"The Dynamics of Economic Functions: Modelling and Forecasting the Yield Curve"
Clive G. Bowsher
Nuffield College, Oxford University
Roland Meeks
Federal Reserve Bank of Dallas
Abstract
The class of Functional Signal plus Noise (FSN) models is introduced that provides a new, general method for modelling
and forecasting time series of economic functions. The underlying, continuous economic function (or `signal') is a
natural cubic spline whose dynamic evolution is driven by a cointegrated vector autoregression for the ordinates
(or `y-values') at the knots of the spline. The natural cubic spline provides flexible cross-sectional fit and
results in a linear, state space model. This FSN model achieves dimension reduction, provides a coherent description
of the observed yield curve and its dynamics as the cross-sectional dimension N becomes large, and can feasibly
be estimated and used for forecasting when N is large. The integration and cointegration properties of the model
are derived. The FSN models are then applied to forecasting 36-dimensional yield curves for US Treasury bonds at
the one month ahead horizon. The method consistently outperforms the Diebold and Li (2006) and random walk forecasts
on the basis of both mean square forecast error criteria and economically relevant loss functions derived from the
realised profits of pairs trading algorithms. The analysis also highlights in a concrete setting the dangers of
attempts to infer the relative economic value of model forecasts on the basis of their associated mean square
forecast errors.
Keywords: FSN-ECM models, functional time series, term structure, forecasting interest rates, natural cubic spline,
state space form:
JEL Classification: C33, C51, C53, E47, G12