23,441 research outputs found
A partial correlation vine based approach for modeling and forecasting multivariate volatility time-series
A novel approach for dynamic modeling and forecasting of realized covariance
matrices is proposed. Realized variances and realized correlation matrices are
jointly estimated. The one-to-one relationship between a positive definite
correlation matrix and its associated set of partial correlations corresponding
to any vine specification is used for data transformation. The model components
therefore are realized variances as well as realized standard and partial
correlations corresponding to a daily log-return series. As such, they have a
clear practical interpretation. A method to select a regular vine structure,
which allows for parsimonious time-series and dependence modeling of the model
components, is introduced. Being algebraically independent the latter do not
underlie any algebraic constraint. The proposed model approach is outlined in
detail and motivated along with a real data example on six highly liquid
stocks. The forecasting performance is evaluated both with respect to
statistical precision and in the context of portfolio optimization. Comparisons
with Cholesky decomposition based benchmark models support the excellent
prediction ability of the proposed model approach
The Rank of the Covariance Matrix of an Evanescent Field
Evanescent random fields arise as a component of the 2-D Wold decomposition
of homogenous random fields. Besides their theoretical importance, evanescent
random fields have a number of practical applications, such as in modeling the
observed signal in the space time adaptive processing (STAP) of airborne radar
data. In this paper we derive an expression for the rank of the low-rank
covariance matrix of a finite dimension sample from an evanescent random field.
It is shown that the rank of this covariance matrix is completely determined by
the evanescent field spectral support parameters, alone. Thus, the problem of
estimating the rank lends itself to a solution that avoids the need to estimate
the rank from the sample covariance matrix. We show that this result can be
immediately applied to considerably simplify the estimation of the rank of the
interference covariance matrix in the STAP problem
Estimating the system order by subspace methods
This paper discusses how to determine the order of a state-space model. To do so, we start by
revising existing approaches and find in them three basic shortcomings: i) some of them have a
poor performance in short samples, ii) most of them are not robust and iii) none of them can
accommodate seasonality. We tackle the first two issues by proposing new and refined criteria.
The third issue is dealt with by decomposing the system into regular and seasonal sub-systems.
The performance of all the procedures considered is analyzed through Monte Carlo simulations
A Generating Function for all Semi-Magic Squares and the Volume of the Birkhoff Polytope
We present a multivariate generating function for all n x n nonnegative
integral matrices with all row and column sums equal to a positive integer t,
the so called semi-magic squares. As a consequence we obtain formulas for all
coefficients of the Ehrhart polynomial of the polytope B_n of n x n
doubly-stochastic matrices, also known as the Birkhoff polytope. In particular
we derive formulas for the volumes of B_n and any of its faces.Comment: 24 pages, 1 figure. To appear in Journal of Algebraic Combinatoric
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