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HAR-NN-library.R
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library(neuralnet)
# r : maximum iteration number needed to converge the coefficients of NN-based HAR models.
HAR_NN.sig <- function(RV.data,i,r,printcoeffi){
## Data handling for fitting HAR model.
Rv.d.y <- as.numeric(as.vector(RV.data[c(2:((nrow(RV.data)-i)+1)),2])) ## from 2 (daily daily time point) ~ (nrow(RV.data)-100)+1 (daily daily time point).
Rv.d.x1 <- as.numeric(as.vector(RV.data[c(1:(nrow(RV.data)-i)),2])) ## from 1 (daily daily time point) ~ (nrow(RV.data)-100) (daily daily time point).
## Weekly RV.
Rv.w <- numeric((nrow(RV.data)-i))
for(j in 23:(nrow(RV.data)-i)){
Rv.w[j] <- (Rv.d.x1[j]+Rv.d.x1[j-1]+Rv.d.x1[j-2]+Rv.d.x1[j-3]+Rv.d.x1[j-4])/5
}
## Monthly RV.
Rv.m <- numeric((nrow(RV.data)-i))
for(q in 23:(nrow(RV.data)-i)){
Rv.m[q] <- (Rv.d.x1[q]+Rv.d.x1[q-1]+Rv.d.x1[q-2]+Rv.d.x1[q-3]
+Rv.d.x1[q-4]+Rv.d.x1[q-5]+Rv.d.x1[q-6]+Rv.d.x1[q-7]
+Rv.d.x1[q-8]+Rv.d.x1[q-9]+Rv.d.x1[q-10]+Rv.d.x1[q-11]
+Rv.d.x1[q-12]+Rv.d.x1[q-13]+Rv.d.x1[q-14]+Rv.d.x1[q-15]
+Rv.d.x1[q-16]+Rv.d.x1[q-17]+Rv.d.x1[q-18]+Rv.d.x1[q-19]
+Rv.d.x1[q-20]+Rv.d.x1[q-21])/22
}
## We need to make the data frame composed of { RV_[t+1d]^(d), RV_[t]^(d), RV_[t]^(w), RV_[t]^(m) } to fit the HAR model to the data.
Rv.d.y2 <- Rv.d.y[23:(nrow(RV.data)-i)]
Rv.d.x1.2 <- Rv.d.x1[23:(nrow(RV.data)-i)]
Rv.w.2 <- Rv.w[23:(nrow(RV.data)-i)]
Rv.m.2 <- Rv.m[23:(nrow(RV.data)-i)]
## Firstly, cbind { Rv_[t+1d]^(d), Rv[t]^(d), Rv[t]^(w), Rv[t]^(m) }.
tomorrow.today.week.month.data.frame <- cbind(Rv.d.y2,Rv.d.x1.2,Rv.w.2,Rv.m.2)
## transform to the data frame.
tomorrow.today.week.month.data.frame <-as.data.frame(tomorrow.today.week.month.data.frame)
colnames(tomorrow.today.week.month.data.frame) <- c("Rv(d)(t+1d)","Rv(d)(t)","Rv(w)(t)","Rv(m)(t)")
## tomorrow.today.week.month.data.frame : A complete data set to run a regression model with 22 points removed.
## Since there are a lot of data, there is no serious problem even if the data from 1th to 22th daily daily time point are removed.
########### STEP 1 : initial HAR model fitting to data set.
initial.HAR.model.fit <- lm(Rv.d.y2~Rv.d.x1.2+Rv.w.2+Rv.m.2)
initial.HAR.model.fit.coeffi <- initial.HAR.model.fit$coefficients
initial.HAR.model.fit.coeffi <- as.vector(initial.HAR.model.fit.coeffi)
## In here, our idea is fitting the single hidden layer feedforward NN model (with 'q' : 5) to
## residuals obtained from fitting HAR model to data set
## with Rv.d.x1.2(=Rv(t)(d)),Rv.w.2(=Rv(t)(w)),Rv.m.2(=Rv(t)(m)).
## Definition of residual data set (Note that when we set the residual set, we need to remove constant term estimated from fitting HAR model to KOSPI RV series.)
## That is, residual in this part is defined as follow : RV_[t+1d]^(d) - ( beta(d)^(hat)*RV_[t]^(d) + beta(w)^(hat)*RV_[t]^(w) + beta(m)^(hat)*RV_[t]^(m) ).
## Why we define the residual data set like above explanation is to make sure that the identifiability of constant term in the NN based HAR models.
## ¡Ø Of course, there is only one constant term in the HAR-NN model, but strictly speaking, two constant terms obtained by two different model fits (HAR & NN, respectively) are added together to form one constant term.
## initial.res : RV_[t+1d]^(d) - ( beta(d)^(hat)*RV_[t]^(d) + beta(w)^(hat)*RV_[t]^(w) + beta(m)^(hat)*RV_[t]^(m) )
initial.res <- Rv.d.y2-(initial.HAR.model.fit.coeffi[2]*Rv.d.x1.2+initial.HAR.model.fit.coeffi[3]*Rv.w.2+initial.HAR.model.fit.coeffi[4]*Rv.m.2)
initial.res.today.week.month.data.frame<- cbind(initial.res,Rv.d.x1.2,Rv.w.2,Rv.m.2)
## Above data set is composed of (initial.res, Rv(t)(d), Rv(t)(w), Rv(t)(m) )
initial.res.today.week.month.data.frame <-as.data.frame(initial.res.today.week.month.data.frame)
colnames(initial.res.today.week.month.data.frame) <- c("initial.res","Rv(d)(t)","Rv(w)(t)","Rv(m)(t)")
########### STEP 2 : Fitting the single hidden layer feedforward NN model (with 'q' : 5) to
########### initial residuals obtained from STEP 1.
initial.NN.model.fit.to.initial.res <- neuralnet(initial.res~Rv.d.x1.2+Rv.w.2+Rv.m.2,data=initial.res.today.week.month.data.frame,
hidden=5,linear.output=T)
## Coefficent values for RV_[t]^(d) (numeric vector for storing updated values.).
HAR.model.coeffi.beta_d.vector <- numeric(r)
u.HAR.model.coeffi.beta_d.vector <- numeric(r) # 'u' : updated.
## Coefficent values for RV_[t]^(w) (numeric vector for storing updated values.).
HAR.model.coeffi.beta_w.vector <- numeric(r)
u.HAR.model.coeffi.beta_w.vector <- numeric(r)
## Coefficent values for RV_[t]^(m) (numeric vector for storing updated values.).
HAR.model.coeffi.beta_m.vector <- numeric(r)
u.HAR.model.coeffi.beta_m.vector <- numeric(r)
########### STEP 3 : Fit the HAR model again to the [ Rv_[t+1d]^(d) - fitted values obtained from step 2 ].
for(p in 1:r){
## Re-fit the HAR model to the [ Rv_[t+1d]^(d) - fitted values obtained from step 2 ].
refit.HAR.model <- lm((Rv.d.y2 - initial.NN.model.fit.to.initial.res$net.result[[1]])~Rv.d.x1.2+Rv.w.2+Rv.m.2)
## Coefficient vector corresponding to the HAR model part in the HAR-NN model with respect to the above refitted HAR model's coefficients.
HAR.model.coeffi.refitted <-(refit.HAR.model$coefficients)
HAR.model.coeffi.refitted <- as.vector(HAR.model.coeffi.refitted)
HAR.model.coeffi.beta_d.vector[p] <- HAR.model.coeffi.refitted[2]
HAR.model.coeffi.beta_w.vector[p] <- HAR.model.coeffi.refitted[3]
HAR.model.coeffi.beta_m.vector[p] <- HAR.model.coeffi.refitted[4]
########### STEP 4 : Fit the single hidden layer feedforward NN model (with 'q' : 5) again to the
########### residuals obtained from re-fitting the HAR model in STEP 3.
## Definition of res2 data set. (Form is similar to 'initial.res' in STEP 1.)
res2 <- Rv.d.y2-(HAR.model.coeffi.refitted[2]*Rv.d.x1.2+HAR.model.coeffi.refitted[3]*Rv.w.2+HAR.model.coeffi.refitted[4]*Rv.m.2)
second.res.today.week.month.data.frame<- cbind(res2,Rv.d.x1.2,Rv.w.2,Rv.m.2)
## Above data set is composed of ( res2, Rv(t)(d), Rv(t)(w),Rv(t)(m) ).
second.res.today.week.month.data.frame <-as.data.frame(second.res.today.week.month.data.frame)
colnames(second.res.today.week.month.data.frame) <- c("res2","Rv(d)(t)","Rv(w)(t)","Rv(m)(t)")
########### Re-Fit the NN model to the residuals (=res2) obtained from re-fitting the HAR model in STEP 3.
refit.NN.to.res2 <- neuralnet(res2~Rv.d.x1.2+Rv.w.2+Rv.m.2,data=second.res.today.week.month.data.frame,
hidden=5,linear.output=T)
########### Return to STEP 3 : Fit the HAR model again to the [ RV_[t+1d]^(d) - fitted values obtained from step 4 ].
