Odtnhj

I am estimating a VAR model to later understand the relationship between my physical prices and financial prices. I work on commodities. I have followed the procedure below but I am not sure it is right. Also, I am not sure what to do since I found that there are ARCH effects.

Can someone please tell me if my methodology is correct? And if the fact that I have ARCH effects is a problem for my VAR and/or my Granger causality test?

##We verify stationarity of the price series:
#if not stationarity, we test co integration. If it is cointegrated, we estimate a VECM.
#If not stationary, we test co integration. If it is not cointegrated,
# I stationnarize the variables and estimate a VAR. 
library(tseries)

adf.test(log_close_wk)
kpss.test(log_close_wk, null="Trend")
adf.test(log_price_wk)
kpss.test(log_price_wk, null="Trend")

#the null hypothesis of the existence of a unit root is NOT rejected hence the series
#is NOT stationary (there is a trend)

#Stationarity can come from the trend also, which is why I test with a KPSS test



#Now see if the spot and futures are partially cointegrated: 



library(egcm)

egcm_finance <- egcm(log_close_wk, matrix(log_price_wk),include.const = T)
plot(egcm_finance$residuals,type = "l")
library(partialCI)
PCI_Spot_Futures<-fit.pci(log_close_wk, matrix(log_price_wk),
 pci_opt_method = c("jp"),
 par_model =c("ar1"), lambda = 0,
 robust = FALSE, nu = 5)


test.pci(log_close_wk, matrix(log_price_wk), irobust=TRUE, alpha = 0.05, null_hyp =
 c( "ar1"),imethod = "wilk",
 pci_opt_method = c("jp"))

test.pci(log_close_wk, matrix(log_price_wk), irobust=TRUE, alpha = 0.05, null_hyp =
 c( "rw"),imethod = "wilk",
 pci_opt_method = c("jp"))


# a time series is classified as partially cointegrated, iif the random
#walk as well as the AR(1)-hypotheses are rejected. The p-value of 0.000 for 
#both null model indicates that both are partially cointegrated in the 
#considered period of time.WHICH IS THE CASE FOR ME!


##NOw we can run a VECM:
#I create dataframe with the couples of prices : 
df_cl<-cbind(log_close_wk,log_price_wk)

library(vars)
#We find the lag order:
VARselect(df_cl) #4 lags / or 2 lags

library(tsDyn)
VECM(df_cl,4)
VECM(df_cl,2)


#Here my ECT coefficient is positive, 
#It implies that the process it not converging in the long run. 
#!It should be negative!!

#So we stationarize our variables and estimate a VAR model. 
log_close_wk<-diff(log_close_wk)
log_price_wk<-diff(log_price_wk)


adf.test(log_close_exp_wk)
adf.test(log_price_wk)
###They are now stationary after one difference. 
df_cl<-cbind(log_close_wk,log_price_wk)


#WE NOW ESTIMATE A VAR model:
#Number of lags: 
library(vars)
#We find the lag order:
VARselect(df_cl) #5 lags / or1

fit<-VAR(df_cl,5)
fit
fit1<-VAR(df_cl,1)
fit1

#I should now test for serial autocorrelation using the Portmanteau test: 


serial.test(fit, lags.pt = 10, type = "PT.asymptotic")
serial.test(fit1, lags.pt = 10, type = "PT.asymptotic") 
#WE REJECT the hyp. of no serial correlation
#So we keep the model with no serial correlation : 
#fit

#ARCH test (Autoregressive conditional heteroscedasdicity)

arch.test(fit, lags.multi = 10)
#so my data is conditionally heteroskedastic
#IS THAT A PROBLEM?????

summary(fit)
summary(fit2)
summary(fit3)

#Should I get rid of the ARCH effects? 

#Granger Causality test
#Does CLOSE granger cause PRICE? ##BETTER?
grangertest(log_price_wk~ log_close_wk, order = 5)

#Does PRICE granger cause CLOSE?
grangertest(log_close_wk~ log_price_wk, order = 5)
#null hypothesis is rejected for both : i reject the hyp of no granger 
causality(small pvalue)