How to "Backcast" a Time Series in R

Some­times it is use­ful to “back­cast” a time series — that is, fore­cast in reverse time. Although there are no in-​​built R func­tions to do this, it is very easy to imple­ment. Sup­pose x is our time series and we want to back­cast for peri­ods. Here is some code that should work for most uni­vari­ate time series. The exam­ple is non-​​seasonal, but the code will also work with sea­sonal data.

library(forecast)
x <- WWWusage
h <- 20
f <- frequency(x)
# Reverse time
revx <- ts(rev(x), frequency=f)
# Forecast
fc <- forecast(auto.arima(revx), h)
plot(fc)
# Reverse time again
fc$mean <- ts(rev(fc$mean),end=tsp(x)[1] - 1/f, frequency=f)
fc$upper <- fc$upper[h:1,]
fc$lower <- fc$lower[h:1,]
fc$x <- x
# Plot result
plot(fc, xlim=c(tsp(x)[1]-h/f, tsp(x)[2]))