require(tseries)

#Multifractal height cross-correlation analysis
MFHXA<-function(x,y,tmin,tmax,q){
	options(warn=-1)
	tau<-rnorm(tmax-tmin+1)
	covxy<-rnorm(tmax-tmin+1)
	covxy_abs<-rnorm(tmax-tmin+1)
	for(nu in tmin:tmax){
		t<-1:ceiling(length(x)/nu)
  		xx<-summary(lm(c(matrix(cumsum(x),nrow=nu)[1,])~t))$res
		yy<-summary(lm(c(matrix(cumsum(y),nrow=nu)[1,])~t))$res
		cov<-(xx[2:length(xx)]-xx[1:(length(xx)-1)])*(yy[2:length(yy)]-yy[1:(length(yy)-1)])
		covxy_abs[(nu-tmin+1)]<-mean((abs(cov))^(q/2))
		tau[(nu-tmin+1)]<-nu
	}
	H<-summary(lm(log10(covxy_abs)~log10(tau)))$coefficients[2]/2
	return(H)
}

#MF-HXA jackknife estimator
MFHXA_jackknife<-function(x,y,tmax1,tmax2,q){
	HH<-rep(0,tmax2-tmax1+1)
	for(i in tmax1:tmax2){
		HH[i-tmax1+1]<-MFHXA(x,y,1,i,q)
	}
	return(c(mean(HH)))
}