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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. 

A central aim of neuroethological research is to discover the mechanisms of natural behaviors in controlled laboratory studies. This goal, however, comes with challenges, namely the selection of experimental paradigms that allow full expression of natural behaviors. Here, we explore this problem in echolocating bats that evolved Doppler shift compensation (DSC) of sonar vocalizations to yield close matching between echo frequency and hearing sensitivity. We ask if behavioral tasks influence the precision of DSC in Pratt’s roundleaf bat, Hipposideros pratti , in three classic laboratory paradigms evoking audio-vocal adjustments: Stationary bats listening to echo playbacks, bats transported on a moving pendulum, and bats flying freely. We found that experimental conditions had a strong influence on the expression of the audiovocal frequency adjustments in bats. H. pratti exhibited robust DSC in both free-flying and moving-pendulum experiments but did not exhibit consistent audiovocal adjustments in echo playback experiments. H. pratti featured a maximum compensation magnitude of 87% and a compensation precision of 0.27% in the free flight experiment. Interestingly, in the moving pendulum experiment H. pratti displayed surprisingly high-precision DSC, with an 84% maximum compensation magnitude and a 0.27% compensation precision. Such DSC performance places H. pratti among the bat species exhibiting the most precise audio-vocal control of echo frequency. These data support the emerging view that Hipposiderid bats have a high-precision DSC system and highlight the importance of selecting experimental paradigms that yield the expression of robust natural behaviors.