1,846 research outputs found
Bayesian inference for a single factor copula stochastic volatility model using Hamiltonian Monte Carlo
For modeling multivariate financial time series we propose a single factor
copula model together with stochastic volatility margins. This model
generalizes single factor models relying on the multivariate normal
distribution and allows for symmetric and asymmetric tail dependence. We
develop joint Bayesian inference using Hamiltonian Monte Carlo (HMC) within
Gibbs sampling. Thus we avoid information loss caused by the two-step approach
for margins and dependence in copula models as followed by Schamberger et
al(2017). Further, the Bayesian approach allows for high dimensional parameter
spaces as they are present here in addition to uncertainty quantification
through credible intervals. By allowing for indicators for different copula
families the copula families are selected automatically in the Bayesian
framework. In a first simulation study the performance of HMC is compared to
the Markov Chain Monte Carlo (MCMC) approach developed by Schamberger et
al(2017) for the copula part. It is shown that HMC considerably outperforms
this approach in terms of effective sample size, MSE and observed coverage
probabilities. In a second simulation study satisfactory performance is seen
for the full HMC within Gibbs procedure. The approach is illustrated for a
portfolio of financial assets with respect to one-day ahead value at risk
forecasts. We provide comparison to a two-step estimation procedure of the
proposed model and to relevant benchmark models: a model with dynamic linear
models for the margins and a single factor copula for the dependence proposed
by Schamberger et al(2017) and a multivariate factor stochastic volatility
model proposed by Kastner et al(2017). Our proposed approach shows superior
performance
Inversion Copulas from Nonlinear State Space Models
We propose to construct copulas from the inversion of nonlinear state space
models. These allow for new time series models that have the same serial
dependence structure of a state space model, but with an arbitrary marginal
distribution, and flexible density forecasts. We examine the time series
properties of the copulas, outline serial dependence measures, and estimate the
models using likelihood-based methods. Copulas constructed from three example
state space models are considered: a stochastic volatility model with an
unobserved component, a Markov switching autoregression, and a Gaussian linear
unobserved component model. We show that all three inversion copulas with
flexible margins improve the fit and density forecasts of quarterly U.S. broad
inflation and electricity inflation
Detecting regime switches in the dependence structure of high dimensional financial data
Misperceptions about extreme dependencies between different financial assets
have been an im- portant element of the recent financial crisis. This paper
studies inhomogeneity in dependence structures using Markov switching regular
vine copulas. These account for asymmetric depen- dencies and tail dependencies
in high dimensional data. We develop methods for fast maximum likelihood as
well as Bayesian inference. Our algorithms are validated in simulations and
applied to financial data. We find that regime switches are present in the
dependence structure of various data sets and show that regime switching models
could provide tools for the accurate description of inhomogeneity during times
of crisis
Modeling high dimensional time-varying dependence using D-vine SCAR models
We consider the problem of modeling the dependence among many time series. We
build high dimensional time-varying copula models by combining pair-copula
constructions (PCC) with stochastic autoregressive copula (SCAR) models to
capture dependence that changes over time. We show how the estimation of this
highly complex model can be broken down into the estimation of a sequence of
bivariate SCAR models, which can be achieved by using the method of simulated
maximum likelihood. Further, by restricting the conditional dependence
parameter on higher cascades of the PCC to be constant, we can greatly reduce
the number of parameters to be estimated without losing much flexibility. We
study the performance of our estimation method by a large scale Monte Carlo
simulation. An application to a large dataset of stock returns of all
constituents of the Dax 30 illustrates the usefulness of the proposed model
class
Simple techniques for likelihood analysis of univariate and multivariate stable distributions: with extensions to multivariate stochastic volatility and dynamic factor models
In this paper we consider a variety of procedures for numerical statistical
inference in the family of univariate and multivariate stable distributions. In
connection with univariate distributions (i) we provide approximations by
finite location-scale mixtures and (ii) versions of approximate Bayesian
computation (ABC) using the characteristic function and the asymptotic form of
the likelihood function. In the context of multivariate stable distributions we
propose several ways to perform statistical inference and obtain the spectral
measure associated with the distributions, a quantity that has been a major
impediment in using them in applied work. We extend the techniques to handle
univariate and multivariate stochastic volatility models, static and dynamic
factor models with disturbances and factors from general stable distributions,
a novel way to model multivariate stochastic volatility through time-varying
spectral measures and a novel way to multivariate stable distributions through
copulae. The new techniques are applied to artificial as well as real data (ten
major currencies, SP100 and individual returns). In connection with ABC special
attention is paid to crafting well-performing proposal distributions for MCMC
and extensive numerical experiments are conducted to provide critical values of
the "closeness" parameter that can be useful for further applied econometric
work
Bayesian optimisation for fast approximate inference in state-space models with intractable likelihoods
We consider the problem of approximate Bayesian parameter inference in
non-linear state-space models with intractable likelihoods. Sequential Monte
Carlo with approximate Bayesian computations (SMC-ABC) is one approach to
approximate the likelihood in this type of models. However, such approximations
can be noisy and computationally costly which hinders efficient implementations
using standard methods based on optimisation and Monte Carlo methods. We
propose a computationally efficient novel method based on the combination of
Gaussian process optimisation and SMC-ABC to create a Laplace approximation of
the intractable posterior. We exemplify the proposed algorithm for inference in
stochastic volatility models with both synthetic and real-world data as well as
for estimating the Value-at-Risk for two portfolios using a copula model. We
document speed-ups of between one and two orders of magnitude compared to
state-of-the-art algorithms for posterior inference.Comment: 24 pages, 7 figures. Submitted to journal for revie
Improving forecasting performance using covariate-dependent copula models
Copulas provide an attractive approach for constructing multivariate
distributions with flexible marginal distributions and different forms of
dependences. Of particular importance in many areas is the possibility of
explicitly forecasting the tail-dependences. Most of the available approaches
are only able to estimate tail-dependences and correlations via nuisance
parameters, but can neither be used for interpretation, nor for forecasting.
