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.

Inference on Causal Effects of Interventions in Time using Gaussian Processes

This paper focuses on drawing inference on the causal impact of an intervention at a specific time point, as manifested in an outcome variable over time. We operate on the interrupted time series framework and expand on approaches such as the synthetic control (Abadie 2003) and Bayesian structural time series (Brodersen et al 2015), by replacing the underlying dynamic linear regression model with a non-parametric formulation based on Gaussian Processes. The developed models possess a high degree of flexibility posing very little limitations on the functional form and allow to incorporate uncertainty, stemming from its estimation, under the Bayesian framework. We introduce two families of non-parametric structural time series models either operating on the trajectory of the outcome variable alone, or in a multivariate setting using multiple output Gaussian processes. The paper engages closely with a case study focusing on the impact of the accelerated UK vaccination schedule, as contrasted with the rest of Europe, to illustrate the methodology and present the implementation procedure.