Modeling joint probability distribution of yield curve parameters

Abstract

US Yield curve has recently collapsed to its most flattened level since subprime crisis and is close to the inversion. This fact has gathered attention of investors around the world and revived the discussion of proper modeling and forecasting yield curve, since changes in interest rate structure are believed to represent investors expectations about the future state of economy and have foreshadowed recessions in the United States. While changes in term structure of interest rates are relatively easy to interpret they are however very difficult to model and forecast due to no proper economic theory underlying such events. Yield curves are usually represented by multivariate sparse time series, at any point in time infinite dimensional curve is portrayed via relatively few points in a multivariate space of data and as a consequence multimodal statistical dependencies behind these curves are relatively hard to extract and forecast via typical multivariate statistical methods.We propose to model yield curves via reconstruction of joint probability distribution of parameters in functional space as a high degree polynomial. Thanks to adoption of an orthonormal basis, the MSE estimation of coefficients of a given function is an average over a data sample in the space of functions. Since such polynomial coefficients are independent and have cumulant-like interpretation ie.describe corresponding perturbation from an uniform joint distribution, our approach can also be extended to any d-dimensional space of yield curve parameters (also in neighboring times) due to controllable accuracy. We believe that this approach to modeling of local behavior of a sparse multivariate curved time series can complement prediction from standard models like ARIMA, that are using long range dependencies, but provide only inaccurate prediction of probability distribution, often as just Gaussian with constant width.