Cepstral-based clustering of financial time series

Abstract

In this paper, following the Partitioning Around Medoids (PAM) approach and the fuzzy theory, we propose a clustering model for financial time series based on the estimated cepstrum which represents the spectrum of the logarithm of the spectral density function. Selecting the optimal set of financial securities to build a portfolio that aims to maximize the risk-return tradeoff is a largely investigated topic in finance. The proposed model inherits all the advantages connected to PAM approach and fuzzy theory and it is able to compute objectively the cepstral weight associated to each cepstral coefficient by means of a suitable weighting system incorporated in the clustering model. In this way, the clustering model is able to tune objectively the different influence of each cepstral coefficient in the clustering process. The proposed clustering model performs better with respect to other clustering models. The proposed clustering model applied to each security sharpe ratio provides an efficient tool of clustering of stocks.