# Re-fit the HAR model to the [ RV_(t+1d)^(d) - fitted values obtained from step 4 ].
rerefit.HAR <- lm((Rv.d.y2 - refit.NN.to.res2$net.result[[1]])~Rv.d.x1.2+Rv.w.2+Rv.m.2)
### Coefficient vector corresponding to the HAR model part in the HAR-NN model.
HAR.model.coeffi.rerefitted <-(rerefit.HAR$coefficients)
HAR.model.coeffi.rerefitted <- as.vector(HAR.model.coeffi.rerefitted)
## Updataed coefficient vectors corresponding to the HAR model part in the HAR-NN model.
u.HAR.model.coeffi.beta_d.vector[p] <- HAR.model.coeffi.rerefitted[2]
u.HAR.model.coeffi.beta_w.vector[p] <- HAR.model.coeffi.rerefitted[3]
u.HAR.model.coeffi.beta_m.vector[p] <- HAR.model.coeffi.rerefitted[4]
## The convergence condition is set when the absolute difference between the
## updated coefficients of the HAR model part in the HAR-NN model and the coefficients of the HAR model part in the same model
## before being updated is smaller than 0.05 in each coefficient. '0.05' is the limit of the error we set in this real data analyis.
diff1=abs(HAR.model.coeffi.beta_d.vector[p]-u.HAR.model.coeffi.beta_d.vector[p])
diff2=abs(HAR.model.coeffi.beta_w.vector[p]-u.HAR.model.coeffi.beta_w.vector[p])
diff3=abs(HAR.model.coeffi.beta_m.vector[p]-u.HAR.model.coeffi.beta_m.vector[p])
if( (diff1<0.05) && (diff2<0.05) && (diff3<0.05) )
{
final.beta_d.coeffi <- as.numeric(u.HAR.model.coeffi.beta_d.vector[p])
final.beta_w.coeffi <- as.numeric(u.HAR.model.coeffi.beta_w.vector[p])
final.beta_m.coeffi <- as.numeric(u.HAR.model.coeffi.beta_m.vector[p])
break
}
########### Repeat the above steps (STEP3-> STEP4-> STEP3) repeatedly until the
########### coefficients ( Beta(d), Beta(w), Beta(m) ) of the HAR model part in the HAR-NN model converge with respect to above criteria.
}
## Final.res data set (This is defined with the use of the converged coefficients of the HAR model part in the HAR-NN model.)
final.res <-(Rv.d.y2-(final.beta_d.coeffi*Rv.d.x1.2+final.beta_w.coeffi*Rv.w.2+final.beta_m.coeffi*Rv.m.2))
final.res.today.week.month.data.frame <- cbind(final.res,Rv.d.x1.2,Rv.w.2,Rv.m.2)
## Above data set is filled with ( final.res, Rv(t)(d), Rv(t)(w), Rv(t)(m) ).
final.res.today.week.month.data.frame <- as.data.frame(final.res.today.week.month.data.frame)
colnames(final.res.today.week.month.data.frame) <- c("final.res","Rv(d)(t)","Rv(w)(t)","Rv(m)(t)")
########### STEP 5 : Fitting the single hidden layer feedforward NN model (with 'q' : 5) lastly to
########### the final residuals (final.res) obtained from re-fitting the HAR model in the previous step with the convergent coefficients.
########### Then, we can get convergent coefficients of the NN model part in the HAR-NN model.
final.NN.fit.to.final.res <- neuralnet(final.res ~ Rv.d.x1.2+Rv.w.2+Rv.m.2,data=final.res.today.week.month.data.frame,
hidden=5,linear.output=T)
########### After implementing the above line, we can make sure that all of the coefficients in the HAR-NN model can be (globally or locally) converged.
########### sigmoid function values.
a1 <- (1/(1+exp(-(final.NN.fit.to.final.res$weights[[1]][[1]][,1][1] + final.NN.fit.to.final.res$weights[[1]][[1]][,1][2]*as.numeric(RV.data[nrow(RV.data)-i,2]) + final.NN.fit.to.final.res$weights[[1]][[1]][,1][3]*Rv.w[nrow(RV.data)-i]+
final.NN.fit.to.final.res$weights[[1]][[1]][,1][4]*Rv.m[nrow(RV.data)-i]))))
a2 <- (1/(1+exp(-(final.NN.fit.to.final.res$weights[[1]][[1]][,2][1] + final.NN.fit.to.final.res$weights[[1]][[1]][,2][2]*as.numeric(RV.data[nrow(RV.data)-i,2]) + final.NN.fit.to.final.res$weights[[1]][[1]][,2][3]*Rv.w[nrow(RV.data)-i]+
final.NN.fit.to.final.res$weights[[1]][[1]][,2][4]*Rv.m[nrow(RV.data)-i]))))
a3 <- (1/(1+exp(-(final.NN.fit.to.final.res$weights[[1]][[1]][,3][1] + final.NN.fit.to.final.res$weights[[1]][[1]][,3][2]*as.numeric(RV.data[nrow(RV.data)-i,2]) + final.NN.fit.to.final.res$weights[[1]][[1]][,3][3]*Rv.w[nrow(RV.data)-i]+
final.NN.fit.to.final.res$weights[[1]][[1]][,3][4]*Rv.m[nrow(RV.data)-i]))))
a4 <- (1/(1+exp(-(final.NN.fit.to.final.res$weights[[1]][[1]][,4][1] + final.NN.fit.to.final.res$weights[[1]][[1]][,4][2]*as.numeric(RV.data[nrow(RV.data)-i,2]) + final.NN.fit.to.final.res$weights[[1]][[1]][,4][3]*Rv.w[nrow(RV.data)-i]+
final.NN.fit.to.final.res$weights[[1]][[1]][,4][4]*Rv.m[nrow(RV.data)-i]))))
a5 <- (1/(1+exp(-(final.NN.fit.to.final.res$weights[[1]][[1]][,5][1] + final.NN.fit.to.final.res$weights[[1]][[1]][,5][2]*as.numeric(RV.data[nrow(RV.data)-i,2]) + final.NN.fit.to.final.res$weights[[1]][[1]][,5][3]*Rv.w[nrow(RV.data)-i]+
final.NN.fit.to.final.res$weights[[1]][[1]][,5][4]*Rv.m[nrow(RV.data)-i]))))
## All of the coefficients in the HAR-NN model.
coefficient.list <- list("Beta_0d" = final.beta_d.coeffi, "Beta_0w" = final.beta_w.coeffi, "Beta_0m" = final.beta_m.coeffi,
"Beta_00" =final.NN.fit.to.final.res$weights[[1]][[2]][[1]],"Beta_1" =final.NN.fit.to.final.res$weights[[1]][[2]][[2]],"gamma_10"=final.NN.fit.to.final.res$weights[[1]][[1]][,1][1],
"gamma_1d"=final.NN.fit.to.final.res$weights[[1]][[1]][,1][2],"gamma_1w"=final.NN.fit.to.final.res$weights[[1]][[1]][,1][3],"gamma_1m"=final.NN.fit.to.final.res$weights[[1]][[1]][,1][4],
"Beta_2" =final.NN.fit.to.final.res$weights[[1]][[2]][[3]],"gamma_20"=final.NN.fit.to.final.res$weights[[1]][[1]][,2][1],"gamma_2d"=final.NN.fit.to.final.res$weights[[1]][[1]][,2][2],
"gamma_2w"=final.NN.fit.to.final.res$weights[[1]][[1]][,2][3],"gamma_2m"=final.NN.fit.to.final.res$weights[[1]][[1]][,2][4],"Beta_3" =final.NN.fit.to.final.res$weights[[1]][[2]][[4]],
"gamma_30"=final.NN.fit.to.final.res$weights[[1]][[1]][,3][1],"gamma_3d"=final.NN.fit.to.final.res$weights[[1]][[1]][,3][2],"gamma_3w"=final.NN.fit.to.final.res$weights[[1]][[1]][,3][3],
"gamma_3m"=final.NN.fit.to.final.res$weights[[1]][[1]][,3][4],"Beta_4" =final.NN.fit.to.final.res$weights[[1]][[2]][[5]],"gamma_40"=final.NN.fit.to.final.res$weights[[1]][[1]][,4][1],
"gamma_4d"=final.NN.fit.to.final.res$weights[[1]][[1]][,4][2],"gamma_4w"=final.NN.fit.to.final.res$weights[[1]][[1]][,4][3],"gamma_4m"=final.NN.fit.to.final.res$weights[[1]][[1]][,4][4],
"Beta_5" =final.NN.fit.to.final.res$weights[[1]][[2]][[6]],"gamma_50"=final.NN.fit.to.final.res$weights[[1]][[1]][,5][1],"gamma_5d"=final.NN.fit.to.final.res$weights[[1]][[1]][,5][2],
"gamma_5w"=final.NN.fit.to.final.res$weights[[1]][[1]][,5][3],"gamma_5m"=final.NN.fit.to.final.res$weights[[1]][[1]][,5][4])
#### Predicted value for RV_[T+1d]^(d), where T = nrow(RV.data)-i.
predicted.values.for.RV.Tplus1d.d <-final.beta_d.coeffi*as.numeric(RV.data[nrow(RV.data)-i,2])+final.beta_w.coeffi*Rv.w[nrow(RV.data)-i]+final.beta_m.coeffi*Rv.m[nrow(RV.data)-i]+
final.NN.fit.to.final.res$weights[[1]][[2]][[1]]+final.NN.fit.to.final.res$weights[[1]][[2]][[2]]*a1+final.NN.fit.to.final.res$weights[[1]][[2]][[3]]*a2+
final.NN.fit.to.final.res$weights[[1]][[2]][[4]]*a3+final.NN.fit.to.final.res$weights[[1]][[2]][[5]]*a4+final.NN.fit.to.final.res$weights[[1]][[2]][[6]]*a5
if(printcoeffi=="YES"){
print(coefficient.list)
}
else if(printcoeffi=="NO"){
print(predicted.values.for.RV.Tplus1d.d)
}
else if(printcoeffi=="BOTH"){
print(coefficient.list)
print(predicted.values.for.RV.Tplus1d.d)
}
else
print("You might have a typo error in 'printcoeffi' argument")
}
#HAR_NN.sig(KOSPI.0615.data.RV,100,200,"YES")
########################################################################
HAR_NN.tanh <- function(RV.data,i,r,printcoeffi){
## Data handling for fitting HAR model.
Rv.d.y <- as.numeric(as.vector(RV.data[c(2:((nrow(RV.data)-i)+1)),2])) ## from 2 (daily daily time point) ~ (nrow(RV.data)-100)+1 (daily daily time point).
