[Highfrequency-commits] r52 - pkg/highfrequency/R
noreply at r-forge.r-project.org
noreply at r-forge.r-project.org
Tue Sep 24 14:17:08 CEST 2013
Author: kboudt
Date: 2013-09-24 14:17:08 +0200 (Tue, 24 Sep 2013)
New Revision: 52
Modified:
pkg/highfrequency/R/highfrequencyGSOC.R
pkg/highfrequency/R/realized.R
Log:
Modified: pkg/highfrequency/R/highfrequencyGSOC.R
===================================================================
--- pkg/highfrequency/R/highfrequencyGSOC.R 2013-09-24 12:16:58 UTC (rev 51)
+++ pkg/highfrequency/R/highfrequencyGSOC.R 2013-09-24 12:17:08 UTC (rev 52)
@@ -1,978 +1,2008 @@
-minRQ = function(rdata,align.by=NULL,align.period = NULL, makeReturns = FALSE,...){
- if (hasArg(data))
- {
- rdata = data
- }
- multixts = highfrequency:::.multixts(rdata)
- if (multixts)
- {
- result = apply.daily(rdata, minRQ, align.by, align.period, makeReturns)
- return(result)
- }
- if (!multixts)
- {
- if ((!is.null(align.by)) && (!is.null(align.period))) {
- rdata = highfrequency:::.aggregatets(rdata, on = align.by, k = align.period)
- }
- if(makeReturns)
- {
- rdata = makeReturns(rdata)
- }
- q=as.zoo(abs(as.numeric(rdata)))
- q=as.numeric(rollapply(q, width = 2, FUN = min, by = 1, align = "left"))
- N=length(q)+1
- minRQ=pi*N/(3*pi-8)*(N/(N-1))*sum(q^4)
- return(minRQ)
- }
-}
-
-
-medRQ = function(rdata, align.by = NULL, align.period = NULL, makeReturns = FALSE,...)
-{
- if (hasArg(data))
- {
- rdata = data
- }
- multixts = highfrequency:::.multixts(rdata)
- if (multixts)
- {
- result = apply.daily(rdata, medRQ, align.by, align.period, makeReturns)
- return(result)
- }
- if (!multixts)
- {
- if ((!is.null(align.by)) && (!is.null(align.period))) {
- rdata = highfrequency:::.aggregatets(rdata, on = align.by, k = align.period)
- }
- if(makeReturns)
- {
- rdata = makeReturns(rdata)
- }
- q = abs(as.numeric(rdata))
- q = as.numeric(rollmedian(q, k = 3,align="center"))
- N = length(q)+2
- medRQ = 3*pi*N/(9*pi+72-53*sqrt(3))*(N/(N-2))*sum(q^4)
- return(medRQ)
- }
-}
-
-rQuar = function(rdata, align.by = NULL, align.period = NULL, makeReturns = FALSE,...)
-{
- if (hasArg(data))
- {
- rdata = data
- }
- multixts = highfrequency:::.multixts(rdata)
- if (multixts)
- {
- result = apply.daily(rdata, rQuar, align.by, align.period,
- makeReturns)
- return(result)
- }
- if (!multixts)
- {
- if ((!is.null(align.by)) && (!is.null(align.period))) {
- rdata = highfrequency:::.aggregatets(rdata, on = align.by, k = align.period)
- }
- if (makeReturns)
- {
- rdata = makeReturns(rdata)
- }
-
- q=as.numeric(rdata)
- N = length(q)+1
- rQuar = N/3*sum(q^4)
- return(rQuar)
- }
-}
-
-
-rQPVar = function(rdata, align.by = NULL, align.period = NULL, makeReturns = FALSE,...)
-{
- if (hasArg(data))
- {
- rdata = data
- }
- multixts =highfrequency::: .multixts(rdata)
- if (multixts)
- {
- result = apply.daily(rdata, rQPVar, align.by, align.period, ##check FUN
- makeReturns)
- return(result)
- }
- if (!multixts)
- {
- if ((!is.null(align.by)) && (!is.null(align.period))) {
- rdata =highfrequency:::.aggregatets(rdata, on = align.by, k = align.period)
- }
- if (makeReturns)
- {
- rdata = makeReturns(rdata)
- }
-
- q=as.numeric(rdata)
- q=abs(rollapply(q,width=4,FUN=prod,align="left"))
- N = length(q)+3
- rQPVar = N/(N-3)*pi^2/4*sum(q)
- return(rQPVar)
- }
-}
-
-
-rTPVar = function(rdata, align.by = NULL, align.period = NULL, makeReturns = FALSE,...)
