  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.
