Journal of Data Science

Loan behavior modeling is crucial in financial engineering. In particular, predicting loan prepayment based on large-scale historical time series data of massive customers is challenging. Existing approaches, such as logistic regression or nonparametric regression, could only model the direct relationship between the features and the prepayments. Motivated by extracting the hidden states of loan behavior, we propose the smoothing spline state space (QuadS) model based on a hidden Markov model with varying transition and emission matrices modeled by smoothing splines. In contrast to existing methods, our method benefits from capturing the loans’ unobserved state transitions, which not only increases prediction performances but also provides more interpretability. The overall model is learned by EM algorithm iterations, and within each iteration, smoothing splines are fitted with penalized least squares. Simulation studies demonstrate the effectiveness of the proposed method. Furthermore, a real-world case study using loan data from the Federal National Mortgage Association illustrates the practical applicability of our model. The QuadS model not only provides reliable predictions but also uncovers meaningful, hidden behavior patterns that can offer valuable insights for the financial industry.

Abstract: Polya tree, by embedding parametric families as a special case, provides natural suit to test goodness of fit of a parametric null with non parametric alternatives. For this purpose, we present a new construction on Polya tree for random probability measure, which aims to perform an easy multiple χ 2 test for goodness of fit. Examples of data analyses are provided in simulation studies to highlight the performance of the proposed methods.