require(fracdiff)
require(tseries)

#Correlated noise
Noise_rho<-function(n,rho){
	e1<-rnorm(n)
	e<-rnorm(n)
	e2<-rho*e1+sqrt(1-rho^2)*e	
	return(matrix(c(e1,e2),ncol=2))
}

#Two ARFIMA processes with correlated innovations
ARFIMA_rho<-function(n,d1,d2,rho){
	e1<-rnorm(n)
	e<-rnorm(n)
	e2<-rho*e1+sqrt(1-rho^2)*e
	x<-fracdiff.sim(n,d=d1,innov=e1)$series
	y<-fracdiff.sim(n,d=d2,innov=e2)$series
	return(matrix(c(x,y),ncol=2))
}

#ARFIMA and AR(1) processes with correlated innovations
ARFIMA_AR<-function(n,d1,theta,rho){
	e1<-rnorm(n)
	e<-rnorm(n)
	e2<-rho*e1+sqrt(1-rho^2)*e
	x<-fracdiff.sim(n,d=d1,innov=e1)$series
	y<-arima.sim(list(order=c(1,0,0),ar=theta),n,innov=e2)	
	return(matrix(c(x,y),ncol=2))	
}

#Two AR(1) processes with correlated innovations
AR_rho<-function(n,theta1,theta2,rho){
	e1<-rnorm(n)
	e<-rnorm(n)
	e2<-rho*e1+sqrt(1-rho^2)*e
	x<-arima.sim(list(order=c(1,0,0),ar=theta1),n,innov=e1)
	y<-arima.sim(list(order=c(1,0,0),ar=theta2),n,innov=e2)	
	return(matrix(c(x,y),ncol=2))	
}

#MC-ARFIMA process with LRC and LRCC (Model 1)
Mixed_ARFIMA_ARFIMA<-function(alpha,beta,gamma,delta,n,d1,d2,d3,d4,rho){
	e<-ARFIMA_rho(n,d2,d3,rho)
	e2<-e[,1]
	e3<-e[,2]
	x<-alpha*fracdiff.sim(n,d=d1)$series+beta*e2
	y<-gamma*e3+delta*fracdiff.sim(n,d=d4)$series
	return(matrix(c(x,y),ncol=2))
}

#MC-ARFIMA process with LRC and SRCC (Model 2)
Mixed_ARFIMA_AR<-function(alpha,beta,gamma,delta,n,d1,d2,theta,rho){
	e<-AR_rho(n,theta,theta,rho)
	e2<-e[,1]
	e3<-e[,2]
	x<-alpha*fracdiff.sim(n,d=d1)$series+beta*e2
	y<-gamma*e3+delta*fracdiff.sim(n,d=d2)$series
	return(matrix(c(x,y),ncol=2))
}

#MC-ARFIMA process with LRC and simple correlation (Model 3)
Mixed_ARFIMA_noise<-function(alpha,beta,gamma,delta,n,d1,d2,rho){
	e<-Noise_rho(n,rho)
	e2<-e[,1]
	e3<-e[,2]
	x<-alpha*fracdiff.sim(n,d=d1)$series+beta*e2
	y<-gamma*e3+delta*fracdiff.sim(n,d=d2)$series
	return(matrix(c(x,y),ncol=2))
}