wave.multiple.cross.regression <- #3.0.0
function(xx, lag.max=NULL, p = .975, ymaxr=NULL) {
sum.of.squares <- function(x) { sum(x^2, na.rm=TRUE) / sum(!is.na(x)) }
sum.of.not.squares <- function(x) { sum(x, na.rm=TRUE) / sum(!is.na(x)) }
asnum <- function(x){setNames(as.numeric(x),names(x))}
d <- length(xx) #number of series
dd <- d*(d-1)/2 #number of correlations
l <- length(xx[[1]]) #number of scales J+1 (wavelet coefficients at levels 1 to J plus the scaling coeffs at level J+1)
N <- length(xx[[1]][[1]]) #number of observations
if(is.null(lag.max)) {lag.max <- trunc(sqrt(length(xx[[1]][[l]]))/2)}
lm <- min(length(xx[[1]][[l]])-1, lag.max, na.rm=TRUE)
x.var <- vector("list", d)
for(j in 1:d) {
x.var[[j]] <- unlist(lapply(xx[[j]], sum.of.squares))
}
xy.cor <- vector("list", dd)
xy <- vector("list", l)
jk <- 0
for(k in 1:(d-1)) {
for(j in (k+1):d) {
jk <- jk+1
for(i in 1:l) {
xy[[i]] <- as.vector(xx[[j]][[i]] * xx[[k]][[i]])
}
xy.cov <- unlist(lapply(xy, sum.of.not.squares))
xy.cor[[jk]] <- xy.cov / sqrt(x.var[[j]] * x.var[[k]])
}}
xy.cor.vec <- matrix(unlist(xy.cor),l,dd)
xy.mulcor <- matrix(0, l, 2*lm+1)
rval <- rstd <- rlow <- rupp <- rtst <- rpva <- rord <- vector("list", l)
# xy.mulreg <- lapply(vector("list", l), function(x) {vector("list",2*lm+1)})
## Note: [ 1 2 ... lm-1 lm | lm+1 | lm+2 ... 2*lm 2*lm+1 ]
## [ ...Pimax var leads | 0 | Pimax var lags... ]
YmaxR <- vector("numeric",l)
for(i in 1:l) {
xy.mulreg <- vector("list",2*lm+1)
r <- xy.cor.vec[i,]
P <- diag(d)/2
P[lower.tri(P)] <- r
P <- P+t(P)
Pidiag <- diag(solve(P))
if(is.null(ymaxr)) {
YmaxR[i] <- Pimax <- which.max(Pidiag) ## detect i | x[i] on rest x gives max R2
} else {YmaxR[i] <- Pimax <- ymaxr}
sgnr <- 1
if (dd==1) sgnr <- sign(r)
xy.mulcor[i,lm+1] <- sgnr*sqrt(1-1/Pidiag[Pimax])
## lag=0: this must be same as in wave.multiple.correlation
x0 <- sapply(xx[-Pimax],'[[',i)
y0 <- sapply(xx[Pimax],'[[',i)
depvar <- matrix(c(-1,0,Inf,0),1,4)
if (is.null(names(xx))) row.names(depvar) <- "Y"
else row.names(depvar) <- names(xx[Pimax])
z0 <- summary(lm(formula = y0 ~ x0))$coefficients
if(Pimax<nrow(z0)) z1 <- z0[(Pimax+1):nrow(z0),,drop=FALSE]
else z1 <- NULL
z0 <- rbind(z0[1:Pimax,,drop=FALSE], depvar, z1)
if (is.null(names(xx))) row.names(z0)[1] <- "b0"
else row.names(z0) <- c("b0",names(xx))
xy.mulreg[[lm+1]] <- z0
# xy.mulreg <- z[order(z[,4]),1:2] #coefficients (and their stdvs) ordered from most to least significant
## lag=0: this must be same as in wave.multiple.regression
if(lm>0) {
x <- x0
z <- y <- y0
vlength <- length(y)
for(j in 1:lm) { ## now we obtain R2 of var[Pimax] with lagged values
