.31 39.96 36.85 39.96 46661100 39.96
## 4 2019-05-15 39.37 41.88 38.95 41.29 36086100 41.29
## 5 2019-05-16 41.48 44.06 41.25 43.00 38115500 43.00
## 6 2019-05-17 41.98 43.29 41.27 41.91 20225700 41.91Initial plotting
#Setting date column as row indexes
rownames(df) <- df[,1]
#converting data frame to xts object for R to know it's time series
df<- xts(df[,-1], df$Date)
chartSeries(df)
Checking daily returns
df.returns <- dailyReturn(df)
colnames(df.returns) <- c("return")
chartSeries(df.returns)
Specifying GARCH Model
It’s in this you can change your model specification like Mean Model from ARIMA(1,0,1) to something you prefer.
ug_spec = ugarchspec()
#If you want to change ARIMA spec. Remove the comment sign and change the parameters
#ug_spec <- ugarchspec(mean.model=list(armaOrder=c(1,0)))
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 : FALSEModel fit
ugfit = ugarchfit(spec = ug_spec, data = df.returns)
ugfit##
## *---------------------------------*
## * 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 0.002639 0.001472 1.79285 0.072998
## ar1 0.321605 0.901716 0.35666 0.721347
## ma1 -0.309773 0.905751 -0.34201 0.732346
## omega 0.000229 0.000068 3.38496 0.000712
## alpha1 0.236495 0.058670 4.03095 0.000056
## beta1 0.592553 0.083886 7.06381 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.002639 0.001467 1.7995 0.071944
## ar1 0.321605 0.205104 1.5680 0.116879
## ma1 -0.309773 0.192572 -1.6086 0.107701
## omega 0.000229 0.000071 3.2073 0.001340
## alpha1 0.236495 0.087062 2.7164 0.006600
## beta1 0.592553 0.089510 6.6200 0.000000
##
## LogLikelihood : 909.5444
##
## Information Criteria
## ------------------------------------
##
## Akaike -3.9030
## Bayes -3.8494
## Shibata -3.9033
## Hannan-Quinn -3.8819
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.004495 0.9465
## Lag[2*(p+q)+(p+q)-1][5] 3.075429 0.4253
## Lag[4*(p+q)+(p+q)-1][9] 5.081392 0.4353
## d.o.f=2
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 8.815e-05 0.9925
## Lag[2*(p+q)+(p+q)-1][5] 2.418e-01 0.9892
## Lag[4*(p+q)+(p+q)-1][9] 1.331e+00 0.9682
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.1585 0.500 2.000 0.6905
## ARCH Lag[5] 0.4715 1.440 1.667 0.8920
## ARCH Lag[7] 1.2863 2.315 1.543 0.8630
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 0.6926
## Individual Statistics:
## mu 0.18993
## ar1 0.08423
## ma1 0.08404
## omega 0.19881
## alpha1 0.17949
## beta1 0.16224
##
## 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 1.507 0.13260
## Negative Sign Bias 2.557 0.01087 **
## Positive Sign Bias 1.568 0.11756
## Joint Effect 9.348 0.02500 **
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 27.93 0.08481
## 2 30 40.26 0.07975
## 3 40 48.88 0.13347
## 4 50 71.67 0.01903
##
##
## Elapsed time : 0.3188Data points that can be taken from the above model
names(ugfit@fit)## [1] "hessian" "cvar" "var" "sigma"
## [5] "condH" "z" "LLH" "log.likelihoods"
## [9] "residuals" "coef" "robust.cvar" "A"
## [13] "B" "scores" "se.coef" "tval"
## [17] "matcoef" "robust.se.coef" "robust.tval" "robust.matcoef"
## [21] "fitted.values" "convergence" "kappa" "persistence"
## [25] "timer" "ipars" "solver"Coefficients
ugfit@fit$coef## mu ar1 ma1 omega alpha1
## 0.0026390092 0.3216047516 -0.3097728219 0.0002288351 0.2364945570
## beta1
## 0.5925527160Plotting residual plot
# save the estimated conditional variances
ug_var <- ugfit@fit$var
# save the estimated squared residuals
ug_res2 <- (ugfit@fit$residuals)^2
plot(ug_res2, type = "l")
lines(ug_var, col = "green")
Forecasting
ugfore <- ugarchforecast(ugfit, n.ahead = 10)
ugfore##
## *------------------------------------*
## * GARCH Model Forecast *
## *------------------------------------*
## Model: sGARCH
## Horizon: 10
## Roll Steps: 0
## Out of Sample: 0
##
## 0-roll forecast [T0=2021-03-11]:
## Series Sigma
## T+1 0.003048 0.03499
## T+2 0.002771 0.03527
## T+3 0.002681 0.03550
## T+4 0.002653 0.03569
## T+5 0.002643 0.03584
## T+6 0.002640 0.03597
## T+7 0.002639 0.03608
## T+8 0.002639 0.03617
## T+9 0.002639 0.03624
## T+10 0.002639 0.03630ug_f <- ugfore@forecast$sigmaFor
plot(ug_f, type = "l")
ug_var_t <- c(tail(ug_var,20),rep(NA,10)) # gets the last 20 observations
ug_res2_t <- c(tail(ug_res2,20),rep(NA,10)) # gets the last 20 observations
ug_f <- c(rep(NA,20),(ug_f)^2)
plot(ug_res2_t, type = "l")
lines(ug_f, col = "orange")
lines(ug_var_t, col = "green")
Example 2
Loading Data
Creating a clean data frame from the given data
df.2 <- read.csv("example2.csv")
df.2$Date <- as.Date(df.2$Date, format = "%d-%m-%Y")
colnames(df.2) <- c("Date", "adjusted")
