13,565 research outputs found
Systematic inference of the long-range dependence and heavy-tail distribution parameters of ARFIMA models
Long-Range Dependence (LRD) and heavy-tailed distributions are ubiquitous in natural and socio-economic data. Such data can be self-similar whereby both LRD and heavy-tailed distributions contribute to the self-similarity as measured by the Hurst exponent. Some methods widely used in the physical sciences separately estimate these two parameters, which can lead to estimation bias. Those which do simultaneous estimation are based on frequentist methods such as Whittle’s approximate maximum likelihood estimator. Here we present a new and systematic Bayesian framework for the simultaneous inference of the LRD and heavy-tailed distribution parameters of a parametric ARFIMA model with non-Gaussian innovations. As innovations we use the α-stable and t-distributions which have power law tails. Our algorithm also provides parameter uncertainty estimates. We test our algorithm using synthetic data, and also data from the Geostationary Operational Environmental Satellite system (GOES) solar X-ray time series. These tests show that our algorithm is able to accurately and robustly estimate the LRD and heavy-tailed distribution parameters
Heavy-Tailed Features and Empirical Analysis of the Limit Order Book Volume Profiles in Futures Markets
This paper poses a few fundamental questions regarding the attributes of the
volume profile of a Limit Order Books stochastic structure by taking into
consideration aspects of intraday and interday statistical features, the impact
of different exchange features and the impact of market participants in
different asset sectors. This paper aims to address the following questions:
1. Is there statistical evidence that heavy-tailed sub-exponential volume
profiles occur at different levels of the Limit Order Book on the bid and ask
and if so does this happen on intra or interday time scales ?
2.In futures exchanges, are heavy tail features exchange (CBOT, CME, EUREX,
SGX and COMEX) or asset class (government bonds, equities and precious metals)
dependent and do they happen on ultra-high (<1sec) or mid-range (1sec -10min)
high frequency data?
3.Does the presence of stochastic heavy-tailed volume profile features evolve
in a manner that would inform or be indicative of market participant behaviors,
such as high frequency algorithmic trading, quote stuffing and price discovery
intra-daily?
4. Is there statistical evidence for a need to consider dynamic behavior of
the parameters of models for Limit Order Book volume profiles on an intra-daily
time scale ?
Progress on aspects of each question is obtained via statistically rigorous
results to verify the empirical findings for an unprecedentedly large set of
futures market LOB data. The data comprises several exchanges, several futures
asset classes and all trading days of 2010, using market depth (Type II) order
book data to 5 levels on the bid and ask
Sloshing in the LNG shipping industry: risk modelling through multivariate heavy-tail analysis
In the liquefied natural gas (LNG) shipping industry, the phenomenon of
sloshing can lead to the occurrence of very high pressures in the tanks of the
vessel. The issue of modelling or estimating the probability of the
simultaneous occurrence of such extremal pressures is now crucial from the risk
assessment point of view. In this paper, heavy-tail modelling, widely used as a
conservative approach to risk assessment and corresponding to a worst-case risk
analysis, is applied to the study of sloshing. Multivariate heavy-tailed
distributions are considered, with Sloshing pressures investigated by means of
small-scale replica tanks instrumented with d >1 sensors. When attempting to
fit such nonparametric statistical models, one naturally faces computational
issues inherent in the phenomenon of dimensionality. The primary purpose of
this article is to overcome this barrier by introducing a novel methodology.
For d-dimensional heavy-tailed distributions, the structure of extremal
dependence is entirely characterised by the angular measure, a positive measure
on the intersection of a sphere with the positive orthant in Rd. As d
increases, the mutual extremal dependence between variables becomes difficult
to assess. Based on a spectral clustering approach, we show here how a low
dimensional approximation to the angular measure may be found. The
nonparametric method proposed for model sloshing has been successfully applied
to pressure data. The parsimonious representation thus obtained proves to be
very convenient for the simulation of multivariate heavy-tailed distributions,
allowing for the implementation of Monte-Carlo simulation schemes in estimating
the probability of failure. Besides confirming its performance on artificial
data, the methodology has been implemented on a real data set specifically
collected for risk assessment of sloshing in the LNG shipping industry
Power-law distributions in binned empirical data
Many man-made and natural phenomena, including the intensity of earthquakes,
population of cities and size of international wars, are believed to follow
power-law distributions. The accurate identification of power-law patterns has
significant consequences for correctly understanding and modeling complex
systems. However, statistical evidence for or against the power-law hypothesis
is complicated by large fluctuations in the empirical distribution's tail, and
these are worsened when information is lost from binning the data. We adapt the
statistically principled framework for testing the power-law hypothesis,
developed by Clauset, Shalizi and Newman, to the case of binned data. This
approach includes maximum-likelihood fitting, a hypothesis test based on the
Kolmogorov--Smirnov goodness-of-fit statistic and likelihood ratio tests for
comparing against alternative explanations. We evaluate the effectiveness of
these methods on synthetic binned data with known structure, quantify the loss
of statistical power due to binning, and apply the methods to twelve real-world
binned data sets with heavy-tailed patterns.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS710 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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