70 research outputs found
On the Zipf strategy for short-term investments in WIG20 futures
We apply the Zipf power law to financial time series of WIG20 index daily
changes (open-close). Thanks to the mapping of time series signal into the
sequence of 2k+1 'spin-like' states, where k=0, 1/2, 1, 3/2, ..., we are able
to describe any time series increments, with almost arbitrary accuracy, as the
one of such 'spin-like' states. This procedure leads in the simplest
non-trivial case (k = 1/2) to the binary data projection. More sophisticated
projections are also possible and mentioned in the article. The introduced
formalism allows then to use Zipf power law to describe the intrinsic structure
of time series. The fast algorithm for this implementation was constructed by
us within Matlab^{TM} software. The method, called Zipf strategy, is then
applied in the simplest case k = 1/2 to WIG 20 open and close daily data to
make short-term predictions for forthcoming index changes. The results of
forecast effectiveness are presented with respect to different time window
sizes and partition divisions (word lengths in Zipf language). Finally, the
various investment strategies improving ROI (return of investment) for WIG20
futures are proposed. We show that the Zipf strategy is the appropriate and
very effective tool to make short-term predictions and therefore, to evaluate
short-term investments on the basis of historical stock index data. Our
findings support also the existence of long memory in financial data, exceeding
the known in literature 3 days span limit.Comment: 13 pages, 6 figures, 1 table, presented at the 5-th FENS symposium on
Physics in Economic and Social Systems, Warsaw 201
Cross-correlation between CMB lensing potential and galaxy catalogues from HELP
We present the study of cross-correlation between Cosmic Microwave Background
(CMB) gravitational lensing potential map released by the \textit{Planck}
collaboration and photometric redshift galaxy catalogues from the
\textit{Herschel} Extragalactic Legacy Project (HELP), divided into four sky
patches: NGP, \textit{Herschel} Stripe-82, and two halves of SGP field,
covering in total deg of the sky. We estimate the galaxy
linear bias parameter, , from joint analysis of cross-power spectrum and
galaxy auto-power spectrum using Maximum Likelihood Estimation technique to
obtain values ranging from for SGP Part-2 to
for SGP Part-1 field. We also estimate the amplitude of cross-correlation and
find the values spanning from for SGP Part-2 to
for SGP Part-1 field, respectively. For NGP and SGP Part-1 fields the amplitude
is consistent with the expected value for the standard cosmological model
within , while for \textit{Herschel} Stripe-82 and SGP Part-2
we find the amplitude to be smaller than expected with and
deviation, respectively. We perform several tests on various
systematic errors to study the reason for the deviation, however, value of the
amplitude turns out to be robust with respect to these errors. The only
significant change in the amplitude is observed when we replace the
minimum-variance CMB lensing map, used in the baseline analysis, by the lensing
map derived from the CMB temperature map with deprojected thermal
Sunyaev-Zeldovich signal.Comment: 15 pages, 13 figures, Published in MNRA
Nonlinearity and stochasticity in the density--velocity relation
We present results of the investigations of the statistical properties of a
joint density and velocity divergence probability distribution function (PDF)
in the mildly non-linear regime. For that purpose we use both perturbation
theory results, extended here for a top-hat filter, and numerical simulations.
In particular we derive the quantitative (complete as possible up to third
order terms) and qualitative predictions for constrained averages and
constrained dispersions -- which describe the nonlinearities and the
stochasticity properties beyond the linear regime -- and compare them against
numerical simulations. We find overall a good agreement for constrained
averages; however, the agreement for constrained dispersions is only
qualitative. Scaling relations for the Omega-dependence of these quantities are
satisfactory reproduced.
Guided by our analytical and numerical results, we finally construct a robust
phenomenological description of the joint PDF in a closed analytic form. The
good agreement of our formula with results of N-body simulations for a number
of cosmological parameters provides a sound validation of the presented
approach.
Our results provide a basis for a potentially powerful tool with which it is
possible to analyze galaxy survey data in order to test the gravitational
instability paradigm beyond the linear regime and put useful constraints on
cosmological parameters. In particular we show how the nonlinearity in the
density--velocity relation can be used to break the so-called Omega-bias
degeneracy in cosmic density-velocity comparisons.Comment: 12 pages, 11 figures; revised version with minor changes in the
presentation, accepted for publication in MNRA
Nonlinear Velocity-Density Coupling: Analysis by Second-Order Perturbation Theory
Cosmological linear perturbation theory predicts that the peculiar velocity
and the matter overdensity at a same point are
statistically independent quantities, as log as the initial density
fluctuations are random Gaussian distributed. However nonlinear gravitational
effects might change the situation. Using framework of second-order
perturbation theory and the Edgeworth expansion method, we study local density
dependence of bulk velocity dispersion that is coarse-grained at a weakly
nonlinear scale. For a typical CDM model, the first nonlinear correction of
this constrained bulk velocity dispersion amounts to (Gaussian
smoothing) at a weakly nonlinear scale with a very weak dependence on
cosmological parameters. We also compare our analytical prediction with
published numerical results given at nonlinear regimes.Comment: 16 pages including 2 figures, ApJ 537 in press (July 1
Non-Gaussianity from Self-Ordering Scalar Fields
The Universe may harbor relics of the post-inflationary epoch in the form of
a network of self-ordered scalar fields. Such fossils, while consistent with
current cosmological data at trace levels, may leave too weak an imprint on the
cosmic microwave background and the large-scale distribution of matter to allow
for direct detection. The non-Gaussian statistics of the density perturbations
induced by these fields, however, permit a direct means to probe for these
relics. Here we calculate the bispectrum that arises in models of self-ordered
scalar fields. We find a compact analytic expression for the bispectrum,
evaluate it numerically, and provide a simple approximation that may be useful
for data analysis. The bispectrum is largest for triangles that are aligned
(have edges ) as opposed to the local-model
bispectrum, which peaks for squeezed triangles (), and
the equilateral bispectrum, which peaks at . We
estimate that this non-Gaussianity should be detectable by the Planck satellite
if the contribution from self-ordering scalar fields to primordial
perturbations is near the current upper limit.Comment: 11 pages, 1 figur
Halo Clustering with Non-Local Non-Gaussianity
We show how the peak-background split can be generalized to predict the
effect of non-local primordial non-Gaussianity on the clustering of halos. Our
approach is applicable to arbitrary primordial bispectra. We show that the
scale-dependence of halo clustering predicted in the peak-background split
(PBS) agrees with that of the local-biasing model on large scales. On smaller
scales, k >~ 0.01 h/Mpc, the predictions diverge, a consequence of the
assumption of separation of scales in the peak-background split. Even on large
scales, PBS and local biasing do not generally agree on the amplitude of the
effect outside of the high-peak limit. The scale dependence of the biasing -
the effect that provides strong constraints to the local-model bispectrum - is
far weaker for the equilateral and self-ordering-scalar-field models of
non-Gaussianity. The bias scale dependence for the orthogonal and folded models
is weaker than in the local model (~ 1/k), but likely still strong enough to be
constraining. We show that departures from scale-invariance of the primordial
power spectrum may lead to order-unity corrections, relative to predictions
made assuming scale-invariance - to the non-Gaussian bias in some of these
non-local models for non-Gaussianity. An Appendix shows that a non-local model
can produce the local-model bispectrum, a mathematical curiosity we uncovered
in the course of this investigation.Comment: 12 pages, 4 figures; submitted to Phys. Rev. D; v2: references added;
v3: some more comments on kernel-bispectrum relation in appendi
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