-{
- if (hasArg(data))
- {
- rdata = data
- }
- multixts = highfrequency:::.multixts(rdata)
- if (multixts)
- {
- result = apply.daily(rdata, rTPVar, align.by, align.period,
- makeReturns)
- return(result)
- }
- if (!multixts)
- {
- if ((!is.null(align.by)) && (!is.null(align.period))) {
- rdata = highfrequency:::.aggregatets(rdata, on = align.by, k = align.period)
- }
- if (makeReturns)
- {
- rdata = makeReturns(rdata)
- }
-
- q=as.numeric(rdata)
- q=abs(rollapply(q,width = 3, FUN = prod, align = "left"))
- N = length(q)+2
- rTPVar= N/(N-2)*gamma(1/2)^2/(4*gamma(7/6)^2)*sum(q^(4/3))
- return(rTPVar)
- }
-}
-
-
-
-## Standard error and confidence band of RV measures
-ivInference = function(rdata, IVestimator="RV", IQestimator="rQuar", confidence=0.95, align.by= NULL, align.period = NULL, makeReturns = FALSE, ...)
-{
- if (hasArg(data)){ rdata = data }
-
- multixts =highfrequency:::.multixts(rdata)
- if (multixts)
- {
- result = apply.daily(rdata, ivInference, align.by, align.period, ##check FUN
- makeReturns)
- return(result)
- }else{
- if((!is.null(align.by)) && (!is.null(align.period))){
- rdata =highfrequency:::.aggregatets(rdata, on = align.by, k = align.period)
- }
-
- if(makeReturns){ rdata=makeReturns(rdata) }
-
- N = length(rdata)
- p = as.numeric(confidence)
-
- iq = .hatiq(rdata,IQestimator)
-
- iv = .IV(IVestimator,iq)
-
-
- hatIV = .hativ(rdata, IVestimator)
-
- stderr= 1/sqrt(N)*iv
-
- ##confidence band
- lowband=as.numeric(hatIV-stderr*qnorm(p))
- highband=as.numeric(hatIV+stderr*qnorm(p))
- cb<-c(lowband,highband)
-
- ## reports:
- out={}
- out$hativ= hatIV
- out$se= stderr
- out$cb= cb
-
- return(out)
- }
-}
-
-thetaROWVar = function( alpha = 0.001 , alphaMCD = 0.5 )
-{
- N = 1;
- q_alpha = qchisq( 1-alpha , df = N );
- c_alpha = (1-alpha)/pchisq( q_alpha , df = N+2 );
- a_alpha = -2*sqrt(q_alpha)*dnorm(sqrt(q_alpha))+1-alpha;
- b_alpha = -2*q_alpha^(3/2)*dnorm(sqrt(q_alpha))+3*a_alpha;
-
- k = qchisq(1-alpha, df= 1); #TODO GIANG ## suggestion in the article.
- halfk = sqrt(k); halfq = sqrt(q_alpha)
-
- Ewu2 = 2*pnorm(halfk)-1;
- Ewu2u2 = -2*halfk*dnorm(halfk)+Ewu2;
- Ewu2u4 = -2*(k^(3/2))*dnorm(halfk)+3*Ewu2u2;
-
- Ewu2u2IF = (-1+c_alpha*q_alpha-(c_alpha*q_alpha)/(1-alpha))*a_alpha+c_alpha*b_alpha/(1-alpha)
- Ewu2u2IF = Ewu2u2IF + 2*(1-c_alpha*q_alpha)*(
- halfk*dnorm(halfk)-halfq*dnorm(halfq) + 1 - alpha/2 - pnorm(halfk) )
- Ewu2IF = (alpha-1-c_alpha*q_alpha*alpha) + c_alpha*a_alpha/(1-alpha) + 2*(c_alpha*q_alpha-1)*( pnorm(halfk)-(1-alpha/2))
- Ederwu2u4 = -k^(3/2)*dnorm(halfk);
- Ederwu2u2 = -halfk*dnorm(halfk);
- c1 = 1/Ewu2u2; c2 = 1/Ewu2; c3 = c2*Ederwu2u2-c1*Ederwu2u4
- Avar0 = .avar_MCD(alpha)
- theta = c3^2*Avar0 + c1^2*Ewu2u4 + c2^2*Ewu2 - 2*c1*c2*Ewu2u2;
- theta = theta + 2*c3*( c1*Ewu2u2IF-c2*Ewu2IF );
-
- return( theta );
-}
-
-##Jump-test: BNS with threshold
-BNSjumptest=function(rdata, IVestimator= "BV", IQestimator= "TP", type= "linear", logtransform= FALSE, max= FALSE,
- align.by= NULL, align.period= NULL, makeReturns = FALSE, startV= NULL,...)
-{
- if (hasArg(data)){ rdata = data }
-
- multixts = highfrequency:::.multixts(rdata)
-
- if (multixts){
- result = apply.daily(rdata, BNSjumptest, align.by, align.period, makeReturns) ##Check FUN
- return(result)
- }else{
- if((!is.null(align.by)) && (!is.null(align.period))) {
- rdata = highfrequency:::.aggregatets(rdata, on = align.by, k = align.period)
- }
-
- if(makeReturns){ rdata = makeReturns(rdata) }
-
- N=length(rdata)
-
- ## hatQV
- hatQV = highfrequency:::RV(rdata)
-
- ## threshold BV
-
- ## hatV: TODO this is not the right place, move to where it is always needed
- if(is.null(startV))
- {
- hatV = medRV(rdata)
- }else{ hatV = startV }
-
- hatIV = .hativ( rdata, IVestimator, hatV=hatV, N=N, ... )
-
- ##theta
- theta = .tt(IVestimator,...)
-
- ##hatIQ
- hatIQ = .hatiq(rdata, IQestimator)
-
- ## linear or ratio
- if(type=="linear")
- {
- ##logtransform
- if(logtransform)
- {
- hatQV = log(highfrequency:::RV(rdata))
- hatIV = log(.hativ(rdata,IVestimator))
- }
- if(!logtransform)
- {
- hatQV = highfrequency:::RV(rdata)
- hatIV = .hativ(rdata,IVestimator)
- }
-
- ## max argument
- if(max)
- {
- product = max(1,.hatiq(rdata,IQestimator)/.hativ(rdata,IVestimator)^2)
- }
- if(!max)
- {
- product = .hatiq(rdata,IQestimator)
- }
- a=sqrt(N)*(hatQV-hatIV)/sqrt((theta-2)*product)
- out={}
- out$ztest=a
- out$critical.value= qnorm(c(0.025,0.975))
- out$pvalue= 2*pnorm(-abs(a))
- return(out)
- }
-
- if(type=="ratio")
- {
- ## max argument
- if(max)
- {
- product = max(1,.hatiq(rdata,IQestimator)/.hativ(rdata,IVestimator)^2)
- }
- if(!max)
- {
- product = .hatiq(rdata,IQestimator)/.hativ(rdata,IVestimator)^2
- }
- a=sqrt(N)*(1-.hativ(rdata,IVestimator)/highfrequency:::RV(rdata))/sqrt((theta-2)*product)
- out={}
- out$ztest=a
- out$critical.value= qnorm(c(0.025,0.975))
- out$pvalue= 2*pnorm(-abs(a))
- return(out)
- }
- }
-}
-
-
-##JOjumptest
- JOjumptest= function(pdata, power=4,...)
-{
- simre=function (pdata)
- {
- l = dim(pdata)[1]
- x = matrix(as.numeric(pdata), nrow = l)
- x[(2:l), ] = x[(2:l), ]/x[(1:(l - 1)), ]-1
- x[1, ] = rep(0, dim(pdata)[2])
- x = xts(x, order.by = index(pdata))
- }
- R=simre(pdata)
- r= makeReturns(pdata)
- N=length(pdata)-1
- bv= highfrequency:::RBPVar(r)
- rv= highfrequency:::RV(r)
-
- SwV=2*sum(R-r)
- mu1=2^(6/2)*gamma(1/2*(6+1))/gamma(1/2)
-
- ##mupower:
- if(power==4)
- {
- q=abs(rollapply(r, width = 4, FUN = prod, align = "left"))
- mu2= 2^((6/4)/2)*gamma(1/2*(6/4+1))/gamma(1/2)
- av=mu1/9 * N^3*(mu2)^(-4)/(N-4-1)*sum(q^(6/4),na.rm= TRUE) ##check formula
- JOtest= N*bv/sqrt(av)*(1- rv/SwV)
-
- out={}
- out$ztest= JOtest
- out$critical.value= qnorm(c(0.025,0.975))
- out$pvalue= 2*pnorm(-abs(JOtest))
- return(out)
- }
- if(power==6)
- {
- q=abs(rollapply(r, width = 6, FUN = prod, align = "left"))
- mu2= 2^((6/6)/2)*gamma(1/2*(6/6+1))/gamma(1/2)
- av=mu1/9 * N^3*(mu2)^(-6)/(N-6-1)*sum(q^(6/6),na.rm= TRUE) ##check formula
- JOtest= N*bv/sqrt(av)*(1- rv/SwV)
-
- out={}
- out$ztest= JOtest
- out$critical.value= qnorm(c(0.025,0.975))
- out$pvalue= 2*pnorm(-abs(JOtest))
- return(out)
- }
-}
-
-
-
-## AJjumptest:
-AJjumptest= function(pdata, p=4 , k=2, align.by= NULL, align.period = NULL, makeReturns= FALSE, ...)
-{
- if (hasArg(data)){ pdata = data }
-
- multixts = highfrequency:::.multixts(pdata)
-
- if (multixts)
- {
- result = apply.daily(pdata, AJjumptest, align.by, align.period, makeReturns) ## Check FUN
- return(result)
- }else{
- pdata = highfrequency:::.aggregatets(pdata, on = "seconds", k = 1)
- }
-
- N = length(pdata)-1
- p = as.numeric(p)
- k = as.numeric(k)
- alpha = (1-1/p)/2 ## discuss this value
- w = 0.47
- cvalue = alpha*(1/N)^w
-
- h = align.period * .scale(align.by)
- hk= h*k
-
- seq1 = seq(1, N, h)
- seq2 = seq(1, N, hk)
-
- # return data
- pdata1 = pdata[seq1]
- pdata2 = pdata[seq2]
-
- r = abs(makeReturns(pdata));
- r1 = abs(makeReturns(pdata1));
- r2 = abs(makeReturns(pdata2));
-
- pv1 = sum(r1^p)
- pv2 = sum(r2^p)
-
- S = pv1/pv2
-
- ## selection return:
- selection <- abs(r) < cvalue
- rse <- abs(makeReturns(pdata[selection]))
-
- ## AJ test:
- AJtest= (S-k^(p/2-1))/sqrt(.V(rse,p,k,N))
-
- out = {};
- out$ztest= AJtest;
- out$critical.value= qnorm(c(0.025,0.975));
- out$pvalue= 2*pnorm(-abs(AJtest));
- return(out)
-}
-
-##Realized semivariance
-rSV= function(rdata, align.by = NULL, align.period = NULL, makeReturns = FALSE,...)
-{
- if (hasArg(data))
- {
- rdata = data
- }
- multixts =highfrequency::: .multixts(rdata)
- if (multixts)
- {
- result = apply.daily(rdata, rSV, align.by, align.period,
- makeReturns)
- return(result)
- }
- if (!multixts)
- {
- if ((!is.null(align.by)) && (!is.null(align.period))) {
- rdata =highfrequency:::.aggregatets(rdata, on = align.by, k = align.period)
- }
- if (makeReturns)
- {
- rdata = makeReturns(rdata)
- }
-
- q=as.numeric(rdata)
- select.down <-rdata <0
- select.up <- rdata >0
-
- rSVd= sum(q[select.down]^2)
- rSVu = sum(q[select.up]^2)
-
- out={}
- out$rSVdownside = rSVd
- out$rSVupside = rSVu
-
- return(out)
-
- }
-}
-
-##Realized skewness
-rSkew= function(rdata, align.by = NULL, align.period = NULL, makeReturns = FALSE,...)
