How to refit a Holt-Winters exponential smoothing model on test data without re-estimation of parameters

Question

I try to generate multiple one-step forecasts by using the HoltWinters method for exponential smoothing. I, therefore, split my data into training and testing and fit a HoltWinters model on my training set. Now I want to produce multiple one-step forecasts for the length of my test data, in a way that the model is "updated" with every new observation of the test set, without re-estimation of the parameters. Kind of in a way rolling origin cross-validation would be done. I found the refit()-function, but that only seems to work with ARIMA models. Does someone know some code that could work? Or somewhere I could read about it?

Answer 1

The Holt-Winters method is a special case of an ETS model. So you can use the ETS function from the fable package like this:

library(fable)
library(dplyr)

fit <- as_tsibble(USAccDeaths) %>%
  filter(lubridate::year(index) < 1977) %>%
  model(ets = ETS(value))

fit %>%
  refit(as_tsibble(USAccDeaths)) %>%
  report()
#> Series: value 
#> Model: ETS(A,N,A) 
#>   Smoothing parameters:
#>     alpha = 0.6570182 
#>     gamma = 0.004485907 
#> 
#>   Initial states:
#>      l[0]      s[0]     s[-1]    s[-2]     s[-3]    s[-4]    s[-5]    s[-6]
#>  9753.881 -30.20712 -286.0886 227.9668 -65.55104 977.0047 1673.521 806.8883
#>     s[-7]     s[-8]     s[-9]    s[-10]   s[-11]
#>  327.0867 -529.6172 -754.7921 -1551.379 -794.833
#> 
#>   sigma^2:  80017.07
#> 
#>      AIC     AICc      BIC 
#> 1131.232 1137.507 1160.828

^{Created on 2022-06-02 by the reprex package (v2.0.1)}

If you specifically wanted the Holt-Winters variant, you could use

model(ets = ETS(value ~ trend("A") + season("M")))

for a multiplicative Holt-Winters model or

model(ets = ETS(value ~ trend("A") + season("A")))

for an additive Holt-Winters model