Rv.d.x1 <- as.numeric(as.vector(RV.data[c(1:(nrow(RV.data)-i)),2])) ## from 1 (daily daily time point) ~ (nrow(RV.data)-100) (daily daily time point).
## Weekly RV.
Rv.w <- numeric((nrow(RV.data)-i))
for(j in 23:(nrow(RV.data)-i)){
Rv.w[j] <- (Rv.d.x1[j]+Rv.d.x1[j-1]+Rv.d.x1[j-2]+Rv.d.x1[j-3]+Rv.d.x1[j-4])/5
}
## Monthly RV.
Rv.m <- numeric((nrow(RV.data)-i))
for(q in 23:(nrow(RV.data)-i)){
Rv.m[q] <- (Rv.d.x1[q]+Rv.d.x1[q-1]+Rv.d.x1[q-2]+Rv.d.x1[q-3]
+Rv.d.x1[q-4]+Rv.d.x1[q-5]+Rv.d.x1[q-6]+Rv.d.x1[q-7]
+Rv.d.x1[q-8]+Rv.d.x1[q-9]+Rv.d.x1[q-10]+Rv.d.x1[q-11]
+Rv.d.x1[q-12]+Rv.d.x1[q-13]+Rv.d.x1[q-14]+Rv.d.x1[q-15]
+Rv.d.x1[q-16]+Rv.d.x1[q-17]+Rv.d.x1[q-18]+Rv.d.x1[q-19]
+Rv.d.x1[q-20]+Rv.d.x1[q-21])/22
}
cbind(Rv.w[23:(nrow(RV.data)-i)],Rv.m[23:(nrow(RV.data)-i)])
## We need to make the data frame composed of { RV_[t+1d]^(d), RV_[t]^(d), RV_[t]^(w), RV_[t]^(m) } to fit the HAR model to the data.
Rv.d.y2 <- Rv.d.y[23:(nrow(RV.data)-i)]
Rv.d.x1.2 <- Rv.d.x1[23:(nrow(RV.data)-i)]
Rv.w.2 <- Rv.w[23:(nrow(RV.data)-i)]
Rv.m.2 <- Rv.m[23:(nrow(RV.data)-i)]
## Firstly, cbind { Rv_[t+1d]^(d), Rv[t]^(d), Rv[t]^(w), Rv[t]^(m) }.
tomorrow.today.week.month.data.frame <- cbind(Rv.d.y2,Rv.d.x1.2,Rv.w.2,Rv.m.2)
## transform to the data frame.
tomorrow.today.week.month.data.frame <-as.data.frame(tomorrow.today.week.month.data.frame)
colnames(tomorrow.today.week.month.data.frame) <- c("Rv(d)(t+1d)","Rv(d)(t)","Rv(w)(t)","Rv(m)(t)")
## tomorrow.today.week.month.data.frame : A complete data set to run a regression model with 22 points removed.
## Since there are a lot of data, there is no serious problem even if the data from 1th to 22th daily daily time point are removed.
########### STEP 1 : initial HAR model fitting to data set.
initial.HAR.model.fit<-lm(Rv.d.y2~Rv.d.x1.2+Rv.w.2+Rv.m.2)
initial.HAR.model.fit.coeffi <- initial.HAR.model.fit$coefficients
initial.HAR.model.fit.coeffi <- as.vector(initial.HAR.model.fit.coeffi)
## In here, our idea is fitting the single hidden layer feedforward NN model (with 'q' : 10) to
## residuals obtained from fitting HAR model to data set
## with Rv.d.x1.2(=Rv(t)(d)),Rv.w.2(=Rv(t)(w)),Rv.m.2(=Rv(t)(m)).
## Definition of residual data set (Note that when we set the residual set, we need to remove constant term estimated from fitting HAR model to KOSPI RV series.)
## That is, residual in this part is defined as follow : RV_[t+1d]^(d) - ( beta(d)^(hat)*RV_[t]^(d) + beta(w)^(hat)*RV_[t]^(w) + beta(m)^(hat)*RV_[t]^(m) ).
## Why we define the residual data set like above explanation is to make sure that the identifiability of constant term in NN based HAR models.
## ¡Ø Of course, there is only one constant term in the HAR-NN model, but strictly speaking, two constant terms obtained by two different model fits (HAR & NN, respectively) are added together to form one constant term.
## initial.res : RV_[t+1d]^(d) - ( beta(d)^(hat)*RV_[t]^(d) + beta(w)^(hat)*RV_[t]^(w) + beta(m)^(hat)*RV_[t]^(m) )
initial.res <- Rv.d.y2-(initial.HAR.model.fit.coeffi[2]*Rv.d.x1.2+initial.HAR.model.fit.coeffi[3]*Rv.w.2+initial.HAR.model.fit.coeffi[4]*Rv.m.2)
initial.res.today.week.month.data.frame<- cbind(initial.res,Rv.d.x1.2,Rv.w.2,Rv.m.2)
## Above data set is composed of ( initial.res, Rv(t)(d), Rv(t)(w), Rv(t)(m) )
initial.res.today.week.month.data.frame <-as.data.frame(initial.res.today.week.month.data.frame)
colnames(initial.res.today.week.month.data.frame) <- c("initial.res","Rv(d)(t)","Rv(w)(t)","Rv(m)(t)")
########### STEP 2 : Fitting the single hidden layer feedforward NN model (with 'q' : 10) to
########### residuals obtained from STEP 1.
initial.NN.model.fit.to.initial.res <- neuralnet(initial.res~Rv.d.x1.2+Rv.w.2+Rv.m.2,data=initial.res.today.week.month.data.frame,
hidden=10,linear.output=T,act.fct = "tanh")
## Coefficent values for RV_[t]^(d) (numeric vector for storing updated values.).
HAR.model.coeffi.beta_d.vector <- numeric(r)
u.HAR.model.coeffi.beta_d.vector <- numeric(r)
## Coefficent values for RV_[t]^(w) (numeric vector for storing updated values.).
HAR.model.coeffi.beta_w.vector <- numeric(r)
u.HAR.model.coeffi.beta_w.vector <- numeric(r)
## Coefficent values for RV_[t]^(m) (numeric vector for storing updated values.).
HAR.model.coeffi.beta_m.vector <- numeric(r)
u.HAR.model.coeffi.beta_m.vector <- numeric(r)
########### STEP 3 : Fit the HAR model again to the [ Rv_[t+1d]^(d) - fitted values obtained from step 2 ].
for(p in 1:r){
## Re-fit the HAR model to the [ Rv_[t+1d]^(d) - fitted values obtained from step 2 ].
refit.HAR.model <- lm((Rv.d.y2 - initial.NN.model.fit.to.initial.res$net.result[[1]])~Rv.d.x1.2+Rv.w.2+Rv.m.2)
## Coefficient vector corresponding to the HAR model part in the HAR-NN model with respect to the above refitted HAR model's coefficients.
HAR.model.coeffi.refitted <-(refit.HAR.model$coefficients)
HAR.model.coeffi.refitted <- as.vector(HAR.model.coeffi.refitted)
HAR.model.coeffi.beta_d.vector[p] <- HAR.model.coeffi.refitted[2]
HAR.model.coeffi.beta_w.vector[p] <- HAR.model.coeffi.refitted[3]
HAR.model.coeffi.beta_m.vector[p] <- HAR.model.coeffi.refitted[4]
########### STEP 4 : Fit the single hidden layer feedforward NN model (with 'q' : 10) again to the
########### residuals obtained from re-fitting the HAR model in STEP 3.
## Definition of res2 data set. (Form is similar to 'initial.res' in STEP 1.)
res2 <- Rv.d.y2-(HAR.model.coeffi.refitted[2]*Rv.d.x1.2+HAR.model.coeffi.refitted[3]*Rv.w.2+HAR.model.coeffi.refitted[4]*Rv.m.2)
second.res.today.week.month.data.frame<- cbind(res2,Rv.d.x1.2,Rv.w.2,Rv.m.2)
## Above data set is composed of ( res2, Rv(t)(d), Rv(t)(w),Rv(t)(m) ).
second.res.today.week.month.data.frame <-as.data.frame(second.res.today.week.month.data.frame)
colnames(second.res.today.week.month.data.frame) <- c("res2","Rv(d)(t)","Rv(w)(t)","Rv(m)(t)")
###### Re-Fit the NN model to the residuals (=res2) obtained from re-fitting the HAR model in STEP 3.
refit.NN.to.res2 <- neuralnet(res2~Rv.d.x1.2+Rv.w.2+Rv.m.2,data=second.res.today.week.month.data.frame,
hidden=10,linear.output=T,act.fct = "tanh")
########### Return to STEP 3 : Fit the HAR model again to the [ RV_[t+1d]^(d) - fitted values obtained from step 4 ].
