That depends on the filter order. Evaluating a FIR is O(N M^2) where N is the number of data points and M is the size of the FIR. Doing the same with an FFT is O(N Mlog(M)).
Neither is particularly "performant." FFTs and FIRs are big guns!
Would FFT even be appropriate for nonstationary time series? Wavelets seem more appropriate for such time series (not sure about how peformant they would be though, the R package runs pretty slow even for small datasets)
Neither is particularly "performant." FFTs and FIRs are big guns!