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I am forecasting a collection of different types of items, using many different forecasting techniques. Some of the techniques I use take the input data as is to produce a distributional forecast. These are easy to combine and produce improved distributions from any model on their own.

For other forecasts, I use different types of data transformations prior to fitting models (box-cox, logs, IHS, etc.) I have noticed that you cannot combine forecast results which produce non-normal distribution estimates. Is there an explanation for this? Is it possible to combine forecasts with the same exact data transformations? (ex: an ARIMA and ETS model that take the natural log of the input data.)

Most of my forecasting and combining is done using the fable package in R.

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    $\begingroup$ What do you mean by "cannot" combine? Why couldn't you? $\endgroup$
    – Chris Haug
    Mar 4, 2021 at 23:54

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You can certainly combine non-normal distributional (density) forecasts.

As a very simple example, your density forecasts may be empirical, derived by resampling in-sample residuals for various models. Then you can simply throw all these resamples into one big pile and get a large empirical predictive distribution.

In the parametric case, you can calculate mixtures of different types of distributions.

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