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Jul 5, 2022 at 21:59 comment added Rob Hyndman The first paper on this was Hyndman & Ullah (CSDA, 2007). Citations of that paper, including the one Stephan mentions, may also be useful.
Jul 5, 2022 at 18:28 comment added Aksakal what you describes sounds like a variation of state space modeling. you essentially posit that the observed data is a representation of some unobserved state variables. so your space of x's, observed, are a transformation with noise x=f(s)+e of unobserved state s. you try to estimate s, then forecast $\hat s$ and transform back to $\hat x$. there are many examples of this approach in different fields.
Jul 5, 2022 at 18:14 history edited Barry CC BY-SA 4.0
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Jul 5, 2022 at 17:30 comment added Stephan Kolassa Forecasting of density function is not a duplicate (it asks for examples, not algorithms), but it might be useful. Unfortunately, there is not a lot of academic work on functional data forecasting. The Hyndman & Shang (2009) paper I referred to at this other thread is the only such paper I am aware of. Searching the agenda of the upcoming International Symposium on Forecasting for "functional" yields a few hits. Consider contacting the presenters?
Jul 5, 2022 at 17:22 history asked Barry CC BY-SA 4.0