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 $h$ 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])) |

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