Dynamic Term Structure Models with Nonlinearities using Gaussian Processes

The importance of unspanned macroeconomic variables for Dynamic Term Structure Models has been intensively discussed in the literature. To our best knowledge the earlier studies considered only linear interactions between the economy and the real-world dynamics of interest rates in DTSMs. We propose a generalized modelling setup for Gaussian DTSMs which allows for unspanned nonlinear associations between the two and we exploit it in forecasting. Specifically, we construct a custom sequential Monte Carlo estimation and forecasting scheme where we introduce Gaussian Process priors to model nonlinearities. Sequential scheme we propose can also be used with dynamic portfolio optimization to assess the potential of generated economic value to investors. The methodology is presented using US Treasury data and selected macroeconomic indices. Namely, we look at core inflation and real economic activity. We contrast the results obtained from the nonlinear model with those stemming from an application of a linear model. Unlike for real economic activity, in case of core inflation we find that, compared to linear models, application of nonlinear models leads to statistically significant gains in economic value across considered maturities.