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Linear Gaussian Affine Term Structure Models with Unobservable Factors: Calibration and Yield Forecasting
This paper provides a significant numerical evidence for out-of-sample forecasting ability of linear Gaussian interest rate models with unobservable underlying factors. We calibrate one, two and three factor linear Gaussian models using the Kalman filter on two different bond yield data sets and compare their out-of-sample
forecasting performance. One step ahead as well as four step ahead out-of-sample forecasts are analyzed based on the weekly data. When evaluating the one step ahead forecasts, it is shown that a one factor model may be adequate when only the short-dated or only the long-dated yields are considered, but two and three factor
models performs significantly better when the entire yield spectrum is considered. Furthermore, the results demonstrate that the predictive ability of multi-factor models remains intact far
ahead out-of-sample, with accurate predictions available up to one year after the last calibration for one data set and up to three
months after the last calibration for the second, more volatile data set. The experimental data denotes two different periods with different yield volatilities, and the stability of model
parameters after calibration in both the cases is
deemed to be both significant and practically useful. When it comes to four step ahead predictions, the quality of forecasts deteriorates for all models, as can be expected, but the advantage of using a multi-factor model as compared to a one factor model is still significant.
In addition to the empirical study above, we also suggest a nonlinear filter based on linear programming for improving the term structure matching at a given point in time. This method,
when used in place of a Kalman filter update, improves the term structure fit significantly with a minimal added computational overhead. The improvement achieved with the proposed method is
illustrated for out-of-sample data for both the data sets. This method can be used to model a parameterized yield curve consistently with the underlying short rate dynamics
Basic Representations of A_{2l}^(2) and D_{l+1}^(2) and the Polynomial Solutions to the Reduced BKP Hierarchies
Basic representations of A_{2l}^(2) and D_{l+1}^(2) are studied. The weight
vectors are represented in terms of Schur's -functions. The method to get
the polynomial solutions to the reduced BKP hierarchies is shown to be
equivalent to a certain rule in Maya game.Comment: January 1994, 11 page
Reflectionless analytic difference operators I. algebraic framework
We introduce and study a class of analytic difference operators admitting
reflectionless eigenfunctions. Our construction of the class is patterned after
the Inverse Scattering Transform for the reflectionless self-adjoint
Schr\"odinger and Jacobi operators corresponding to KdV and Toda lattice
solitons
Isospectral flow in Loop Algebras and Quasiperiodic Solutions of the Sine-Gordon Equation
The sine-Gordon equation is considered in the hamiltonian framework provided
by the Adler-Kostant-Symes theorem. The phase space, a finite dimensional
coadjoint orbit in the dual space \grg^* of a loop algebra \grg, is
parametrized by a finite dimensional symplectic vector space embedded into
\grg^* by a moment map. Real quasiperiodic solutions are computed in terms of
theta functions using a Liouville generating function which generates a
canonical transformation to linear coordinates on the Jacobi variety of a
suitable hyperelliptic curve.Comment: 12 pg
A Symmetric Generalization of Linear B\"acklund Transformation associated with the Hirota Bilinear Difference Equation
The Hirota bilinear difference equation is generalized to discrete space of
arbitrary dimension. Solutions to the nonlinear difference equations can be
obtained via B\"acklund transformation of the corresponding linear problems.Comment: Latex, 12 pages, 1 figur
Geometric and combinatorial realizations of crystal graphs
For irreducible integrable highest weight modules of the finite and affine
Lie algebras of type A and D, we define an isomorphism between the geometric
realization of the crystal graphs in terms of irreducible components of
Nakajima quiver varieties and the combinatorial realizations in terms of Young
tableaux and Young walls. For affine type A, we extend the Young wall
construction to arbitrary level, describing a combinatorial realization of the
crystals in terms of new objects which we call Young pyramids.Comment: 34 pages, 17 figures; v2: minor typos corrected; v3: corrections to
section 8; v4: minor typos correcte
Commuting Flows and Conservation Laws for Noncommutative Lax Hierarchies
We discuss commuting flows and conservation laws for Lax hierarchies on
noncommutative spaces in the framework of the Sato theory. On commutative
spaces, the Sato theory has revealed essential aspects of the integrability for
wide class of soliton equations which are derived from the Lax hierarchies in
terms of pseudo-differential operators. Noncommutative extension of the Sato
theory has been already studied by the author and Kouichi Toda, and the
existence of various noncommutative Lax hierarchies are guaranteed. In the
present paper, we present conservation laws for the noncommutative Lax
hierarchies with both space-space and space-time noncommutativities and prove
the existence of infinite number of conserved densities. We also give the
explicit representations of them in terms of Lax operators. Our results include
noncommutative versions of KP, KdV, Boussinesq, coupled KdV, Sawada-Kotera,
modified KdV equations and so on.Comment: 22 pages, LaTeX, v2: typos corrected, references added, version to
appear in JM
Dual Resonance Model Solves the Yang-Baxter Equation
The duality of dual resonance models is shown to imply that the four point
string correlation function solves the Yang-Baxter equation. A reduction of
transfer matrices to symmetry is described by a restriction of the KP
function to Toda molecules.Comment: 10 pages, LaTe
Integrable hierarchy underlying topological Landau-Ginzburg models of D-type
A universal integrable hierarchy underlying topological Landau-Ginzburg
models of D-tye is presented. Like the dispersionless Toda hierarchy, the new
hierarchy has two distinct (``positive" and ``negative") set of flows. Special
solutions corresponding to topological Landau-Ginzburg models of D-type are
characterized by a Riemann-Hilbert problem, which can be converted into a
generalized hodograph transformation. This construction gives an embedding of
the finite dimensional small phase space of these models into the full space of
flows of this hierarchy. One of flat coordinates in the small phase space turns
out to be identical to the first ``negative" time variable of the hierarchy,
whereas the others belong to the ``positive" flows.Comment: 14 pages, Kyoto University KUCP-0061/9
Highest weight representations of the quantum algebra U_h(gl_\infty)
A class of highest weight irreducible representations of the quantum algebra
U_h(gl_\infty) is constructed. Within each module a basis is introduced and the
transformation relations of the basis under the action of the Chevalley
generators are explicitly written.Comment: 7 pages, PlainTe
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