77,320 research outputs found
Properties of the sample autocorrelations of non-linear transformations in long memory stochastic volatility models
The autocorrelations of log-squared, squared, and absolute financial returns are often used to infer the dynamic properties of the underlying volatility. This article shows that, in the context of long-memory stochastic volatility models, these autocorrelations are smaller than the autocorrelations of the log volatility and so is the rate of decay for squared and absolute returns. Furthermore, the corresponding sample autocorrelations could have severe negative biases, making the identification of conditional heteroscedasticity and long memory a difficult task. Finally, we show that the power of some popular tests for homoscedasticity is larger when they are applied to absolute returns.Publicad
The Kovacs effect in the one-dimensional Ising model: a linear response analysis
We analyze the so-called Kovacs effect in the one-dimensional Ising model
with Glauber dynamics. We consider small enough temperature jumps, for which a
linear response theory has been recently derived. Within this theory, the
Kovacs hump is directly related to the monotonic relaxation function of the
energy. The analytical results are compared with extensive Monte Carlo
simulations, and an excellent agreement is found. Remarkably, the position of
the maximum in the Kovacs hump depends on the fact that the true asymptotic
behavior of the relaxation function is different from the stretched exponential
describing the relevant part of the relaxation at low temperatures.Comment: accepted for publication in Phys. Rev.
Frames of subspaces and operators
We study the relationship between operators, orthonormal basis of subspaces
and frames of subspaces (also called fusion frames) for a separable Hilbert
space . We get sufficient conditions on an orthonormal basis of
subspaces of a Hilbert space
and a surjective in order that
is a frame of subspaces with respect to a computable
sequence of weights. We also obtain generalizations of results in [J. A.
Antezana, G. Corach, M. Ruiz and D. Stojanoff, Oblique projections and frames.
Proc. Amer. Math. Soc. 134 (2006), 1031-1037], which related frames of
subspaces (including the computation of their weights) and oblique projections.
The notion of refinament of a fusion frame is defined and used to obtain
results about the excess of such frames. We study the set of admissible weights
for a generating sequence of subspaces. Several examples are given.Comment: 21 pages, LaTeX; added references and comments about fusion frame
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