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We propose a new data-driven method to select the optimal number of relevantcomponents in Principal Component Analysis (PCA). This new method applies tocorrelation matrices whose time autocorrelation function decays more slowlythan an exponential, giving rise to long memory effects. In comparison withother available methods present in the literature, our procedure does not relyon subjective evaluations and is computationally inexpensive. The underlyingbasic idea is to use a suitable factor model to analyse the residual memoryafter sequentially removing more and more components, and stopping the processwhen the maximum amount of memory has been accounted for by the retainedcomponents. We validate our methodology on both synthetic and real financialdata, and find in all cases a clear and computationally superior answerentirely compatible with available heuristic criteria, such as cumulativevariance and cross-validation.

A memory-based method to select the number of relevant components in Principal Component Analysis