-{
- if (hasArg(data))
- {
- rdata = data
- }
- multixts =highfrequency::: .multixts(rdata)
- if (multixts)
- {
- result = apply.daily(rdata, rSkew, align.by, align.period,
- makeReturns)
- return(result)
- }
- if (!multixts)
- {
- if ((!is.null(align.by)) && (!is.null(align.period))) {
- rdata =highfrequency:::.aggregatets(rdata, on = align.by, k = align.period)
- }
- if (makeReturns)
- {
- rdata = makeReturns(rdata)
- }
-
- q=as.numeric(rdata)
- N= length(q)
-
- rv= highfrequency:::RV(rdata)
-
- rSkew= sqrt(N)*sum(q^3)/rv^(3/2)
-
- return(rSkew)
-
- }
-}
-
-##Realized kurtosis
-rKurt= function(rdata, align.by = NULL, align.period = NULL, makeReturns = FALSE,...)
-{
- if (hasArg(data))
- {
- rdata = data
- }
- multixts =highfrequency::: .multixts(rdata)
- if (multixts)
- {
- result = apply.daily(rdata, rKurt, align.by, align.period,
- makeReturns)
- return(result)
- }
- if (!multixts)
- {
- if ((!is.null(align.by)) && (!is.null(align.period))) {
- rdata =highfrequency:::.aggregatets(rdata, on = align.by, k = align.period)
- }
- if (makeReturns)
- {
- rdata = makeReturns(rdata)
- }
-
- q=as.numeric(rdata)
- N= length(q)
-
- rv= highfrequency:::RV(rdata)
-
- rkurt= N*sum(q^4)/rv^(2)
-
- return(rkurt)
-
- }
-}
-
-##Realized Multipower Variation (MPV)
-rMPV= function(rdata, m= 2, p=2, align.by= NULL, align.period= NULL, makeReturns= FALSE,...)
-{
- if (hasArg(data))
- {
- rdata = data
- }
- multixts =highfrequency::: .multixts(rdata)
- if (multixts)
- {
- result = apply.daily(rdata, rMPV, align.by, align.period, makeReturns)
- return(result)
- }
- if (!multixts)
- {
- if ((!is.null(align.by)) && (!is.null(align.period))) {
- rdata =highfrequency:::.aggregatets(rdata, on = align.by, k = align.period)
- }
- if (makeReturns)
- {
- rdata = makeReturns(rdata)
- }
-
-
- if(m>p/2)
- { m= as.numeric(m) ##m> p/2
- p= as.numeric(p)
- q=as.numeric(rdata)
- q=abs(rollapply(q,width=m,FUN=prod,align="left"))
- N = length(rdata)
-
- dmp= (2^((p/m)/2)*gamma((p/m+1)/2)/gamma(1/2))^(-m)
-
- rmpv = dmp* N^(p/2)/(N-m+1)*sum(q^(p/m))
- return(rmpv)
- }
- else{warning("Please supply m>p/2 for the arguments m and p")}
-
- }
-}
-
-
-
-
-##Preaveraging estimators (matrix)
- ##Preaverage return:
-hatreturn= function(pdata,kn)
-{
- rdata=makeReturns(pdata)
- kn=as.numeric(kn)
- if(kn==1){ hatre = rdata}
- else{
- x = (1:(kn-1) )/kn
- x[x > (1-x)] = (1-x)[x > (1-x)]
- weightedsum = function(series){ return( sum(x*series) )}
- hatre= rollapply(rdata,width = kn-1, FUN = weightedsum, align = "left")
- hatre[is.na(hatre)] = rdata[is.na(hatre)]
- }
- return(hatre)
-}
- ##gfunction:
-gfunction = function(x){
- # returns the minimum of x and 1-x
- # whenevr x > 1-x , replace with 1-x
