3,886 research outputs found
Optimal spectral bandwidth for long memory
For long range dependent time series with a spectral singularity at frequency zero, a theory for optimal bandwidth choice in non-parametric analysis ofthe singularity was developed by Robinson (1991b). The optimal bandwidths are described and compared with those in case of analysis of a smooth spectrum. They are also analysed in case of fractional ARIMA models and calculated as a function of the self similarity parameter in some special cases. Feasible data dependent approximations to the optimal bandwidth are discussed
New methods for the analysis of long memory time series: application to Spanish inflation
Models for long-memory time series are considered, in which the autocovariance sequence is only parameterized at very long lags, or the spectral density is only parametized at very low frequencies. Various recently proposed methods for estimating the differencing parameters are reviewed, and applied to an economic time series of prices in Spain
Comparison of Molecular Dynamics with Hybrid Continuum-Molecular Dynamics for a Single Tethered Polymer in a Solvent
We compare a newly developed hybrid simulation method which combines
classical molecular dynamics (MD) and computational fluid dynamics (CFD) to a
simulation consisting only of molecular dynamics. The hybrid code is composed
of three regions: a classical MD region, a continuum domain where the dynamical
equations are solved by standard CFD methods, and an overlap domain where
transport information from the other two domains is exchanged. The exchange of
information in the overlap region ensures that momentum, energy and mass are
conserved. The validity of the hybrid code is demonstrated by studying a single
polymer tethered to a hard wall immersed in explicit solvent and undergoing
shear flow. In classical molecular dynamics simulation a great deal of
computational time is devoted to simulating solvent molecules, although the
solvent itself is of no direct interest. By contrast, the hybrid code simulates
the polymer and surrounding solvent explicitly, whereas the solvent farther
away from the polymer is modeled using a continuum description. In the hybrid
simulations the MD domain is an open system whose number of particles is
controlled to filter the perturbative density waves produced by the polymer
motion.We compare conformational properties of the polymer in both simulations
for various shear rates. In all cases polymer properties compare extremely well
between the two simulation scenarios, thereby demonstrating that this hybrid
method is a useful way to model a system with polymers and under nonzero flow
conditions. There is also good agreement between the MD and hybrid schemes and
experimental data on tethered DNA in flow. The computational cost of the hybrid
protocol can be reduced to less than 6% of the cost of updating the MD forces,
confirming the practical value of the method.Comment: 13 pages, 8 figure
Tractable nonlinear memory functions as a tool to capture and explain dynamical behaviours
Mathematical approaches from dynamical systems theory are used in a range of
fields. This includes biology where they are used to describe processes such as
protein-protein interaction and gene regulatory networks. As such networks
increase in size and complexity, detailed dynamical models become cumbersome,
making them difficult to explore and decipher. This necessitates the
application of simplifying and coarse graining techniques in order to derive
explanatory insight. Here we demonstrate that Zwanzig-Mori projection methods
can be used to arbitrarily reduce the dimensionality of dynamical networks
while retaining their dynamical properties. We show that a systematic expansion
around the quasi-steady state approximation allows an explicit solution for
memory functions without prior knowledge of the dynamics. The approach not only
preserves the same steady states but also replicates the transients of the
original system. The method also correctly predicts the dynamics of multistable
systems as well as networks producing sustained and damped oscillations.
Applying the approach to a gene regulatory network from the vertebrate neural
tube, a well characterised developmental transcriptional network, identifies
features of the regulatory network responsible dfor its characteristic
transient behaviour. Taken together, our analysis shows that this method is
broadly applicable to multistable dynamical systems and offers a powerful and
efficient approach for understanding their behaviour.Comment: (8 pages, 8 figures
Quadratic Divergences in Kaluza-Klein Theories
We investigate the so-called ``Kaluza-Klein regularisation'' procedure in
supersymmetric extensions of the standard model with additional compact
dimensions and Scherk-Schwarz mechanism for supersymmetry breaking. This
procedure uses a specific mathematical manipulation to obtain a finite result
for the scalar potential. By performing the full calculation, we show that the
finiteness of this result is not only a consequence of the underlying
supersymmetry, but also the result of an implicit fine-tuning of the
coefficients of the terms that control the ultraviolet behaviour. The
finiteness of the Higgs mass at one-loop level seems therefore to be an
artefact of the regularisation scheme, and quadratic divergences are expected
to reappear in higher orders of perturbation theory.Comment: 10 pages, LaTe
Non-nested testing of spatial correlation
We develop non-nested tests in a general spatial, spatio-temporal or panel data context. The spatial aspect can be interpreted quite generally, in either a geographical sense, or employing notions of economic distance, or when parametric modelling arises in part from a common factor or other structure. In the former case, observations may be regularly-spaced across one or more dimensions, as is typical with much spatio-temporal data, or irregularly-spaced across all dimensions; both isotropic models and non-isotropic models can be considered, and a wide variety of correlation structures. In the second case, models involving spatial weight matrices are covered, such as “spatial autoregressive models”. The setting is sufficiently general to potentially cover other parametric structures such as certain factor models, and vector-valued observations, and here our preliminary asymptotic theory for parameter estimates is of some independent value. The test statistic is based on a Gaussian pseudo-likelihood ratio, and is shown to have an asymptotic standard normal distribution under the null hypothesis that one of the two models is correct; this limit theory rests strongly on a central limit theorem for the Gaussian pseudo-maximum likelihood parameter estimates. A small Monte Carlo study of finite-sample performance is included
New Methods for the Analysis of Long-Memory Time Series
Some recent developments in the analysis of time series are applied to real economic data. It is assumed that any stochastic or nonstochastic trends have been removed from the raw observed time series. Models for long-memory time series are considered in which the autocovariance sequence is parameterized only at very long lags or the spectral density is parameterized only at very low frequencies. The recently proposed methods for estimating the differencing parameters are applied to an economic time series of prices in Spain. The results consistently indicate that the inflation series suffers from long memory. The corelogram and periodogram for the resulting filtered series are plotted. The autocorrelation estimates are very close to zero. However, the seasonal peaks are still presentPublicad
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