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Panel data is defined in wikipedia as:

In statistics and econometrics, panel data and longitudinal data are both multi-dimensional data involving measurements over time. Panel data is a subset of longitudinal data where observations are for the same subjects each time.

While functional data is defined as:

Functional data analysis (FDA) is a branch of statistics that analyzes data providing information about curves, surfaces or anything else varying over a continuum.

As far as I read, it is common to consider time as the continuum over which FDA data varies. And methodologies in FDA seem to work by "projecting" the infinite dimensional space of time into a finite dimensional space that yields to a multivariate problem.

So how is then FDA different than panel data?

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I understand the Question, since panel data (and multiple, parallel time series and ...) can look like examples for functional data analysis. But functional data analysis is much more general and cover much more.

For examples look t some earlier posts:

The answers to this questions (and many others) can be summarized swiftly by saying that functional data analysis answers other questions, and is more general.

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