Now how can this be done, you might ask? A common approach would be to use basis expansion. This way we are also able to induce smoothing, which can be desirable to reduce noise. But we can estimate the underlying functions to our data. Well yes, it is in fact true, that measurements are not continuous. Aren’t we forgetting something here?įunctions are continous, measurements are not. If we view our data as function, comparison becomes much easier. Comparing those would then be problematic. It often happens that you want to compare timeseries, but they have measurements not taken at the same time, or one has more measurements than the other. Measurements do not have to be taken at the same point in time to be comparable.

functions can provide a much more natural and intuitive view on our data.Functions can be registered very easily to a common timescale.We can analyze the derivatives of functions.A function usually can be evaluated at any point in time.This has multiple upsides over the traditional timeseries view. Now in functional data analysis, we do not interpret our measured data as a sequence of observations, but as a single function or curve. In fact, one could say, that there is an underlying function of time, that gives rise to your measurements. Well, this is quite obvious, we live by this pattern after all. If you then look at the accumulated data, you might come to the conclusion, that the temperature somewhat behaves similar over one year. Say you are measuring the temperature in your hometown each day for multiple years.

A typical example of functional data (Image by author) Functional Data

Functional analysis