Partial Cross-correlation in R - r

Question

I think the title is fairly self-explanatory. I want to compute the cross-correlation between two time series controlled for the values at other lags. I can't find any existing R code to do this, and I'm not at all confident enough in my knowledge of statistics (or R) to try to write something myself. It would be analogous to the partial autocorrelation function, just for the cross-correlation instead of the autocorrelation.
If it helps at all, my larger objective is to look for lagged correlations between different measurements of a physical system (to start with, flux and photon index from gamma ray measurements of blazars), with the goal of building a general linear model to try to predict flaring events.

Answer 1

Look at my answer to my own question (same as the one you posted).
You can make use of the pacf function in R, extending it to a matrix with 2 or more time series. I have checked results between the multivariate acf and ccf functions and they yield the same results, so the same can be concluded about the multivariate pacfand the non-existing pccf.

Answer 2

I believe this work,
pccf <- function(x,y,nlags=7,partial=TRUE){
# x (numeric): variable that leads y
# y (numeric): variable of interest
# nlags (integer): number of lags (uncluding zero)
# partial (boolean): partial or absolute correlation
# trim y
y <- y[-(1:(nlags-1))]
# lagged matrix of x
x_lagged <- embed(x,nlags)
# process for each lag
rho <- lag <- NULL
for(i in 1:(nlags)){
if(partial){
# residuals of x at lag of interest regressed on all other lags of x
ex <- lm(x_lagged[,i] ~ x_lagged[,-i])$residuals
# residuals of y regressed on all lags of x but the one of interest
ey <- lm(y ~ x_lagged[,-i])$residuals
}else{
ex <- x_lagged[,i]
ey <- y
}
# calculate correlation
rho[i] = cor(ex,ey, use="pairwise.complete.obs")
lag[i] = i-1
}
return(
tibble(lag=lag, rho=rho) %>%
arrange(lag)
)
}
# test
n <- 200 # count
nlag <- 6 # number of lags
x <- as.numeric(arima.sim(n=n,list(ar=c(phi=0.9)),sd=1)) # simulate times series x
y <- lag(x,nlag) + rnorm(n,0,0.5) # simulate y to lag x
y <- y[(nlag+1):n] # remove NAs from lag
x <- x[(nlag+1):n] # align with y
pccf(x,y,nlags=10,partial=FALSE) %>%
mutate(type='Cross correlation') %>%
bind_rows(
pccf(x,y,nlags=10,partial=TRUE) %>%
mutate(type='Partial cross correlation')
) %>%
ggplot() +
geom_col(aes(-lag,rho),width=0.1) +
facet_wrap(~type,scales='free_y', ncol=1) +
scale_x_continuous(breaks=-10:0) +
theme_bw(base_size=20)