R Notebook

 packages = c('quantmod')

# Install all Packages with Dependencies
install.packages(packages, dependencies = TRUE)

Error in install.packages : Updating loaded packages

# Load all Packages
lapply(packages, require, character.only = TRUE)

[[1]]
[1] TRUE

# Required Packages
packages = c('tseries', 'forecast')

# Install all Packages with Dependencies
install.packages(packages, dependencies = TRUE)

Error in install.packages : Updating loaded packages

# Load all Packages
lapply(packages, require, character.only = TRUE)

[[1]]
[1] TRUE

[[2]]
[1] TRUE

# Required Packages
packages = c('FinTS', 'rugarch')

# Install all Packages with Dependencies
install.packages(packages, dependencies = TRUE)

Error in install.packages : Updating loaded packages

# Load all Packages
lapply(packages, require, character.only = TRUE)

[[1]]
[1] TRUE

[[2]]
[1] TRUE

# Create an environment to store the data
stock_data <- new.env()

# Define the stock symbol
stock_symbol <- 'ADANIENT.BO'  # ADANIENT.BO is the ticker symbol for Adani Enterprises Ltd on BSE

# Define the start and end dates
start_date <- as.Date('2019-01-01')
end_date <- as.Date('2023-12-31')

# Fetch the stock data
getSymbols(Symbols = stock_symbol, src = 'yahoo', from = start_date, to = end_date, env = stock_data)

Warning: ADANIENT.BO 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] "ADANIENT.BO"

# Extract closing prices
adani_prices <- Cl(stock_data[[stock_symbol]])

# Remove missing values
adani_prices <- na.omit(adani_prices)

# View the resulting closing prices
head(adani_prices)

           ADANIENT.BO.Close
2019-01-01            157.20
2019-01-02            154.75
2019-01-03            152.55
2019-01-04            152.35
2019-01-07            151.00
2019-01-08            153.40

plot(adani_prices)

# Check the class of the stock_price object
class(adani_prices)

[1] "xts" "zoo"

# Augmented Dickey-Fuller (ADF) Test for Stationarity with Adani Enterprises Ltd on BSE Data
# *******************************************************************

# Perform Augmented Dickey-Fuller (ADF) Test
adf_result <- adf.test(adani_prices)

# Print the ADF test result
print(adf_result)

    Augmented Dickey-Fuller Test

data:  adani_prices
Dickey-Fuller = -2.4007, Lag order = 10, p-value = 0.4087
alternative hypothesis: stationary

#In this case, since the p-value (0.4087) is greater than a typical significance
#level like 0.05, we fail to reject the null hypothesis.
#Therefore, we do not have enough evidence to conclude that the time series is stationary.

adani_ds = diff(adani_prices);  
adani_ds

           ADANIENT.BO.Close
2019-01-01                NA
2019-01-02        -2.4499969
2019-01-03        -2.1999969
2019-01-04        -0.1999969
2019-01-07        -1.3500061
2019-01-08         2.3999939
2019-01-09        -4.0999908
2019-01-10         1.8000031
2019-01-11         0.2999878
2019-01-14        -3.0999908
       ...                  
2023-12-15        96.1499023
2023-12-18       -11.0000000
2023-12-19       -38.1999512
2023-12-20      -155.5000000
2023-12-21        16.0500488
2023-12-22         5.7998047
2023-12-26        61.4001465
2023-12-27       -26.0000000
2023-12-28       -30.3000488
2023-12-29        36.5000000

  # Adani Enterprises Ltd  (First)return Difference Time-Series

adani_ds=na.omit(adani_ds)
 
adf_test_adani_ds = adf.test(adani_ds); adf_test_adani_ds

Warning: p-value smaller than printed p-value

    Augmented Dickey-Fuller Test

data:  adani_ds
Dickey-Fuller = -9.532, Lag order = 10, p-value = 0.01
alternative hypothesis: stationary

# Ljung-Box Test for Autocorrelation -  Data
# ***********************************************

lb_test_adani_ds = Box.test(adani_ds)# Inference : adani Difference (Stationary)
 lb_test_adani_ds

    Box-Pierce test

data:  adani_ds
X-squared = 16.087, df = 1, p-value = 6.049e-05

#In this case, since the p-value (4.294e-05) is much smaller than a typical significance level like 0.05,
#we reject the null hypothesis. Therefore, we have evidence to suggest that there is significant autocorrelation in the time series. | NULL: No Auto correlation | Alternate: Auto Correlation

#Autocorrelation Function (ACF) | Partial Autocorrelation Function (PACF)
# *****************************************************************************

acf(adani_prices) # ACF of adani Series

pacf(adani_prices) # PACF of adani Series

acf(adani_ds) # ACF of adani Series

pacf(adani_ds) # PACF of adani Difference (Stationary) Series

arma_pq_adani_ds = auto.arima(adani_ds); arma_pq_adani_ds

Series: adani_ds 
ARIMA(1,0,1) with zero mean 

Coefficients:
          ar1     ma1
      -0.4124  0.5489
s.e.   0.1092  0.0989

sigma^2 = 3478:  log likelihood = -6676.7
AIC=13359.4   AICc=13359.42   BIC=13374.71

adani_ds_fpq = forecast(arma_pq_adani_ds, h = 500)
plot(adani_ds_fpq)

lb_test_arma_pq_adani_ds = Box.test(arma_pq_adani_ds$residuals); lb_test_arma_pq_adani_ds

