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Data‐driven dimension reduction in functional principal component analysis identifying the change‐point in functional data

Functional principal component analysis (FPCA) is the most commonly used technique to analyze infinite‐dimensional functional data in finite lower‐dimensional space for the ease of computational intensity. However, the power of a test detecting the existence of a change‐point falls with the inclusion of more principal dimensions explaining a larger proportion of variability. We propose a new methodology for dynamically selecting the dimensions in FPCA that are used further for the testing of the existence of any change‐point in the given data. This data‐driven and efficient approach leads to a more powerful test than those available in the literature. We illustrate this method on the monthly global average anomaly of temperatures.