104 research outputs found
Constructing matrix geometric means
In this paper, we analyze the process of "assembling" new matrix geometric
means from existing ones, through function composition or limit processes. We
show that for n=4 a new matrix mean exists which is simpler to compute than the
existing ones. Moreover, we show that for n>4 the existing proving strategies
cannot provide a mean computationally simpler than the existing ones
The Pad\'e iterations for the matrix sign function and their reciprocals are optimal
It is proved that among the rational iterations locally converging with order
s>1 to the sign function, the Pad\'e iterations and their reciprocals are the
unique rationals with the lowest sum of the degrees of numerator and
denominator
A Perron iteration for the solution of a quadratic vector equation arising in Markovian Binary Trees
We propose a novel numerical method for solving a quadratic vector equation
arising in Markovian Binary Trees. The numerical method consists in a fixed
point iteration, expressed by means of the Perron vectors of a sequence of
nonnegative matrices. A theoretical convergence analysis is performed. The
proposed method outperforms the existing methods for close-to-critical
problems
A note on forecasting demand using the multivariate exponential smoothing framework
Simple exponential smoothing is widely used in forecasting economic time
series. This is because it is quick to compute and it generally delivers
accurate forecasts. On the other hand, its multivariate version has received
little attention due to the complications arising with the estimation. Indeed,
standard multivariate maximum likelihood methods are affected by numerical
convergence issues and bad complexity, growing with the dimensionality of the
model. In this paper, we introduce a new estimation strategy for multivariate
exponential smoothing, based on aggregating its observations into scalar models
and estimating them. The original high-dimensional maximum likelihood problem
is broken down into several univariate ones, which are easier to solve.
Contrary to the multivariate maximum likelihood approach, the suggested
algorithm does not suffer heavily from the dimensionality of the model. The
method can be used for time series forecasting. In addition, simulation results
show that our approach performs at least as well as a maximum likelihood
estimator on the underlying VMA(1) representation, at least in our test
problems
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