glimpse(df.2)## Rows: 465
## Columns: 2
## $ Date <date> 2019-05-10, 2019-05-13, 2019-05-14, 2019-05-15, 2019-05-1...
## $ adjusted <dbl> 41.57, 37.10, 39.96, 41.29, 43.00, 41.91, 41.59, 41.50, 41...#Removing NA values
df.2 <- na.omit(df.2)
#Setting date column as row indexes
rownames(df.2) <- df.2[,1]
#converting data frame to xts object for R to know it's time series
df.2<- xts(df.2[,-1], df.2$Date)
chartSeries(df.2)
df.returns.2 <- dailyReturn(df.2)
colnames(df.returns.2) <- c("return")
chartSeries(df.returns.2)
## Model fit
ugfit.2 = ugarchfit(spec = ug_spec, data = df.returns.2)
ugfit.2##
## *---------------------------------*
## * 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 0.002606 0.001447 1.8009 0.071725
## ar1 -0.794624 0.680320 -1.1680 0.242801
## ma1 0.785901 0.694128 1.1322 0.257544
## omega 0.000228 0.000067 3.4004 0.000673
## alpha1 0.233026 0.057624 4.0439 0.000053
## beta1 0.595774 0.082998 7.1781 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.002606 0.001465 1.7786 0.075313
## ar1 -0.794624 0.346383 -2.2941 0.021787
## ma1 0.785901 0.351437 2.2363 0.025335
## omega 0.000228 0.000071 3.2156 0.001302
## alpha1 0.233026 0.085402 2.7286 0.006361
## beta1 0.595774 0.087598 6.8012 0.000000
##
## LogLikelihood : 909.4766
##
## Information Criteria
## ------------------------------------
##
## Akaike -3.9027
## Bayes -3.8491
## Shibata -3.9030
## Hannan-Quinn -3.8816
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.1692 0.6808
## Lag[2*(p+q)+(p+q)-1][5] 3.2321 0.3344
## Lag[4*(p+q)+(p+q)-1][9] 5.3673 0.3739
## d.o.f=2
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.002107 0.9634
## Lag[2*(p+q)+(p+q)-1][5] 0.240521 0.9894
## Lag[4*(p+q)+(p+q)-1][9] 1.315906 0.9692
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.2042 0.500 2.000 0.6513
## ARCH Lag[5] 0.4545 1.440 1.667 0.8970
## ARCH Lag[7] 1.2574 2.315 1.543 0.8684
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 0.719
## Individual Statistics:
## mu 0.20656
## ar1 0.04110
## ma1 0.04014
## omega 0.20038
## alpha1 0.18320
## beta1 0.16218
##
## 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 1.366 0.17263
## Negative Sign Bias 2.414 0.01618 **
## Positive Sign Bias 1.542 0.12382
## Joint Effect 8.629 0.03466 **
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 27.24 0.09924
## 2 30 33.13 0.27237
## 3 40 61.67 0.01183
## 4 50 70.59 0.02336
##
##
## Elapsed time : 0.3416889
#### Data points that can be taken from the above model
names(ugfit.2@fit)## [1] "hessian" "cvar" "var" "sigma"
## [5] "condH" "z" "LLH" "log.likelihoods"
## [9] "residuals" "coef" "robust.cvar" "A"
## [13] "B" "scores" "se.coef" "tval"
## [17] "matcoef" "robust.se.coef" "robust.tval" "robust.matcoef"
## [21] "fitted.values" "convergence" "kappa" "persistence"
## [25] "timer" "ipars" "solver"Coefficients
ugfit.2@fit$coef## mu ar1 ma1 omega alpha1
## 0.0026061520 -0.7946241498 0.7859013778 0.0002277885 0.2330256877
## beta1
## 0.5957740135Plotting residual plot
# save the estimated conditional variances
ug_var2 <- ugfit.2@fit$var
# save the estimated squared residuals
ug_res22 <- (ugfit.2@fit$residuals)^2
plot(ug_res22, type = "l")
lines(ug_var2, col = "green")
Forecasting
ugfore2 <- ugarchforecast(ugfit.2, n.ahead = 10)
ugfore2##
## *------------------------------------*
## * GARCH Model Forecast *
## *------------------------------------*
## Model: sGARCH
## Horizon: 10
## Roll Steps: 0
## Out of Sample: 0
##
## 0-roll forecast [T0=2021-03-11]:
## Series Sigma
## T+1 0.001913 0.03494
## T+2 0.003157 0.03521
## T+3 0.002169 0.03543
## T+4 0.002954 0.03561
## T+5 0.002330 0.03576
## T+6 0.002826 0.03589
## T+7 0.002432 0.03599
## T+8 0.002745 0.03607
## T+9 0.002496 0.03614
## T+10 0.002694 0.03620ug_f2 <- ugfore2@forecast$sigmaFor
plot(ug_f2, type = "l")
ug_var_t2 <- c(tail(ug_var2,20),rep(NA,10)) # gets the last 20 observations
ug_res2_t2 <- c(tail(ug_res22,20),rep(NA,10)) # gets the last 20 observations
ug_f2 <- c(rep(NA,20),(ug_f2)^2)
plot(ug_res2_t2, type = "l")
lines(ug_f2, col = "orange")
lines(ug_var_t2, col = "green")