Some known limitations have to be taken into consideration when applying cross-validation techniques. In particular, cross-validation approaches only yield meaningful results if the validation set and training set used are drawn from the same population (without overlap between sets), and if human biases are controlled. For example, it is unrealistic to treat data as being drawn from the same population when using dissimilar time periods for validation and training sets, as this shift in time will introduce systematic differences into the sets being considered. As such, alignment of features to ensure consistency is again advisable for fair comparisons of time series. Similarly, training models based on a specific group of a population (e.g. young people), does not enable generalisation of cross-validated training results to the wider population as predictions could differ greatly to actual results.

Functional data analysis

Most statistical analysis techniques assume that the data points being evaluated are unrelated, and can be treated as independent entities. This is not generally true of time series, where there is often a derivative function that connects adjoining data points together. To address these scenarios, functional data analysis approaches were developed to enable statistical analysis and model construction based on whole functions rather than a collection of independent data points, making these approaches well suited to time series data \cite{Ramsay_2009}\cite{Ramsay_2009}. Additionally, functional data analytics has proved to be suitable for conditions where phase variations are present in data (such as in growth data and historical trends where curves start at different times/stages). Methods such as nonlinear mixed models, repeated measure ANOVA, and principal components analysis do not consider these differences in timing \cite{When_and_where_to_use_FDA}.
Functional data approaches are built on the principal of using 'basis functions' to represent data series as a 'functional data object' \cite{Ramsay_2009}. Basis functions are defined by: