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]))
R (programming language)
Time series
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