Aiming to improve copula forecasting performance, we propose a general Bayesian
approach for modeling and forecasting tail-dependences and correlations as
explicit functions of covariates. The proposed covariate-dependent copula model
also allows for Bayesian variable selection among covariates from the marginal
models as well as the copula density. The copulas we study include Joe-Clayton
copula, Clayton copula, Gumbel copula and Student's \emph{t}-copula. Posterior
inference is carried out using an efficient MCMC simulation method. Our
approach is applied to both simulated data and the S\&P 100 and S\&P 600 stock
indices. The forecasting performance of the proposed approach is compared with
other modeling strategies based on log predictive scores. Value-at-Risk
evaluation is also preformed for model comparisons
Computationally Efficient Estimation of Factor Multivariate Stochastic Volatility Models
An MCMC simulation method based on a two stage delayed rejection
Metropolis-Hastings algorithm is proposed to estimate a factor multivariate
stochastic volatility model. The first stage uses kstep iteration towards the
mode, with k small, and the second stage uses an adaptive random walk proposal
density. The marginal likelihood approach of Chib (1995) is used to choose the
number of factors, with the posterior density ordinates approximated by
Gaussian copula. Simulation and real data applications suggest that the
proposed simulation method is computationally much more efficient than the
approach of Chib. Nardari and Shephard (2006}. This increase in computational
efficiency is particularly important in calculating marginal likelihoods
because it is necessary to carry out the simulation a number of times to
estimate the posterior ordinates for a given marginal likelihood. In addition
to the MCMC method, the paper also proposes a fast approximate EM method to
estimate the factor multivariate stochastic volatility model. The estimates
from the approximate EM method are of interest in their own right, but are
especially useful as initial inputs to MCMC methods, making them more efficient
computationally. The methodology is illustrated using simulated and real
examples.Comment: 32 pages, 3 Figure
Spatial Regression and the Bayesian Filter
Regression for spatially dependent outcomes poses many challenges, for
inference and for computation. Non-spatial models and traditional spatial
mixed-effects models each have their advantages and disadvantages, making it
difficult for practitioners to determine how to carry out a spatial regression
analysis. We discuss the data-generating mechanisms implicitly assumed by
various popular spatial regression models, and discuss the implications of
these assumptions. We propose Bayesian spatial filtering as an approximate
middle way between non-spatial models and traditional spatial mixed models. We
show by simulation that our Bayesian spatial filtering model has several
desirable properties and hence may be a useful addition to a spatial
statistician's toolkit
Spatially adaptive, Bayesian estimation for probabilistic temperature forecasts
Uncertainty in the prediction of future weather is commonly assessed through
the use of forecast ensembles that employ a numerical weather prediction model
in distinct variants. Statistical postprocessing can correct for biases in the
numerical model and improves calibration. We propose a Bayesian version of the
standard ensemble model output statistics (EMOS) postprocessing method, in
which spatially varying bias coefficients are interpreted as realizations of
Gaussian Markov random fields. Our Markovian EMOS (MEMOS) technique utilizes
the recently developed stochastic partial differential equation (SPDE) and
integrated nested Laplace approximation (INLA) methods for computationally
efficient inference. The MEMOS approach shows good predictive performance in a
comparative study of 24-hour ahead temperature forecasts over Germany based on
the 50-member ensemble of the European Centre for Medium-Range Weather
Forecasting (ECMWF)
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