How to forecast from a fitted ETS model, and check whether it beats the baselines
Today let's turn a fitted ETS model into an actual forecast, and then check whether that forecast is any good.
Take Australia's quarterly natural gas production, measured in petajoules, from the first quarter of 1956 to the second quarter of 2010. That's 218 quarters of real production numbers. Output climbs across those five and a half decades, from single digits in the 1950s to well over 200 petajoules a quarter by 2010, and the swing between a quarter's low and high grows right along with it. Here is all 218 quarters of it, plotted in order.
Look at how far apart a low quarter and a high quarter sit once you get to the 2000s, compared to how close together they were in the 1950s. In the steps ahead, you will take a model already fitted on exactly this series and turn it into a forecast, two different kinds of interval around that forecast, and a check on whether it actually beats the simple methods.
Fit the ETS model this lesson forecasts from
Fit ETS() on the whole Gas series, with no formula, so it searches out and picks all three letters itself.
ETS() picked ETS(M,A,M): multiplicative error, additive trend, multiplicative season. alpha = 0.653 says the level updates fast on new data. beta = 0.144 says the trend updates more slowly. gamma = 0.098 says the seasonal pattern barely moves from one year to the next.
gas_fit is now the one object every later step forecasts from, plots, checks and benchmarks.