# Re-fit the HAR model to the [ RV_(t+1d)^(d) - fitted values obtained from step 4 ].
rerefit.HAR <- lm((Rv.d.y2 - refit.NN.to.res2$net.result[[1]])~Rv.d.x1.2+Rv.w.2+Rv.m.2)
### Coefficient vector corresponding to the HAR model part in the HAR-NN model.
HAR.model.coeffi.rerefitted <-(rerefit.HAR$coefficients)
HAR.model.coeffi.rerefitted <- as.vector(HAR.model.coeffi.rerefitted)
## Updataed coefficient vectors corresponding to the HAR model part in the HAR-NN model.
u.HAR.model.coeffi.beta_d.vector[p] <- HAR.model.coeffi.rerefitted[2]
u.HAR.model.coeffi.beta_w.vector[p] <- HAR.model.coeffi.rerefitted[3]
u.HAR.model.coeffi.beta_m.vector[p] <- HAR.model.coeffi.rerefitted[4]
## The convergence condition is set when the absolute difference between the
## updated coefficients of the HAR model part in the HAR-NN model and the coefficients of the HAR model part in the same model
## before being updated is smaller than 0.05 in each coefficient. '0.05' is the limit of the error we set in this real data analyis.
diff1=abs(HAR.model.coeffi.beta_d.vector[p]-u.HAR.model.coeffi.beta_d.vector[p])
diff2=abs(HAR.model.coeffi.beta_w.vector[p]-u.HAR.model.coeffi.beta_w.vector[p])
diff3=abs(HAR.model.coeffi.beta_m.vector[p]-u.HAR.model.coeffi.beta_m.vector[p])
if( (diff1<0.05) && (diff2<0.05) && (diff3<0.05) )
{
final.beta_d.coeffi <- as.numeric(u.HAR.model.coeffi.beta_d.vector[p])
final.beta_w.coeffi <- as.numeric(u.HAR.model.coeffi.beta_w.vector[p])
final.beta_m.coeffi <- as.numeric(u.HAR.model.coeffi.beta_m.vector[p])
break
}
########### Repeat the above steps (STEP3-> STEP4-> STEP3) repeatedly until the
########### coefficients ( Beta(d), Beta(w), Beta(m) ) of the HAR model part in the HAR-NN model converge with respect to above criteria.
}
## Final.res data set (This is defined with the use of the converged coefficients of the HAR model part in the HAR-NN model.)
final.res <-(Rv.d.y2-(final.beta_d.coeffi*Rv.d.x1.2+final.beta_w.coeffi*Rv.w.2+final.beta_m.coeffi*Rv.m.2))
final.res.today.week.month.data.frame <- cbind(final.res,Rv.d.x1.2,Rv.w.2,Rv.m.2)
## Above data set is filled with ( final.res, Rv(t)(d), Rv(t)(w), Rv(t)(m) ).
final.res.today.week.month.data.frame <- as.data.frame(final.res.today.week.month.data.frame)
colnames(final.res.today.week.month.data.frame) <- c("final.res","Rv(d)(t)","Rv(w)(t)","Rv(m)(t)")
########### STEP 5 : Fitting the single hidden layer feedforward NN model (with 'q' : 10) lastly to
########### the final residuals (final.res) obtained from re-fitting the HAR model in the previous step with the convergent coefficients.
########### Then, we can get convergent coefficients of the NN model part in the HAR-NN model.
final.NN.fit.to.final.res <- neuralnet(final.res ~ Rv.d.x1.2+Rv.w.2+Rv.m.2,data=final.res.today.week.month.data.frame,
hidden=10,linear.output=T,act.fct = "tanh")
########### After implementing the above line, we can make sure that all of the coefficients in the HAR-NN model can be (globally or locally) converged.
########### tanh function values.
a1 <- tanh((final.NN.fit.to.final.res$weights[[1]][[1]][,1][1] + final.NN.fit.to.final.res$weights[[1]][[1]][,1][2]*as.numeric(RV.data[nrow(RV.data)-i,2]) + final.NN.fit.to.final.res$weights[[1]][[1]][,1][3]*Rv.w[nrow(RV.data)-i]+
final.NN.fit.to.final.res$weights[[1]][[1]][,1][4]*Rv.m[nrow(RV.data)-i]))
a2 <- tanh((final.NN.fit.to.final.res$weights[[1]][[1]][,2][1] + final.NN.fit.to.final.res$weights[[1]][[1]][,2][2]*as.numeric(RV.data[nrow(RV.data)-i,2]) + final.NN.fit.to.final.res$weights[[1]][[1]][,2][3]*Rv.w[nrow(RV.data)-i]+
final.NN.fit.to.final.res$weights[[1]][[1]][,2][4]*Rv.m[nrow(RV.data)-i]))
a3 <- tanh((final.NN.fit.to.final.res$weights[[1]][[1]][,3][1] + final.NN.fit.to.final.res$weights[[1]][[1]][,3][2]*as.numeric(RV.data[nrow(RV.data)-i,2]) + final.NN.fit.to.final.res$weights[[1]][[1]][,3][3]*Rv.w[nrow(RV.data)-i]+
final.NN.fit.to.final.res$weights[[1]][[1]][,3][4]*Rv.m[nrow(RV.data)-i]))
a4 <- tanh((final.NN.fit.to.final.res$weights[[1]][[1]][,4][1] + final.NN.fit.to.final.res$weights[[1]][[1]][,4][2]*as.numeric(RV.data[nrow(RV.data)-i,2]) + final.NN.fit.to.final.res$weights[[1]][[1]][,4][3]*Rv.w[nrow(RV.data)-i]+
final.NN.fit.to.final.res$weights[[1]][[1]][,4][4]*Rv.m[nrow(RV.data)-i]))
a5 <- tanh((final.NN.fit.to.final.res$weights[[1]][[1]][,5][1] + final.NN.fit.to.final.res$weights[[1]][[1]][,5][2]*as.numeric(RV.data[nrow(RV.data)-i,2]) + final.NN.fit.to.final.res$weights[[1]][[1]][,5][3]*Rv.w[nrow(RV.data)-i]+
final.NN.fit.to.final.res$weights[[1]][[1]][,5][4]*Rv.m[nrow(RV.data)-i]))
a6 <- tanh(final.NN.fit.to.final.res$weights[[1]][[1]][,6][1] + final.NN.fit.to.final.res$weights[[1]][[1]][,6][2]*as.numeric(RV.data[nrow(RV.data)-i,2]) + final.NN.fit.to.final.res$weights[[1]][[1]][,6][3]*Rv.w[nrow(RV.data)-i]+
final.NN.fit.to.final.res$weights[[1]][[1]][,6][4]*Rv.m[nrow(RV.data)-i])
a7 <- tanh(final.NN.fit.to.final.res$weights[[1]][[1]][,7][1] + final.NN.fit.to.final.res$weights[[1]][[1]][,7][2]*as.numeric(RV.data[nrow(RV.data)-i,2]) + final.NN.fit.to.final.res$weights[[1]][[1]][,7][3]*Rv.w[nrow(RV.data)-i]+
final.NN.fit.to.final.res$weights[[1]][[1]][,7][4]*Rv.m[nrow(RV.data)-i])
a8 <- tanh(final.NN.fit.to.final.res$weights[[1]][[1]][,8][1] + final.NN.fit.to.final.res$weights[[1]][[1]][,8][2]*as.numeric(RV.data[nrow(RV.data)-i,2]) + final.NN.fit.to.final.res$weights[[1]][[1]][,8][3]*Rv.w[nrow(RV.data)-i]+
final.NN.fit.to.final.res$weights[[1]][[1]][,8][4]*Rv.m[nrow(RV.data)-i])
a9 <- tanh(final.NN.fit.to.final.res$weights[[1]][[1]][,9][1] + final.NN.fit.to.final.res$weights[[1]][[1]][,9][2]*as.numeric(RV.data[nrow(RV.data)-i,2]) + final.NN.fit.to.final.res$weights[[1]][[1]][,9][3]*Rv.w[nrow(RV.data)-i]+
final.NN.fit.to.final.res$weights[[1]][[1]][,9][4]*Rv.m[nrow(RV.data)-i])
a10 <- tanh(final.NN.fit.to.final.res$weights[[1]][[1]][,10][1] + final.NN.fit.to.final.res$weights[[1]][[1]][,10][2]*as.numeric(RV.data[nrow(RV.data)-i,2]) + final.NN.fit.to.final.res$weights[[1]][[1]][,10][3]*Rv.w[nrow(RV.data)-i]+
final.NN.fit.to.final.res$weights[[1]][[1]][,10][4]*Rv.m[nrow(RV.data)-i])
