I can't really comment on how accurate the Tableau forecasting model is, it kinda depends on whether your data will benefit from exponential smoothing being applied to the forecasting model or not.
However as soon as you find yourself wanting a more advanced way to forecast your data, why not use R? R is integrated in Tableau since version 8.1 I believe.With R you can go really crazy with regard to your forecasting model.
I am not a heavy R user but I am sure there might be a written code somewhere on forecasting in R but I have an individual Tableau license I am not sure if i can use the R functionality in tableau without setting up some kind of a R server. I may be completely wrong.
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R is free, and if you are only going to use Tableau desktop with a single license, then it is very easy to set R up. You can run it on the same client as the one you are using Tableau desktop on.
Turning your R program into a "Rserver" is as simple as entering the following line into R, after you have opened R:
- first time: install.packages("Rserve"); library(Rserve); Rserve()
- Every consecutive time R is started: library(Rserve); Rserve()
See for a guide on how to setup R for Tableau and some examples: Tableau 8.1 and R | Tableau Software
This is very helpful since i can run the script you provided into my Rstudio and manage my Rconnection into my desktop connecting thru localhost. But different procedure for enterprise Tableau server as there has to be a linux host server.
To be clear Tableau already supports Holt-Winters. You may have heard people mention the term "simple exponential smoothing" in some cases when talking about Tableau's forecasting but model being used is a matter of what your data has e.g. whether it as a trend or if it is additive or multiplicative. R's forecasting package will also do simple exponential smoothing for an ANN model. Mention of simple exponential smoothing doesn't mean forecasting feature is simple or inaccurate.
The author of what is considered the best forecasting package in R who also happens to be one of the leading experts in forecasting, Prof. Rob J. Hyndman worked with Tableau as an advisor when this feature was built. Tableau runs tests to compare results with other forecasting packages regularly. So I am not sure what led you to thinking Tableau wasn't using Holt-Winters or the results were incorrect. That being said, Tableau doesn't capture all cases covered in the R forecasting package so with some datasets, you may not get a result from Tableau (i.e. a flat line) where R would give you a forecast. For example R package also has ARIMA which Tableau doesn't currently have.
If you could share them, I would love to see the datasets you are getting conflicting predictions from Tableau and R.