Gaussian Process kernels for popular state-space time series models

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. Experimental 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.