How to loop the Holt's Double Exponential Smoothing by sampling beta?

Question

I want to forecast like hundreds records with some various alpha and beta in looping. My goal is to loop the holt result by 2 samples of beta (0.1 and 0.9) in RStudio. Here's the code:

library(forecast)
library(tidyverse)
library(magicfor)
magic_for(silent =  TRUE)

    dataset<- c(100,200,300,400,500,600,700,800,900,800,700)
    x<-c(0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9)

#-----------HOLT FOR BETA 0.1------------------

for (alpha in x) {
  des<-holt(dataset, alpha = alpha, beta=0.1)
  mape<-mean(abs(des$residuals)/des$x)*100
  put(beta=0.1, mape)
}
result01<-magic_result_as_dataframe()

#-----------HOLT FOR BETA 0.9------------------

for (alpha in x) {
  des<-holt(dataset, alpha = alpha, beta=0.9)
  mape<-mean(abs(des$residuals)/des$x)*100
  put(beta=0.9, mape)
}
result02<-magic_result_as_dataframe()

But I got an error in beta=0.9 and here's the notification:

[1] "Model: ETS(A,A,N)" Error in ets(x, "AAN", alpha = alpha, beta = beta, phi = phi, damped = damped, : No model able to be fitted

I've found the problem is about the dataset where if I put 8 records or less, it could forecast with beta=0.1, 0.9, and various sample of alpha and beta well. but if it has more than 8 records, it only can forecast with beta=0.1 and lower (0.1, 0.01, 0.001, 0.0001 only) but it could be error if the beta is upper than 0.1

could you help me to fix this? Thanks in advance

Answer 1

In the parameterization used by holt() , beta must be less than alpha. See https://otexts.com/fpp2/estimation-and-model-selection.html for a discussion of this.

Here is some code to do what you want for a range of alpha and beta values.

library(forecast)
library(tidyverse)

dataset <- c(100, 200, 300, 400, 500, 600, 700, 800, 900, 800, 700)
get_mape <- function(x, alpha, beta) {
  des <- holt(dataset, alpha=alpha, beta=beta)
  mean(abs(des$residuals) / des$x) * 100
}
holt_mape <- expand.grid(
    alpha = c(0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9),
    betastar = c(0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9)
  ) %>%
  mutate(
    beta = betastar * alpha,
    mape = map2_dbl(alpha, beta, get_mape, x=dataset)
  ) %>%
  as_tibble()
holt_mape
#> # A tibble: 81 x 4
#>    alpha betastar   beta  mape
#>    <dbl>    <dbl>  <dbl> <dbl>
#>  1   0.1      0.1 0.01   18.5 
#>  2   0.2      0.1 0.02   17.9 
#>  3   0.3      0.1 0.03   16.7 
#>  4   0.4      0.1 0.04   14.7 
#>  5   0.5      0.1 0.05   13.6 
#>  6   0.6      0.1 0.06   12.5 
#>  7   0.7      0.1 0.0700 11.5 
#>  8   0.8      0.1 0.08   10.6 
#>  9   0.9      0.1 0.09    9.64
#> 10   0.1      0.2 0.02   19.1 
#> # … with 71 more rows

^{Created on 2020-06-26 by the reprex package (v0.3.0)}

However, note that MAPE is computed here on the training data. Normally it would be computed on the test data.