Clustering Financial Time Series: How Long is Enough?
This addresses a practical issue for financial researchers and practitioners in time series analysis, but it is incremental as it builds on existing clustering practices.
The paper tackles the problem of determining the optimal length of financial time series for clustering based on correlations, showing that clustering is statistically consistent and providing an empirical answer to avoid spurious clusters or smoothed dynamics.
Researchers have used from 30 days to several years of daily returns as source data for clustering financial time series based on their correlations. This paper sets up a statistical framework to study the validity of such practices. We first show that clustering correlated random variables from their observed values is statistically consistent. Then, we also give a first empirical answer to the much debated question: How long should the time series be? If too short, the clusters found can be spurious; if too long, dynamics can be smoothed out.