- x[x > (1-x)] = (1-x)[x > (1-x)]
- return(x)
-
-}
-
- #r#Univariate estimation:
-crv=function(pdata)
-{
- N= nrow(pdata)
- theta= 0.8 ##recommendation by Hautsch and Podolskij
- kn= floor(theta*sqrt(N))
-
- ##psi:
- psi1= 1
- psi2= 1/12
-
- psi1kn= kn* sum((gfunction((1:kn)/kn) - gfunction(( (1:kn) - 1 )/kn ) )^2 )
-
- psi2kn= 1/kn*sum(gfunction((1:kn)/kn)^2)
-
- r1= hatreturn(pdata,kn=kn)
- rdata = makeReturns(pdata)
- crv= 1/(sqrt(N)*theta*psi2kn)*sum(r1^2,na.rm=TRUE) - psi1kn*(1/N)/(2*theta^2*psi2kn)*sum(rdata^2,na.rm=TRUE)
- return(crv)
-}
-
- ##preav_bi
-preav_bi= function(pdata1, pdata2)
-{
- x = refreshTime(list(pdata1, pdata2))
- newprice1 = x[, 1]
- newprice2 = x[, 2]
-
- N= nrow(x)
- theta= 0.8 ##recommendation by Hautsch and Podolskij
- kn= floor(theta*sqrt(N))
-
- ##psi:
- psi1= 1
- psi2= 1/12
-
- psi1kn= kn* sum((gfunction((1:kn)/kn) - gfunction(( (1:kn) - 1 )/kn ) )^2 )
-
- psi2kn= 1/kn*sum(gfunction((1:kn)/kn)^2)
-
-
- r1 = hatreturn(newprice1,kn=kn)
- r2 = hatreturn(newprice2,kn=kn)
-
- mrc= N/(N-kn+2)*1/(psi2*kn)*(sum(r1*r2,na.rm=TRUE))
-
- return(mrc)
-}
-
-
- ##Preaveraging
-MRC= function(pdata, pairwise = FALSE , makePsd= FALSE,...)
-{
-
- if (!is.list(pdata)) {
- n = 1
- }else {
- n = length(pdata)
- }
- if (n == 1) {
- multixts = highfrequency:::.multixts(pdata);
- if(multixts){ stop("This function does not support having an xts object of multiple days as input. Please provide a timeseries of one day as input"); }
- mrc = crv(pdata)
- }
-
-
- if (n > 1) {
- multixts = highfrequency:::.multixts(pdata[[1]]);
- if(multixts){ stop("This function does not support having an xts object of multiple days as input. Please provide a timeseries of one day as input"); }
-
- if(pairwise){
- cov = matrix(rep(0, n * n), ncol = n)
- diagonal = c()
- for (i in 1:n) {
- diagonal[i] = crv(pdata[[i]])
- }
- diag(cov) = diagonal
-
- for (i in 2:n) {
- for (j in 1:(i - 1)) {
- cov[i, j] = cov[j, i] = preav_bi(pdata[[i]], pdata[[j]])
- }
- }
-
- mrc = cov
-
- if(makePsd)
- {
- mrc=makePsd(mrc)
- }
-
- }else{
- x = refreshTime(pdata)
- N= nrow(x)
- theta= 0.8 ##recommendation by Hautsch and Podolskij
- kn= floor(theta*sqrt(N))
-
- ##psi:
- psi1= 1
- psi2= 1/12
-
- psi1kn= kn* sum((gfunction((1:kn)/kn) - gfunction(( (1:kn) - 1 )/kn ) )^2 )
- psi2kn= 1/kn*sum(gfunction((1:kn)/kn)^2)
-
- preavreturn = c()
- for( i in 1:ncol(x)){
- preavreturn = cbind( preavreturn , hatreturn(x[,i],kn) )
- }
-
- S = rCov(preavreturn)
-
- mrc= N/(N-kn+2)*1/(psi2*kn)*S
-
- if(makePsd)
- {
- mrc=makePsd(mrc)
- }
-
- }
- }
- return(mrc)
-}
-
-
-##Realized beta:
-rBeta= function(rdata, rindex, RCOVestimator= "rCov", RVestimator= "RV", makeReturns= FALSE,...)
