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I want to learn some functional analysis for time series. I've heard from my professor that functional analysis becomes more popular in Data Science research. Can somebody give me some hints what are connections of Time Series theory and Functional Analysis and where can I read about them.

I look forward for your respond

kjetil b halvorsen
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user10880031
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  • See https://stats.stackexchange.com/questions/419167/statistics-and-machine-learning-references-which-require-functional-analysis-bac/419176#419176 – kjetil b halvorsen Apr 17 '20 at 15:40
  • I wonder if “functional analysis” (vector spaces with norms defined by Lebesgue integrals) are what you’re looking to do. Do you mean functional data analysis? There may be a connection to functional analysis, but I seriously doubt it’s necessary to get into Banach spaces, etc, to do good work with functional data. – Dave Apr 17 '20 at 15:50
  • I saw that 1 step linear prediction uses Hilbert space, so I thought that there can be more things relating to Time Series – user10880031 Apr 17 '20 at 16:15
  • Chapter 2 of Brockwell and Davis---a standard text on time series---is titled "Hilbert space Theory". That's pretty close, although not all, to all the functional analysis relevant to time series---about the first week of a standard functional analysis class. Basically, you view a time series as a sequence in the Hilbert space L^2. This perspective is convenient when applicable but the more probabilistic aspects are not visible. – Michael Apr 17 '20 at 20:54

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