    Box-Pierce test

data:  arma_pq_adani_ds$residuals
X-squared = 0.065799, df = 1, p-value = 0.7976

# Test for Volatility Clustering or Heteroskedasticity: Box Test
adani_ret_sq = arma_pq_adani_ds$residuals^2 # Residual Variance (Since Mean Returns is approx. 0)
plot(adani_ret_sq)

adani_ret_sq_box_test = Box.test(adani_ret_sq,lag = 1 ) # H0: Return Variance Series is Not Serially Correlated
adani_ret_sq_box_test # Inference : Return Variance Series is Autocorrelated (Has Volatility Clustering)

    Box-Pierce test

data:  adani_ret_sq
X-squared = 73.953, df = 1, p-value < 2.2e-16

# Test for Volatility Clustering or Heteroskedasticity: ARCH Test
adani_ret_arch_test = ArchTest(arma_pq_adani_ds$residuals^2,lag = 1) # H0: No ARCH Effects
adani_ret_arch_test # Inference : Return Series is Heteroskedastic (Has Volatility Clustering)

    ARCH LM-test; Null hypothesis: no ARCH effects

data:  arma_pq_adani_ds$residuals^2
Chi-squared = 8.8783, df = 1, p-value = 0.002886

# GARCH Model
garch_model1 = ugarchspec(variance.model = list(model = 'sGARCH', garchOrder = c(1,1)), mean.model = list(armaOrder = c(1,1), include.mean = TRUE))
adani_ret_garch1 = ugarchfit(garch_model1, data = arma_pq_adani_ds$residuals^2); adani_ret_garch1

*---------------------------------*
*          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     3.4699e+03  6.1907e+02    5.605        0
ar1    8.9790e-01  2.2387e-02   40.108        0
ma1    3.2756e-01  4.2282e-02    7.747        0
omega  6.2943e+05  4.8466e+04   12.987        0
alpha1 9.3997e-02  4.4700e-03   21.031        0
beta1  9.0500e-01  2.5030e-03  361.602        0

Robust Standard Errors:
         Estimate  Std. Error  t value Pr(>|t|)
mu     3.4699e+03  2.5313e+03  1.37078 0.170442
ar1    8.9790e-01  2.4815e-02 36.18427 0.000000
ma1    3.2756e-01  4.1287e-01  0.79337 0.427563
omega  6.2943e+05  1.4553e+05  4.32516 0.000015
alpha1 9.3997e-02  1.8087e-02  5.19680 0.000000
beta1  9.0500e-01  1.8557e-02 48.77013 0.000000

LogLikelihood : -12321.53 

Information Criteria
------------------------------------
                   
Akaike       20.292
Bayes        20.317
Shibata      20.292
Hannan-Quinn 20.302

Weighted Ljung-Box Test on Standardized Residuals
------------------------------------
                        statistic p-value
Lag[1]                      187.7       0
Lag[2*(p+q)+(p+q)-1][5]     196.1       0
Lag[4*(p+q)+(p+q)-1][9]     198.8       0
d.o.f=2
H0 : No serial correlation

Weighted Ljung-Box Test on Standardized Squared Residuals
------------------------------------
                        statistic p-value
Lag[1]                      5.377 0.02040
Lag[2*(p+q)+(p+q)-1][5]     6.411 0.07187
Lag[4*(p+q)+(p+q)-1][9]     7.113 0.18986
d.o.f=2

Weighted ARCH LM Tests
------------------------------------
            Statistic Shape Scale P-Value
ARCH Lag[3]     1.146 0.500 2.000  0.2844
ARCH Lag[5]     2.040 1.440 1.667  0.4625
ARCH Lag[7]     2.206 2.315 1.543  0.6736

Nyblom stability test
------------------------------------
Joint Statistic:  -147.6846
Individual Statistics:               
mu     18.93294
ar1     0.07298
ma1     0.11990
omega  39.02396
alpha1  0.24817
beta1   0.30111

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
------------------------------------

Adjusted Pearson Goodness-of-Fit Test:
------------------------------------
  group statistic p-value(g-1)
1    20      5113            0
2    30      4851            0
3    40      6251            0
4    50      5244            0


Elapsed time : 0.336184 

# GARCH Forecast
adani_ret_garch_forecast1 = ugarchforecast(adani_ret_garch1, n.ahead = 500); adani_ret_garch_forecast1

*------------------------------------*
*       GARCH Model Forecast         *
*------------------------------------*
Model: sGARCH
Horizon: 500
Roll Steps: 0
Out of Sample: 0

0-roll forecast [T0=1215-01-01]:
      Series Sigma
T+1     1630 32706
T+2     1818 32700
T+3     1987 32693
T+4     2138 32686
T+5     2274 32679
T+6     2396 32673
T+7     2506 32666
T+8     2604 32659
T+9     2693 32653
T+10    2772 32646
T+11    2843 32639
T+12    2907 32633
T+13    2965 32626
T+14    3016 32619
T+15    3063 32613
T+16    3104 32606
T+17    3141 32599
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T+473   3470 30066
T+474   3470 30062
T+475   3470 30057
T+476   3470 30053
T+477   3470 30048
T+478   3470 30044
T+479   3470 30039
T+480   3470 30034
T+481   3470 30030
T+482   3470 30025
T+483   3470 30021
T+484   3470 30016
T+485   3470 30012
T+486   3470 30007
T+487   3470 30003
T+488   3470 29998
T+489   3470 29994
T+490   3470 29989
T+491   3470 29985
T+492   3470 29980
T+493   3470 29976
T+494   3470 29971
T+495   3470 29967
T+496   3470 29962
T+497   3470 29958
T+498   3470 29953
T+499   3470 29949
T+500   3470 29944

plot(adani_ret_garch_forecast1, which = 1)

# Plot the specified aspect of the GARCH forecast
plot(adani_ret_garch_forecast1, which = 3)