Gaussian Process Kernels for Popular State-Space Time Series Models
This work facilitates idea-sharing between state-space and Gaussian Process modeling approaches for time series analysis, though it is incremental in nature.
The paper transforms several widely used state-space time series models into continuous-time form and derives corresponding Gaussian Process kernels, demonstrating experimentally that these kernels are correct and appropriate for Gaussian Process Regression, with identical modeling results on a real-world dataset.
In this paper we investigate a link between state- space models and Gaussian Processes (GP) for time series modeling and forecasting. In particular, several widely used state- space models are transformed into continuous time form and corresponding Gaussian Process kernels are derived. Experimen- tal results demonstrate that the derived GP kernels are correct and appropriate for Gaussian Process Regression. An experiment with a real world dataset shows that the modeling is identical with state-space models and with the proposed GP kernels. The considered connection allows the researchers to look at their models from a different angle and facilitate sharing ideas between these two different modeling approaches.