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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 resultplot(fc, xlim=c(tsp(x)[1]-h/f, tsp(x)[2]))

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