-{
- if (hasArg(data))
- {
- rdata = data
- }
-
- if (makeReturns)
- {
- rdata = makeReturns(rdata)
- rindex= makeReturns(rindex)
- }
-
- multixts = highfrequency:::.multixts(rdata)
-
- if (multixts)
- {
- print("No support for multiple days")
- }
- if (!multixts)
- {
- if(RCOVestimator=="rRTSCov" | RCOVestimator=="rTSCov"){
- if( min(rdata) <0 ){
- print("when using rRTSCov, rTSCov, introduce price data - transformation to price data done")
- rdata = exp(cumsum(rdata))
- }
- if( min(rindex) <0 ){
- print("when using rRTSCov, rTSCov, introduce price data - transformation to price data done")
- rindex = exp(cumsum(rindex))
- }
- }
- rcovfun= function(rdata, rindex, RCOVestimator)
- {
- switch(RCOVestimator,
- rCov= rCov(cbind(rdata,rindex) )[1,2],
- rAVGCov= rAVGCov(list(rdata, rindex) )[1,2],
- rBPCov= rBPCov(cbind(rdata, rindex) )[1,2],
- rHYCov= rHYCov(list(rdata, rindex) )[1,2],
- rKernelCov= rKernelCov(list(rdata, rindex) )[1,2],
- rOWCov= rOWCov(cbind(rdata, rindex) )[1,2],
- rRTSCov= rRTSCov(list(rdata, rindex))[1,2],
- rThresholdCov= rThresholdCov(cbind(rdata, rindex) )[1,2],
- rTSCov= rTSCov(list(rdata, rindex))[1,2]
- )
-
- }
- rcov= rcovfun(rdata,rindex,RCOVestimator)
-
- if( is.null(RVestimator) ){ RVestimator = RCOVestimator }
-
- rvfun= function(rindex, RVestimator)
- {
-
- switch(RVestimator,
- RV= highfrequency:::RV(rindex),
- BV= highfrequency:::RBPVar(rindex),
- minRV= minRV(rindex ),
- medRV= medRV(rindex ),
- rCov= rCov(rindex ) ,
- rAVGCov= rAVGCov(rindex ) ,
- rBPCov= rBPCov(rindex ) ,
- rHYCov= rHYCov(rindex ) ,
- rKernelCov= rKernelCov(rindex ) ,
- rOWCov= rOWCov(rindex ) ,
- rRTSCov= rRTSCov(rindex) ,
- rThresholdCov= rThresholdCov(rindex ) ,
- rTSCov= rTSCov(rindex)
- )
-
- }
- rv=rvfun(rindex,RVestimator)
-
- rbeta = rcov/rv
- return(rbeta)
- }
-}
-
-############### INTERNAL HELP FUNCTIONS ###############
-### thetaROWVar help functions:
-.IF_MCD = function( x, alpha ){
- N = 1
- q = qchisq( 1-alpha , df = N )
- calpha = (1-alpha)/pchisq( q , df = N+2 )
- out = ( (x^2-q)/(1-alpha) )*( abs(x) <= sqrt(q) )
-
- return( -1+q*calpha + calpha*out )
-}
-
-# .int = function(x){
-# return( .IF_MCD(x)^2*dnorm(x) )
-# }
-
-.avar_MCD = function(alpha){
- N = 1
- q_alpha = qchisq( 1-alpha , df = N )
- c_alpha = (1-alpha)/pchisq( q_alpha , df = N+2 )
- a_alpha = -2*sqrt(q_alpha)*dnorm(sqrt(q_alpha))+1-alpha
- b_alpha = -2*q_alpha^(3/2)*dnorm(sqrt(q_alpha))+3*a_alpha
-
- avar = c_alpha^2*q_alpha^2+1-2*c_alpha*q_alpha
- avar = avar + c_alpha^2/(1-alpha)^2*(b_alpha+q_alpha^2*(1-alpha)-2*q_alpha*a_alpha)
- avar = avar + 2*( c_alpha*q_alpha - 1)*c_alpha*(1/(1-alpha))*(-q_alpha*(1-alpha)+a_alpha)
-
- return(avar)
-}
-
-
-### ivInference help functions:
-##IQ estimator:
-.hatiq = function(rdata,IQestimator)
