12.6 Backcasting

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 easy to implement. The following functions reverse a ts object and a forecast object.

# Function to reverse time
reverse_ts <- function(y)
{
  ts(rev(y), start=tsp(y)[1L], frequency=frequency(y))
}
# Function to reverse a forecast
reverse_forecast <- function(object)
{
  h <- length(object[["mean"]])
  f <- frequency(object[["mean"]])
  object[["x"]] <- reverse_ts(object[["x"]])
  object[["mean"]] <- ts(rev(object[["mean"]]),
    end=tsp(object[["x"]])[1L]-1/f, frequency=f)
  object[["lower"]] <- object[["lower"]][h:1L,]
  object[["upper"]] <- object[["upper"]][h:1L,]
  return(object)
}

Then we can apply these functions to backcast any time series. Here is an example applied to quarterly retail trade in the Euro area. The data are from 1996 to 2011. We backcast to predict the years 1994-1995.

# Backcast example
euretail %>%
  reverse_ts() %>%
  auto.arima() %>%
  forecast() %>%
  reverse_forecast() -> bc
autoplot(bc) +
  ggtitle(paste("Backcasts from",bc[["method"]]))

Figure 12.6: Backcasts for quarterly retail trade in the Euro area using an ARIMA model.