## All of the coefficients in the HAR-NN model.
coefficient.list <- list("Beta_0d" = final.beta_d.coeffi, "Beta_0w" = final.beta_w.coeffi, "Beta_0m" = final.beta_m.coeffi,
"Beta_00" =final.NN.fit.to.final.res$weights[[1]][[2]][[1]],"Beta_1" =final.NN.fit.to.final.res$weights[[1]][[2]][[2]],"gamma_10"=final.NN.fit.to.final.res$weights[[1]][[1]][,1][1],
"gamma_1d"=final.NN.fit.to.final.res$weights[[1]][[1]][,1][2],"gamma_1w"=final.NN.fit.to.final.res$weights[[1]][[1]][,1][3],"gamma_1m"=final.NN.fit.to.final.res$weights[[1]][[1]][,1][4],
"Beta_2" =final.NN.fit.to.final.res$weights[[1]][[2]][[3]],"gamma_20"=final.NN.fit.to.final.res$weights[[1]][[1]][,2][1],"gamma_2d"=final.NN.fit.to.final.res$weights[[1]][[1]][,2][2],
"gamma_2w"=final.NN.fit.to.final.res$weights[[1]][[1]][,2][3],"gamma_2m"=final.NN.fit.to.final.res$weights[[1]][[1]][,2][4],"Beta_3" =final.NN.fit.to.final.res$weights[[1]][[2]][[4]],
"gamma_30"=final.NN.fit.to.final.res$weights[[1]][[1]][,3][1],"gamma_3d"=final.NN.fit.to.final.res$weights[[1]][[1]][,3][2],"gamma_3w"=final.NN.fit.to.final.res$weights[[1]][[1]][,3][3],
"gamma_3m"=final.NN.fit.to.final.res$weights[[1]][[1]][,3][4],"Beta_4" =final.NN.fit.to.final.res$weights[[1]][[2]][[5]],"gamma_40"=final.NN.fit.to.final.res$weights[[1]][[1]][,4][1],
"gamma_4d"=final.NN.fit.to.final.res$weights[[1]][[1]][,4][2],"gamma_4w"=final.NN.fit.to.final.res$weights[[1]][[1]][,4][3],"gamma_4m"=final.NN.fit.to.final.res$weights[[1]][[1]][,4][4],
"Beta_5" =final.NN.fit.to.final.res$weights[[1]][[2]][[6]],"gamma_50"=final.NN.fit.to.final.res$weights[[1]][[1]][,5][1],"gamma_5d"=final.NN.fit.to.final.res$weights[[1]][[1]][,5][2],
"gamma_5w"=final.NN.fit.to.final.res$weights[[1]][[1]][,5][3],"gamma_5m"=final.NN.fit.to.final.res$weights[[1]][[1]][,5][4],"Beta_6" =final.NN.fit.to.final.res$weights[[1]][[2]][[7]],
"gamma_60"=final.NN.fit.to.final.res$weights[[1]][[1]][,6][1],"gamma_6d"=final.NN.fit.to.final.res$weights[[1]][[1]][,6][2],"gamma_6w"=final.NN.fit.to.final.res$weights[[1]][[1]][,6][3],
"gamma_6m"=final.NN.fit.to.final.res$weights[[1]][[1]][,6][4],"Beta_7" =final.NN.fit.to.final.res$weights[[1]][[2]][[8]],"gamma_70"=final.NN.fit.to.final.res$weights[[1]][[1]][,7][1],
"gamma_7d"=final.NN.fit.to.final.res$weights[[1]][[1]][,7][2],"gamma_7w"=final.NN.fit.to.final.res$weights[[1]][[1]][,7][3],"gamma_7m"=final.NN.fit.to.final.res$weights[[1]][[1]][,7][4],
"Beta_8" =final.NN.fit.to.final.res$weights[[1]][[2]][[9]],"gamma_80"=final.NN.fit.to.final.res$weights[[1]][[1]][,8][1],"gamma_8d"=final.NN.fit.to.final.res$weights[[1]][[1]][,8][2],
"gamma_8w"=final.NN.fit.to.final.res$weights[[1]][[1]][,8][3],"gamma_8m"=final.NN.fit.to.final.res$weights[[1]][[1]][,8][4],"Beta_9" =final.NN.fit.to.final.res$weights[[1]][[2]][[10]],
"gamma_90"=final.NN.fit.to.final.res$weights[[1]][[1]][,9][1],"gamma_9d"=final.NN.fit.to.final.res$weights[[1]][[1]][,9][2],"gamma_9w"=final.NN.fit.to.final.res$weights[[1]][[1]][,9][3],
"gamma_9m"=final.NN.fit.to.final.res$weights[[1]][[1]][,9][4],"Beta_10" =final.NN.fit.to.final.res$weights[[1]][[2]][[11]],"gamma_10_0"=final.NN.fit.to.final.res$weights[[1]][[1]][,10][1],
"gamma_10d"=final.NN.fit.to.final.res$weights[[1]][[1]][,10][2],"gamma_10w"=final.NN.fit.to.final.res$weights[[1]][[1]][,10][3],"gamma_10m"=final.NN.fit.to.final.res$weights[[1]][[1]][,10][4])
#### Predicted value for RV_[T+1d]^(d), where T = nrow(RV.data)-i.
predicted.values.for.RV.Tplus1d.d <- final.beta_d.coeffi*as.numeric(RV.data[nrow(RV.data)-i,2])+final.beta_w.coeffi*Rv.w[nrow(RV.data)-i]+final.beta_m.coeffi*Rv.m[nrow(RV.data)-i]+
final.NN.fit.to.final.res$weights[[1]][[2]][[1]]+final.NN.fit.to.final.res$weights[[1]][[2]][[2]]*a1+final.NN.fit.to.final.res$weights[[1]][[2]][[3]]*a2+
final.NN.fit.to.final.res$weights[[1]][[2]][[4]]*a3+final.NN.fit.to.final.res$weights[[1]][[2]][[5]]*a4+final.NN.fit.to.final.res$weights[[1]][[2]][[6]]*a5+
final.NN.fit.to.final.res$weights[[1]][[2]][[7]]*a6+final.NN.fit.to.final.res$weights[[1]][[2]][[8]]*a7+final.NN.fit.to.final.res$weights[[1]][[2]][[9]]*a8+
final.NN.fit.to.final.res$weights[[1]][[2]][[10]]*a9+final.NN.fit.to.final.res$weights[[1]][[2]][[11]]*a10
if(printcoeffi=="YES"){
print(coefficient.list)
}
else if(printcoeffi=="NO"){
print(predicted.values.for.RV.Tplus1d.d)
}
else if(printcoeffi=="BOTH"){
print(coefficient.list)
print(predicted.values.for.RV.Tplus1d.d)
}
else
print("You might have a typo error in 'printcoeffi' argument")
}
#HAR_NN.tanh(KOSPI.0615.data.RV,100,200,"YES")
##### HAR-NN forecasting function.
HAR_NN_forecast <- function(RV.data,i,r,acti.fun){
if(acti.fun=="logistic"){
########### Predicted value for RV_[T+1d]^(d), where T = nrow(RV.data)-i
HAR_NN.sig(KOSPI.0615.data.RV,i,r,"NO")
}
else if(acti.fun=="tanh"){
########### Predicted value for RV_[T+1d]^(d), where T = nrow(RV.data)-i
HAR_NN.tanh(KOSPI.0615.data.RV,i,r,"NO")
}
else
print("You might have a typo error in 'acti.fun' argument")
}
#HAR_NN_forecast(KOSPI.0615.data.RV,100,200,"logistic")
#HAR_NN_forecast(KOSPI.0615.data.RV,100,200,"tanh")
#HAR_NN_forecast(KOSPI.0615.data.RV,100,200,"asdf")
########### HAR-infty-NN model : the second NN-based HAR model.
########### The optimal q is the same as the above case. (sigmoid=logistic : q=5) & (tanh : q=10) for KOSPI RV series.
HAR_infty_NN.sig <- function(RV.data,i,r,printcoeffi){
Rv.d.y <- as.numeric(as.vector(RV.data[c(2:((nrow(RV.data)-i)+1)),2])) ## from 2 (daily time point) ~ (nrow(RV.data)-100)+1 (daily daily time point).
Rv.d.x1 <- as.numeric(as.vector(RV.data[c(1:(nrow(RV.data)-i)),2])) ## from 1 (daily time point) ~ (nrow(RV.data)-100) (daily daily time point).
## Data handling for AR(22) model fitting
Rv.d.y2 <- Rv.d.y[23:(nrow(RV.data)-i)] # (t+1d) daily time point series data
Rv.d.x1.2 <- Rv.d.x1[23:(nrow(RV.data)-i)] # (t) daily time point series data
########### STEP 1 : Initial AR(22) model fitting to data set.
