# An R function to shift vectors by a specified lag

Quite of bit of my work involves looking at “shifts” between two time series. There are lots of reasons why shifts are interesting, including such things as:

• phase differences in the tides at two different locations,

• physical separation between sensors on a profiling instrument, and

• clock drifts between two logging sensors.

To accomplish the actual shifting of the vectors (I’m not going to discuss here how to determine the amount by which the series should be shifted, since that depends on the parameters of the problem), I created the following function:

shift <- function(x, lag) {
n <- length(x)
xnew <- rep(NA, n)
if (lag < 0) {
xnew[1:(n-abs(lag))] <- x[(abs(lag)+1):n]
} else if (lag > 0) {
xnew[(lag+1):n] <- x[1:(n-lag)]
} else {
xnew <- x
}
return(xnew)
}

The function takes as input the vector x and a specified integer lag, and shifts the input series by that amount. NA’s are added to either the beginning or the end (depending on the sign of lag) to pad the shifted vector to be the same length as the input. Note that lag is defined so that a positive lag shifts x “to the right”, i.e. moves values to a higher index.