y <- c(y[2:vlength], NA)
z <- c(NA, z[1:(vlength-1)])
lm_yx <- summary(lm(formula = y ~ x))
lm_zx <- summary(lm(formula = z ~ x))
sgnr <- 1
if (dd==1) sgnr <- sign(cor(y,x,use="complete.obs"))
xy.mulcor[i,lm+1+j] <- sgnr*sqrt( lm_yx$r.squared )
## Note: var[Pimax] lags behind the others: y[t+j]<--x[t]hat
zjr <- lm_yx$coefficients
if(Pimax<nrow(zjr)) z1 <- zjr[(Pimax+1):nrow(zjr),,drop=FALSE]
else z1 <- NULL
zjr <- rbind(zjr[1:Pimax,,drop=FALSE], depvar, z1)
if (is.null(names(xx))) row.names(zjr)[1] <- "b0"
else row.names(zjr) <- c("b0",names(xx))
xy.mulreg[[lm+1+j]] <- zjr
sgnr <- 1
if (dd==1) sgnr <- sign(cor(z,x,use="complete.obs"))
xy.mulcor[i,lm+1-j] <- sgnr*sqrt( lm_zx$r.squared )
## Note: var[Pimax] leads the others: x[t]hat<--z[t-j]
zjl <- lm_zx$coefficients
if(Pimax<nrow(zjl)) z1 <- zjl[(Pimax+1):nrow(zjl),,drop=FALSE]
else z1 <- NULL
zjl <- rbind(zjl[1:Pimax,,drop=FALSE], depvar, z1)
if (is.null(names(xx))) row.names(zjl)[1] <- "b0"
else row.names(zjl) <- c("b0",names(xx))
xy.mulreg[[lm+1-j]] <- zjl
}}
rval[[i]] <- lapply(xy.mulreg, function(x){x[,'Estimate']})
rstd[[i]] <- lapply(xy.mulreg, function(x){x[,'Std. Error']})
rlow[[i]] <- lapply(xy.mulreg, function(x){x[,'Estimate']-qt(p,N-d)*x[,'Std. Error']})
rupp[[i]] <- lapply(xy.mulreg, function(x){x[,'Estimate']+qt(p,N-d)*x[,'Std. Error']})
rtst[[i]] <- lapply(xy.mulreg, function(x){x[,'t value']})
rpva[[i]] <- lapply(xy.mulreg, function(x){x[,'Pr(>|t|)']})
rord[[i]] <- lapply(xy.mulreg, function(x){match(abs(x[,'t value']),sort(abs(x[,'t value']),decreasing=TRUE))})
rval[[i]] <- t(sapply(rval[[i]],asnum))
rstd[[i]] <- t(sapply(rstd[[i]],asnum))
rlow[[i]] <- t(sapply(rlow[[i]],asnum))
rupp[[i]] <- t(sapply(rupp[[i]],asnum))
rtst[[i]] <- t(sapply(rtst[[i]],asnum))
rpva[[i]] <- t(sapply(rpva[[i]],asnum))
rord[[i]] <- t(sapply(rord[[i]],asnum))
} # end for(i in 1:l) loop
lags <- length(-lm:lm)
oldw <- getOption("warn")
options(warn = -1)
sqrtn <- sqrt(matrix(trunc(N/2^(1:l)), nrow=l, ncol=lags) - 3)
options(warn = oldw)
alow <- atanh(xy.mulcor)-qnorm(p)/sqrtn
if (dd>1) alow <- pmax(alow,0) ## wavemulcor can only be negative in bivariate case
aupp <- atanh(xy.mulcor)+qnorm(p)/sqrtn
ci.mulcor <- list( lower=tanh(alow), upper=tanh(aupp) )
xy.mulreg <- list( rval=rval, rstd=rstd, rlow=rlow, rupp=rupp,
rtst=rtst, rord=rord, rpva=rpva )
xy.mulreg <- lapply(xy.mulreg,setNames,names(xx[[1]]))
#) #vars=t(sapply(rval,names)) --> names of variables: useful if somehow reordered
Lst <- list(xy.mulcor=xy.mulcor,ci.mulcor=ci.mulcor,xy.mulreg=xy.mulreg,YmaxR=YmaxR,data=xx)
return(Lst)
}
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