initial.AR22.model.fit <- arima(Rv.d.y2,order=c(22,0,0),method="CSS")
initial.AR22.model.coeffi <- initial.AR22.model.fit$coef
initial.AR22.model.coeffi <- as.vector(initial.AR22.model.coeffi)
# (t-1d) daily time point series data
Rv.d.x1.2.1 <- c(Rv.d.x1[22],Rv.d.x1.2[-length(Rv.d.x1.2)])
# (t-2d) daily time point series data
Rv.d.x1.2.2 <- c(Rv.d.x1[21],Rv.d.x1[22],Rv.d.x1.2[-(length(Rv.d.x1.2)-1):-length(Rv.d.x1.2)])
# (t-3d) daily time point series data
Rv.d.x1.2.3 <- c(Rv.d.x1[20],Rv.d.x1[21],Rv.d.x1[22],Rv.d.x1.2[-(length(Rv.d.x1.2)-2):-length(Rv.d.x1.2)])
# (t-4d) daily time point series data
Rv.d.x1.2.4 <- c(Rv.d.x1[19],Rv.d.x1[20],Rv.d.x1[21],Rv.d.x1[22],Rv.d.x1.2[-(length(Rv.d.x1.2)-3):-length(Rv.d.x1.2)])
# (t-5d) daily time point series data
Rv.d.x1.2.5 <- c(Rv.d.x1[18],Rv.d.x1[19],Rv.d.x1[20],Rv.d.x1[21],Rv.d.x1[22],Rv.d.x1.2[-(length(Rv.d.x1.2)-4):-length(Rv.d.x1.2)])
# (t-6d) daily time point series data
Rv.d.x1.2.6 <- c(Rv.d.x1[17],Rv.d.x1[18],Rv.d.x1[19],Rv.d.x1[20],Rv.d.x1[21],Rv.d.x1[22],Rv.d.x1.2[-(length(Rv.d.x1.2)-5):-length(Rv.d.x1.2)])
# (t-7d) daily time point series data
Rv.d.x1.2.7 <- c(Rv.d.x1[16],Rv.d.x1[17],Rv.d.x1[18],Rv.d.x1[19],Rv.d.x1[20],Rv.d.x1[21],Rv.d.x1[22],Rv.d.x1.2[-(length(Rv.d.x1.2)-6):-length(Rv.d.x1.2)])
# (t-8d) daily time point series data
Rv.d.x1.2.8 <- c(Rv.d.x1[15],Rv.d.x1[16],Rv.d.x1[17],Rv.d.x1[18],Rv.d.x1[19],Rv.d.x1[20],Rv.d.x1[21],Rv.d.x1[22],Rv.d.x1.2[-(length(Rv.d.x1.2)-7):-length(Rv.d.x1.2)])
# (t-9d) daily time point series data
Rv.d.x1.2.9 <- c(Rv.d.x1[14],Rv.d.x1[15],Rv.d.x1[16],Rv.d.x1[17],Rv.d.x1[18],Rv.d.x1[19],Rv.d.x1[20],Rv.d.x1[21],Rv.d.x1[22],Rv.d.x1.2[-(length(Rv.d.x1.2)-8):-length(Rv.d.x1.2)])
# (t-10d) daily time point series data
Rv.d.x1.2.10 <- c(Rv.d.x1[13],Rv.d.x1[14],Rv.d.x1[15],Rv.d.x1[16],Rv.d.x1[17],Rv.d.x1[18],Rv.d.x1[19],Rv.d.x1[20],Rv.d.x1[21],Rv.d.x1[22],Rv.d.x1.2[-(length(Rv.d.x1.2)-9):-length(Rv.d.x1.2)])
# (t-11d) daily time point series data
Rv.d.x1.2.11 <- c(Rv.d.x1[12],Rv.d.x1[13],Rv.d.x1[14],Rv.d.x1[15],Rv.d.x1[16],Rv.d.x1[17],Rv.d.x1[18],Rv.d.x1[19],Rv.d.x1[20],Rv.d.x1[21],Rv.d.x1[22],Rv.d.x1.2[-(length(Rv.d.x1.2)-10):-length(Rv.d.x1.2)])
# (t-12d) daily time point series data
Rv.d.x1.2.12 <- c(Rv.d.x1[11],Rv.d.x1[12],Rv.d.x1[13],Rv.d.x1[14],Rv.d.x1[15],Rv.d.x1[16],Rv.d.x1[17],Rv.d.x1[18],Rv.d.x1[19],Rv.d.x1[20],Rv.d.x1[21],Rv.d.x1[22],Rv.d.x1.2[-(length(Rv.d.x1.2)-11):-length(Rv.d.x1.2)])
# (t-13d) daily time point series data
Rv.d.x1.2.13 <- c(Rv.d.x1[10],Rv.d.x1[11],Rv.d.x1[12],Rv.d.x1[13],Rv.d.x1[14],Rv.d.x1[15],Rv.d.x1[16],Rv.d.x1[17],Rv.d.x1[18],Rv.d.x1[19],Rv.d.x1[20],Rv.d.x1[21],Rv.d.x1[22],Rv.d.x1.2[-(length(Rv.d.x1.2)-12):-length(Rv.d.x1.2)])
# (t-14d) daily time point series data
Rv.d.x1.2.14 <- c(Rv.d.x1[9],Rv.d.x1[10],Rv.d.x1[11],Rv.d.x1[12],Rv.d.x1[13],Rv.d.x1[14],Rv.d.x1[15],Rv.d.x1[16],Rv.d.x1[17],Rv.d.x1[18],Rv.d.x1[19],Rv.d.x1[20],Rv.d.x1[21],Rv.d.x1[22],Rv.d.x1.2[-(length(Rv.d.x1.2)-13):-length(Rv.d.x1.2)])
# (t-15d) daily time point series data
Rv.d.x1.2.15 <- c(Rv.d.x1[8],Rv.d.x1[9],Rv.d.x1[10],Rv.d.x1[11],Rv.d.x1[12],Rv.d.x1[13],Rv.d.x1[14],Rv.d.x1[15],Rv.d.x1[16],Rv.d.x1[17],Rv.d.x1[18],Rv.d.x1[19],Rv.d.x1[20],Rv.d.x1[21],Rv.d.x1[22],Rv.d.x1.2[-(length(Rv.d.x1.2)-14):-length(Rv.d.x1.2)])
# (t-16d) daily time point series data
Rv.d.x1.2.16 <- c(Rv.d.x1[7],Rv.d.x1[8],Rv.d.x1[9],Rv.d.x1[10],Rv.d.x1[11],Rv.d.x1[12],Rv.d.x1[13],Rv.d.x1[14],Rv.d.x1[15],Rv.d.x1[16],Rv.d.x1[17],Rv.d.x1[18],Rv.d.x1[19],Rv.d.x1[20],Rv.d.x1[21],Rv.d.x1[22],Rv.d.x1.2[-(length(Rv.d.x1.2)-15):-length(Rv.d.x1.2)])
# (t-17d) daily time point series data
Rv.d.x1.2.17 <- c(Rv.d.x1[6],Rv.d.x1[7],Rv.d.x1[8],Rv.d.x1[9],Rv.d.x1[10],Rv.d.x1[11],Rv.d.x1[12],Rv.d.x1[13],Rv.d.x1[14],Rv.d.x1[15],Rv.d.x1[16],Rv.d.x1[17],Rv.d.x1[18],Rv.d.x1[19],Rv.d.x1[20],Rv.d.x1[21],Rv.d.x1[22],Rv.d.x1.2[-(length(Rv.d.x1.2)-16):-length(Rv.d.x1.2)])
# (t-18d) daily time point series data
Rv.d.x1.2.18 <- c(Rv.d.x1[5],Rv.d.x1[6],Rv.d.x1[7],Rv.d.x1[8],Rv.d.x1[9],Rv.d.x1[10],Rv.d.x1[11],Rv.d.x1[12],Rv.d.x1[13],Rv.d.x1[14],Rv.d.x1[15],Rv.d.x1[16],Rv.d.x1[17],Rv.d.x1[18],Rv.d.x1[19],Rv.d.x1[20],Rv.d.x1[21],Rv.d.x1[22],Rv.d.x1.2[-(length(Rv.d.x1.2)-17):-length(Rv.d.x1.2)])
# (t-19d) daily time point series data
Rv.d.x1.2.19 <- c(Rv.d.x1[4],Rv.d.x1[5],Rv.d.x1[6],Rv.d.x1[7],Rv.d.x1[8],Rv.d.x1[9],Rv.d.x1[10],Rv.d.x1[11],Rv.d.x1[12],Rv.d.x1[13],Rv.d.x1[14],Rv.d.x1[15],Rv.d.x1[16],Rv.d.x1[17],Rv.d.x1[18],Rv.d.x1[19],Rv.d.x1[20],Rv.d.x1[21],Rv.d.x1[22],Rv.d.x1.2[-(length(Rv.d.x1.2)-18):-length(Rv.d.x1.2)])
# (t-20d) daily time point series data
Rv.d.x1.2.20 <- c(Rv.d.x1[3],Rv.d.x1[4],Rv.d.x1[5],Rv.d.x1[6],Rv.d.x1[7],Rv.d.x1[8],Rv.d.x1[9],Rv.d.x1[10],Rv.d.x1[11],Rv.d.x1[12],Rv.d.x1[13],Rv.d.x1[14],Rv.d.x1[15],Rv.d.x1[16],Rv.d.x1[17],Rv.d.x1[18],Rv.d.x1[19],Rv.d.x1[20],Rv.d.x1[21],Rv.d.x1[22],Rv.d.x1.2[-(length(Rv.d.x1.2)-19):-length(Rv.d.x1.2)])
# (t-21d) daily time point series data
Rv.d.x1.2.21 <- c(Rv.d.x1[2],Rv.d.x1[3],Rv.d.x1[4],Rv.d.x1[5],Rv.d.x1[6],Rv.d.x1[7],Rv.d.x1[8],Rv.d.x1[9],Rv.d.x1[10],Rv.d.x1[11],Rv.d.x1[12],Rv.d.x1[13],Rv.d.x1[14],Rv.d.x1[15],Rv.d.x1[16],Rv.d.x1[17],Rv.d.x1[18],Rv.d.x1[19],Rv.d.x1[20],Rv.d.x1[21],Rv.d.x1[22],Rv.d.x1.2[-(length(Rv.d.x1.2)-20):-length(Rv.d.x1.2)])
## initial residual
initial.res <-(Rv.d.y2-initial.AR22.model.coeffi[1]*Rv.d.x1.2-initial.AR22.model.coeffi[2]*Rv.d.x1.2.1-initial.AR22.model.coeffi[3]*Rv.d.x1.2.2
-initial.AR22.model.coeffi[4]*Rv.d.x1.2.3-initial.AR22.model.coeffi[5]*Rv.d.x1.2.4-initial.AR22.model.coeffi[6]*Rv.d.x1.2.5-initial.AR22.model.coeffi[7]*Rv.d.x1.2.6
-initial.AR22.model.coeffi[8]*Rv.d.x1.2.7-initial.AR22.model.coeffi[9]*Rv.d.x1.2.8-initial.AR22.model.coeffi[10]*Rv.d.x1.2.9-initial.AR22.model.coeffi[11]*Rv.d.x1.2.10-initial.AR22.model.coeffi[12]*Rv.d.x1.2.11
-initial.AR22.model.coeffi[13]*Rv.d.x1.2.12-initial.AR22.model.coeffi[14]*Rv.d.x1.2.13-initial.AR22.model.coeffi[15]*Rv.d.x1.2.14-initial.AR22.model.coeffi[16]*Rv.d.x1.2.15
-initial.AR22.model.coeffi[17]*Rv.d.x1.2.16-initial.AR22.model.coeffi[18]*Rv.d.x1.2.17-initial.AR22.model.coeffi[19]*Rv.d.x1.2.18-initial.AR22.model.coeffi[20]*Rv.d.x1.2.19-initial.AR22.model.coeffi[21]*Rv.d.x1.2.20
-initial.AR22.model.coeffi[22]*Rv.d.x1.2.21)
RVcombined.data <- cbind(initial.res,Rv.d.x1.2,Rv.d.x1.2.1,Rv.d.x1.2.2,Rv.d.x1.2.3,
Rv.d.x1.2.4,Rv.d.x1.2.5,Rv.d.x1.2.6,Rv.d.x1.2.7,Rv.d.x1.2.8
,Rv.d.x1.2.9,Rv.d.x1.2.10,Rv.d.x1.2.11,Rv.d.x1.2.12,Rv.d.x1.2.13
,Rv.d.x1.2.14,Rv.d.x1.2.15,Rv.d.x1.2.16,Rv.d.x1.2.17,Rv.d.x1.2.18
,Rv.d.x1.2.19,Rv.d.x1.2.20,Rv.d.x1.2.21)
########### STEP 2 : Initial NN fitting to initial residual set.
