A PIT State Space Model for Non-Gaussian Streamflow Forecasting

This paper presents a novel state space framework, the PIT state space model (PIT SSM), which incorporates non-Gaussian predictive distributions while preserving the tractability of linear Gaussian models. By applying the probability integral transform, the approach yields a closed-form likelihood and enables PIT filtering and smoothing. The GB2 distribution is adopted for its flexibility in capturing skewness and heavy tails in streamflow series. An empirical application to monthly streamflow data shows that structural components such as trend and seasonality are robust to distributional assumptions. The GB2 specification provides the best in-sample fit and competitive out-of-sample performance, while maintaining predictive intervals consistent with the positive support of streamflow. The PIT SSM also outperforms the Gaussian Kalman filter specification, SARIMA, and GAS-GB2 in likelihood-based in-sample criteria. These results demonstrate its usefulness for modeling and forecasting non-Gaussian streamflow series.