Wavelet-based Time Series Cluster Analysis of Mortgage Risk

Author: Dhananjay Salgaocar
Degree: M.S. in Financial Engineering
Year: 2019
Advisory Committee: Dr. Dragos Bozdog, Dr. Ionut Florescu

Abstract: In this thesis, we implement the discrete wavelet transform (DWT) to categorize mortgages based on the payment history. The wavelet transform is applied to the time series of payments to perform a multiresolution analysis. The resulting wavelet coefficients are used to cluster loans into three rating groups by using the various kMeans clustering methods. The first model proposed uses the wavelet coefficients corresponding to each scale to cluster the time series. The second model improves upon the first, by using an iterative procedure derived from the i-kMeans model that uses the final centers from clustering the higher scale coefficients to initialize the clustering for the next level. The third model makes use of the energy decomposition of wavelet coefficients to cluster the payment histories. It is seen that the k-Means algorithm fails to converge at lower scales when random centers are used. The i-kMeans algorithm addresses this problem by using cluster assignments from higher levels to initialize the centroids for the k-Means algorithm applied to lower level coefficients. The clusters are evaluated by observing the cluster assignments at the time of default. The clusters formed by the i-kMeans algorithm provide better separation than using individual-level coefficients while clustering based on energy decomposition manages to group all the defaults in a single cluster but has large numbers of false positives.