## NN model fitting to initial res data.
NN.model.fitting.to.initial.res <- neuralnet(initial.res~Rv.d.x1.2+Rv.d.x1.2.1+Rv.d.x1.2.2+Rv.d.x1.2.3+
Rv.d.x1.2.4+Rv.d.x1.2.5+Rv.d.x1.2.6+Rv.d.x1.2.7+Rv.d.x1.2.8
+Rv.d.x1.2.9+Rv.d.x1.2.10+Rv.d.x1.2.11+Rv.d.x1.2.12+Rv.d.x1.2.13
+Rv.d.x1.2.14+Rv.d.x1.2.15+Rv.d.x1.2.16+Rv.d.x1.2.17+Rv.d.x1.2.18
+Rv.d.x1.2.19+Rv.d.x1.2.20+Rv.d.x1.2.21,data=RVcombined.data,
hidden=5,linear.output=T)
## The AR(22) model coefficient value corresponding to RV_[t] (numeric vector to store the updated value)
AR22.model.coeffi.beta01.vector <- numeric(r) #
u.AR22.model.coeffi.beta01.vector <- numeric(r) # u : updated
## The AR(22) model coefficient value corresponding to RV_[t-1d]
AR22.model.coeffi.beta02.vector <- numeric(r)
u.AR22.model.coeffi.beta02.vector <- numeric(r)
## The same to RV_[t-2d]
AR22.model.coeffi.beta03.vector <- numeric(r)
u.AR22.model.coeffi.beta03.vector <- numeric(r)
## The same to RV_[t-3d]
AR22.model.coeffi.beta04.vector <- numeric(r)
u.AR22.model.coeffi.beta04.vector <- numeric(r)
## The same to RV_[t-4d]
AR22.model.coeffi.beta05.vector <- numeric(r)
u.AR22.model.coeffi.beta05.vector <- numeric(r)
## The same to RV_[t-5d]
AR22.model.coeffi.beta06.vector <- numeric(r)
u.AR22.model.coeffi.beta06.vector <- numeric(r)
## The same to RV_[t-6d]
AR22.model.coeffi.beta07.vector <- numeric(r)
u.AR22.model.coeffi.beta07.vector <- numeric(r)
## The same to RV_[t-7d]
AR22.model.coeffi.beta08.vector <- numeric(r)
u.AR22.model.coeffi.beta08.vector <- numeric(r)
## The same to RV_[t-8d]
AR22.model.coeffi.beta09.vector <- numeric(r)
u.AR22.model.coeffi.beta09.vector <- numeric(r)
## The same to RV_[t-9d]
AR22.model.coeffi.beta010.vector <- numeric(r)
u.AR22.model.coeffi.beta010.vector <- numeric(r)
## The same to RV_[t-10d]
AR22.model.coeffi.beta011.vector <- numeric(r)
u.AR22.model.coeffi.beta011.vector <- numeric(r)
## The same to RV_[t-11d]
AR22.model.coeffi.beta012.vector <- numeric(r)
u.AR22.model.coeffi.beta012.vector <- numeric(r)
## The same to RV_[t-12d]
AR22.model.coeffi.beta013.vector <- numeric(r)
u.AR22.model.coeffi.beta013.vector <- numeric(r)
## The same to RV_[t-13d]
AR22.model.coeffi.beta014.vector <- numeric(r)
u.AR22.model.coeffi.beta014.vector <- numeric(r)
## The same to RV_[t-14d]
AR22.model.coeffi.beta015.vector <- numeric(r)
u.AR22.model.coeffi.beta015.vector <- numeric(r)
## The same to RV_[t-15d]
AR22.model.coeffi.beta016.vector <- numeric(r)
u.AR22.model.coeffi.beta016.vector <- numeric(r)
## The same to RV_[t-16d]
AR22.model.coeffi.beta017.vector <- numeric(r)
u.AR22.model.coeffi.beta017.vector <- numeric(r)
## The same to RV_[t-17d]
AR22.model.coeffi.beta018.vector <- numeric(r)
u.AR22.model.coeffi.beta018.vector <- numeric(r)
## The same to RV_[t-18d]
AR22.model.coeffi.beta019.vector <- numeric(r)
u.AR22.model.coeffi.beta019.vector <- numeric(r)
## The same to RV_[t-19d]
AR22.model.coeffi.beta020.vector <- numeric(r)
u.AR22.model.coeffi.beta020.vector <- numeric(r)
## The same to RV_[t-20d]
AR22.model.coeffi.beta021.vector <- numeric(r)
u.AR22.model.coeffi.beta021.vector <- numeric(r)
## The same to RV_[t-21d]
AR22.model.coeffi.beta022.vector <- numeric(r)
u.AR22.model.coeffi.beta022.vector <- numeric(r)
for(p in 1:r){
########### STEP 3 : refit.AR22.model to ( Rv_[t+1d](d) - fitted.value of 'NN.model.fitting.to.initial.res' )
refit.AR22.model <- arima((Rv.d.y2 - NN.model.fitting.to.initial.res$net.result[[1]]),order=c(22,0,0),method="CSS")
### coefficient
refit.AR22.model.coeffi <-(refit.AR22.model$coef)
refit.AR22.model.coeffi <- as.vector(refit.AR22.model.coeffi)
refit.AR22.model.coeffi ##
## store AR(22) Coefficients obtained from STEP 3
AR22.model.coeffi.beta01.vector[p] <- refit.AR22.model.coeffi[1]
AR22.model.coeffi.beta02.vector[p] <- refit.AR22.model.coeffi[2]
AR22.model.coeffi.beta03.vector[p] <- refit.AR22.model.coeffi[3]
AR22.model.coeffi.beta04.vector[p] <- refit.AR22.model.coeffi[4]
AR22.model.coeffi.beta05.vector[p] <- refit.AR22.model.coeffi[5]
AR22.model.coeffi.beta06.vector[p] <- refit.AR22.model.coeffi[6]
AR22.model.coeffi.beta07.vector[p] <- refit.AR22.model.coeffi[7]
AR22.model.coeffi.beta08.vector[p] <- refit.AR22.model.coeffi[8]
AR22.model.coeffi.beta09.vector[p] <- refit.AR22.model.coeffi[9]
AR22.model.coeffi.beta010.vector[p] <- refit.AR22.model.coeffi[10]
AR22.model.coeffi.beta011.vector[p] <- refit.AR22.model.coeffi[11]
AR22.model.coeffi.beta012.vector[p] <- refit.AR22.model.coeffi[12]
AR22.model.coeffi.beta013.vector[p] <- refit.AR22.model.coeffi[13]
AR22.model.coeffi.beta014.vector[p] <- refit.AR22.model.coeffi[14]
AR22.model.coeffi.beta015.vector[p] <- refit.AR22.model.coeffi[15]
AR22.model.coeffi.beta016.vector[p] <- refit.AR22.model.coeffi[16]
AR22.model.coeffi.beta017.vector[p] <- refit.AR22.model.coeffi[17]
AR22.model.coeffi.beta018.vector[p] <- refit.AR22.model.coeffi[18]
AR22.model.coeffi.beta019.vector[p] <- refit.AR22.model.coeffi[19]
AR22.model.coeffi.beta020.vector[p] <- refit.AR22.model.coeffi[20]
AR22.model.coeffi.beta021.vector[p] <- refit.AR22.model.coeffi[21]
AR22.model.coeffi.beta022.vector[p] <- refit.AR22.model.coeffi[22]
########### STEP 4 : Fit NN again to second.res data.
