EC 422/522 · Lecture 6 · Bootstrapped density forecasts

Seasonal random walk: bootstrapped sample paths

Victoria (AU) café, restaurant and takeaway turnover, $ million per month. Each path adds residuals drawn at random from the training sample to the seasonal random walk.

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How each path is built

  1. Draw a residual at random, with replacement, from the training-sample residuals et = yt − yt−12 (demeaned).
  2. Add it to the seasonal random walk forecast to simulate yT+1.
  3. For horizons beyond one month, feed simulated values back in and repeat out to the horizon. Months more than a year out build on the simulated value from 12 months earlier.

What to look for

At a 1-month horizon each simulation is a single possible value for next month. At longer horizons, a few paths show what single possible futures look like. As the number of paths grows, they fill in the forecast distribution. Switch to Interval forecast to replace the paths with their percentiles: the 10th and 90th give the 80% interval, and the 2.5th and 97.5th give the 95% interval. This matches generate(bootstrap = TRUE) and forecast(bootstrap = TRUE) in fable. Data: aus_retail (fpp3), April 1982 to December 2018.