Detecting patterns in financial data through weighted time-frequency domain clustering

The paper introduces a strategy for identifying representative patterns in financial time series data from both temporal and frequency perspectives. To this end, a wavelet transformation of the time series is adopted as pre-processing step. Wavelets provide a multi-resolution representation of the time series, which is represented as the sum of a coarse approximation and a set of multiscale detail coefficients providing information about the temporal data at different frequency levels. This allows highlighting trends and cycles in the time domain, also assessing variance at different frequency levels. The contribution of this paper is the development of a clustering method for time series, represented as a matrix of wavelet coefficients to discover interesting patterns. To this end, an optimally weighted Euclidean distance is proposed, giving weights to frequency components. Thus, a new clustering objective function and an algorithm that allows optimizing it are proposed. The effectiveness of the method is evaluated on real and simulated data. The real dataset consists of a set of time series that record the Purchase Price for End Customers (PUN) of the Italian electricity market from 2016 to 2023, while the simulated dataset consists of time series generated by overlapping sinusoids with different amplitudes, frequencies, and phases.