# second.res
second.res <-(Rv.d.y2-AR22.model.coeffi.beta01.vector[p]*Rv.d.x1.2-AR22.model.coeffi.beta02.vector[p]*Rv.d.x1.2.1-AR22.model.coeffi.beta03.vector[p]*Rv.d.x1.2.2-AR22.model.coeffi.beta04.vector[p]*Rv.d.x1.2.3-AR22.model.coeffi.beta05.vector[p]*Rv.d.x1.2.4-AR22.model.coeffi.beta06.vector[p]*Rv.d.x1.2.5-AR22.model.coeffi.beta07.vector[p]*Rv.d.x1.2.6-AR22.model.coeffi.beta08.vector[p]*Rv.d.x1.2.7
-AR22.model.coeffi.beta09.vector[p]*Rv.d.x1.2.8-AR22.model.coeffi.beta010.vector[p]*Rv.d.x1.2.9-AR22.model.coeffi.beta011.vector[p]*Rv.d.x1.2.10-AR22.model.coeffi.beta012.vector[p]*Rv.d.x1.2.11
-AR22.model.coeffi.beta013.vector[p]*Rv.d.x1.2.12-AR22.model.coeffi.beta014.vector[p]*Rv.d.x1.2.13-AR22.model.coeffi.beta015.vector[p]*Rv.d.x1.2.14-AR22.model.coeffi.beta016.vector[p]*Rv.d.x1.2.15
-AR22.model.coeffi.beta017.vector[p]*Rv.d.x1.2.16-AR22.model.coeffi.beta018.vector[p]*Rv.d.x1.2.17-AR22.model.coeffi.beta019.vector[p]*Rv.d.x1.2.18-AR22.model.coeffi.beta020.vector[p]*Rv.d.x1.2.19-AR22.model.coeffi.beta021.vector[p]*Rv.d.x1.2.20
-AR22.model.coeffi.beta022.vector[p]*Rv.d.x1.2.21)
RVcombined.data2 <- cbind(second.res,Rv.d.x1.2,Rv.d.x1.2.1,Rv.d.x1.2.2,Rv.d.x1.2.3,
Rv.d.x1.2.4,Rv.d.x1.2.5,Rv.d.x1.2.6,Rv.d.x1.2.7,Rv.d.x1.2.8
,Rv.d.x1.2.9,Rv.d.x1.2.10,Rv.d.x1.2.11,Rv.d.x1.2.12,Rv.d.x1.2.13
,Rv.d.x1.2.14,Rv.d.x1.2.15,Rv.d.x1.2.16,Rv.d.x1.2.17,Rv.d.x1.2.18
,Rv.d.x1.2.19,Rv.d.x1.2.20,Rv.d.x1.2.21)
## re-fit NN model to second.res data.
refit.NN.model.to.second.res <- neuralnet(second.res~Rv.d.x1.2+Rv.d.x1.2.1+Rv.d.x1.2.2+Rv.d.x1.2.3+
Rv.d.x1.2.4+Rv.d.x1.2.5+Rv.d.x1.2.6+Rv.d.x1.2.7+Rv.d.x1.2.8
+Rv.d.x1.2.9+Rv.d.x1.2.10+Rv.d.x1.2.11+Rv.d.x1.2.12+Rv.d.x1.2.13
+Rv.d.x1.2.14+Rv.d.x1.2.15+Rv.d.x1.2.16+Rv.d.x1.2.17+Rv.d.x1.2.18
+Rv.d.x1.2.19+Rv.d.x1.2.20+Rv.d.x1.2.21,data=RVcombined.data2,
hidden=5,linear.output=T)
############ return to the STEP 3 : rerefit.AR22.model to ( Rv_[t+1d](d) - fitted.value of 'refit.NN.model.to.second.res' )
rere.AR22.model.fit <- arima((Rv.d.y2 - refit.NN.model.to.second.res$net.result[[1]]),order=c(22,0,0),method="CSS")
### coefficient
rere.AR22.model.coeffi <-(rere.AR22.model.fit$coef)
rere.AR22.model.coeffi <- as.vector(rere.AR22.model.coeffi)
## store updated AR(22) Coefficients obtained from 'return to the STEP 3'.
u.AR22.model.coeffi.beta01.vector[p] <- rere.AR22.model.coeffi[1]
u.AR22.model.coeffi.beta02.vector[p] <- rere.AR22.model.coeffi[2]
u.AR22.model.coeffi.beta03.vector[p] <- rere.AR22.model.coeffi[3]
u.AR22.model.coeffi.beta04.vector[p] <- rere.AR22.model.coeffi[4]
u.AR22.model.coeffi.beta05.vector[p] <- rere.AR22.model.coeffi[5]
u.AR22.model.coeffi.beta06.vector[p] <- rere.AR22.model.coeffi[6]
u.AR22.model.coeffi.beta07.vector[p] <- rere.AR22.model.coeffi[7]
u.AR22.model.coeffi.beta08.vector[p] <- rere.AR22.model.coeffi[8]
u.AR22.model.coeffi.beta09.vector[p] <- rere.AR22.model.coeffi[9]
u.AR22.model.coeffi.beta010.vector[p] <- rere.AR22.model.coeffi[10]
u.AR22.model.coeffi.beta011.vector[p] <- rere.AR22.model.coeffi[11]
u.AR22.model.coeffi.beta012.vector[p] <- rere.AR22.model.coeffi[12]
u.AR22.model.coeffi.beta013.vector[p] <- rere.AR22.model.coeffi[13]
u.AR22.model.coeffi.beta014.vector[p] <- rere.AR22.model.coeffi[14]
u.AR22.model.coeffi.beta015.vector[p] <- rere.AR22.model.coeffi[15]
u.AR22.model.coeffi.beta016.vector[p] <- rere.AR22.model.coeffi[16]
u.AR22.model.coeffi.beta017.vector[p] <- rere.AR22.model.coeffi[17]
u.AR22.model.coeffi.beta018.vector[p] <- rere.AR22.model.coeffi[18]
u.AR22.model.coeffi.beta019.vector[p] <- rere.AR22.model.coeffi[19]
u.AR22.model.coeffi.beta020.vector[p] <- rere.AR22.model.coeffi[20]
u.AR22.model.coeffi.beta021.vector[p] <- rere.AR22.model.coeffi[21]
u.AR22.model.coeffi.beta022.vector[p] <- rere.AR22.model.coeffi[22]
##
diff1=abs(AR22.model.coeffi.beta01.vector[p]-u.AR22.model.coeffi.beta01.vector[p])
diff2=abs(AR22.model.coeffi.beta02.vector[p]-u.AR22.model.coeffi.beta02.vector[p])
diff3=abs(AR22.model.coeffi.beta03.vector[p]-u.AR22.model.coeffi.beta03.vector[p])
diff4=abs(AR22.model.coeffi.beta04.vector[p]-u.AR22.model.coeffi.beta04.vector[p])
diff5=abs(AR22.model.coeffi.beta05.vector[p]-u.AR22.model.coeffi.beta05.vector[p])
diff6=abs(AR22.model.coeffi.beta06.vector[p]-u.AR22.model.coeffi.beta06.vector[p])
diff7=abs(AR22.model.coeffi.beta07.vector[p]-u.AR22.model.coeffi.beta07.vector[p])
diff8=abs(AR22.model.coeffi.beta08.vector[p]-u.AR22.model.coeffi.beta08.vector[p])
diff9=abs(AR22.model.coeffi.beta09.vector[p]-u.AR22.model.coeffi.beta09.vector[p])
diff10=abs(AR22.model.coeffi.beta010.vector[p]-u.AR22.model.coeffi.beta010.vector[p])
diff11=abs(AR22.model.coeffi.beta011.vector[p]-u.AR22.model.coeffi.beta011.vector[p])
diff12=abs(AR22.model.coeffi.beta012.vector[p]-u.AR22.model.coeffi.beta012.vector[p])
diff13=abs(AR22.model.coeffi.beta013.vector[p]-u.AR22.model.coeffi.beta013.vector[p])
diff14=abs(AR22.model.coeffi.beta014.vector[p]-u.AR22.model.coeffi.beta014.vector[p])
diff15=abs(AR22.model.coeffi.beta015.vector[p]-u.AR22.model.coeffi.beta015.vector[p])
diff16=abs(AR22.model.coeffi.beta016.vector[p]-u.AR22.model.coeffi.beta016.vector[p])
diff17=abs(AR22.model.coeffi.beta017.vector[p]-u.AR22.model.coeffi.beta017.vector[p])
diff18=abs(AR22.model.coeffi.beta018.vector[p]-u.AR22.model.coeffi.beta018.vector[p])
diff19=abs(AR22.model.coeffi.beta019.vector[p]-u.AR22.model.coeffi.beta019.vector[p])
diff20=abs(AR22.model.coeffi.beta020.vector[p]-u.AR22.model.coeffi.beta020.vector[p])
diff21=abs(AR22.model.coeffi.beta021.vector[p]-u.AR22.model.coeffi.beta021.vector[p])
diff22=abs(AR22.model.coeffi.beta022.vector[p]-u.AR22.model.coeffi.beta022.vector[p])
if( sum(c(diff1,diff2,diff3,diff4,diff5,diff6,diff7,diff8,diff9,diff10,diff11,diff12,diff13,diff14,diff15,diff16,diff17,diff18,diff19,diff20,diff21,diff22)<0.4)==22 )
{
# convergent coefficient corresponding to RV_[t] in AR(22) model part of HAR-infty-NN model.
AR22.model.t.coeffi <- as.numeric(AR22.model.coeffi.beta01.vector[p])
# The same to RV_[t-1d]
AR22.model.t.1.coeffi <- as.numeric(AR22.model.coeffi.beta02.vector[p])
# The same to RV_[t-2d]
AR22.model.t.2.coeffi <- as.numeric(AR22.model.coeffi.beta03.vector[p])
# The same to RV_[t-3d]
AR22.model.t.3.coeffi <- as.numeric(AR22.model.coeffi.beta04.vector[p])
# The same to RV_[t-4d]