-{
- switch(IQestimator,
- RQuart = rQuar(rdata),
- QP = rQPVar(rdata),
- TP = rTPVar(rdata),
- minRQ = minRQ(rdata),
- medRQ = medRQ(rdata))
-}
-
-
-##Standard error of IVestimator:
-.IV=function(IVestimator,iq)
-{
- switch(IVestimator,
- RV= sqrt(2*iq),
- BV= sqrt(2.61*iq),
- TV= sqrt(3.06*iq),
- minRV= sqrt(3.81*iq),
- medRV= sqrt(2.96*iq))
-}
-
-
-### AJjumptest help functions:
-## scale
-.scale = function(align.by){
- switch(align.by,
- "seconds"= as.numeric(1),
- "minutes"= as.numeric(60),
- "hours"= as.numeric(3600))
-}
-
-## mupk
-.fmupk = function(p,k){
- mupk = NULL;
- if(p==2){
- mupk = switch(as.character(k),
- "2" = 4.00,
- "3" = 5.00,
- "4" = 6.00)
- }
- if(p==3){
- mupk = switch(as.character(k),
- "2" = 24.07,
- "3" = 33.63,
- "4" = 43.74)
- }
- if(p==4){
- mupk = switch(as.character(k),
- "2" = 204.04,
- "3" = 320.26,
- "4" = 455.67)
- }
- if(is.null(mupk)){
- # reduce simulation error by taking large T and large nrep
- nrep = 100;
- vmupk = rep(NA,times= nrep)
- # TODO GIANG CHECK THIS BUG
- for( i in 1:nrep){
- print(i)
- vmupk[i] = .fmupk(p,k) #TODO: check, is this recursive call correct??
- }
- mupk = round(mean(vmupk),2)
- }
- return(mupk)
-}
-
-.Npk = function(p,k){
- mup= 2^(p/2)*gamma(1/2*(p+1))/gamma(1/2)
- mu2p= 2^((2*p)/2)*gamma(1/2*((2*p)+1))/gamma(1/2)
- npk= (1/mup^2)*(k^(p-2)*(1+k))*mu2p + k^(p-2)*(k-1)*mup^2-2*k^(p/2-1)*.fmupk(p,k)
- return(npk)
-}
-
-.V = function(rse,p,k,N){
- mup = 2^(p/2)*gamma(1/2*(p+1))/gamma(1/2)
- muhalfp = 2^(p/4)*gamma(1/2*(p/2+1))/gamma(1/2)
- A2p = (1/N)^(1-p/2)/mup*sum(rse^p)
- Ap = (1/N)^(1-p/4)/muhalfp*sum(rse^(p/2)) ##check formula
-
- V = .Npk(p,k) *A2p/(N*Ap) ##check formula: A(p), A(2p)
- return(V)
-}
-
-## BNSJumptest help functions:
-# TODO THIS FUNCTION IS NOT USED??
-.gaus.ker= function(y)
-{
- ky=(1/sqrt(2*pi)*exp(-y^2/2))
-}
-
-## zgamma function:
-.zgamma = function(x,y){
- if(x^2<y)
- {
- out = abs(x)
- }
- else(out=1.094*sqrt(y))
- return(out)
-}
-
-##corrected threshold bipower variation:
-.ctBV = function(rdata,hatV,N){
- q = as.numeric(rdata)
-
- v = 3^2*hatV
- z1 = .zgamma(rdata[2:N],v) ##check formula TODO
- z2 = .zgamma(rdata[1:(N-1),v]) ##check formula TODO
-
- ctbv= (pi/2)*sum(z1*z2)
-
- return(ctbv)
-}
-
-## hatIV
-.hativ = function( rdata, IVestimator,...)
-{
- switch(IVestimator,
- RV = highfrequency:::RV(rdata),
- BV = highfrequency:::RBPVar(rdata),
- TV = rTPVar(rdata),
- minRV = minRV(rdata),
- medRV = medRV(rdata),
- ROWvar = rOWCov(rdata,...),
- CTBV = .ctBV(rdata, hatV, N,...))
-}
-
-
-.tt = function(IVestimator,...)
-{
- switch(IVestimator,
- BV= 2.61,
- minRV= 3.81,
- medRV= 2.96,
- ROWVar = thetaROWVar(alpha, alphaMCD))
-}
\ No newline at end of file
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