1,191 research outputs found
Copula Processes
We define a copula process which describes the dependencies between
arbitrarily many random variables independently of their marginal
distributions. As an example, we develop a stochastic volatility model,
Gaussian Copula Process Volatility (GCPV), to predict the latent standard
deviations of a sequence of random variables. To make predictions we use
Bayesian inference, with the Laplace approximation, and with Markov chain Monte
Carlo as an alternative. We find both methods comparable. We also find our
model can outperform GARCH on simulated and financial data. And unlike GARCH,
GCPV can easily handle missing data, incorporate covariates other than time,
and model a rich class of covariance structures.Comment: 11 pages, 1 table, 1 figure. Submitted for publication. Since last
version: minor edits and reformattin
Model and distribution uncertainty in multivariate GARCH estimation: a Monte Carlo analysis
Multivariate GARCH models are in principle able to accommodate the features of the dynamic conditional correlations processes, although with the drawback, when the number of financial returns series considered increases, that the parameterizations entail too many parameters.In general, the interaction between model parametrization of the second conditional moment and the conditional density of asset returns adopted in the estimation determines the fitting of such models to the observed dynamics of the data. This paper aims to evaluate the interactions between conditional second moment specifications and probability distributions adopted in the likelihood computation, in forecasting volatilities and covolatilities. We measure the relative performances of alternative conditional second moment and probability distributions specifications by means of Monte Carlo simulations, using both statistical and financial forecasting loss functions.Multivariate GARCH models; Model uncertainty; Quasi-maximum likelihood; Monte Carlo methods
Modeling and predicting market risk with Laplace-Gaussian mixture distributions
While much of classical statistical analysis is based on Gaussian distributional assumptions, statistical modeling with the Laplace distribution has gained importance in many applied fields. This phenomenon is rooted in the fact that, like the Gaussian, the Laplace distribution has many attractive properties. This paper investigates two methods of combining them and their use in modeling and predicting financial risk. Based on 25 daily stock return series, the empirical results indicate that the new models offer a plausible description of the data. They are also shown to be competitive with, or superior to, use of the hyperbolic distribution, which has gained some popularity in asset-return modeling and, in fact, also nests the Gaussian and Laplace. Klassifikation: C16, C50 . March 2005
Approximated maximum likelihood estimation in multifractal random walks
We present an approximated maximum likelihood method for the multifractal
random walk processes of [E. Bacry et al., Phys. Rev. E 64, 026103 (2001)]. The
likelihood is computed using a Laplace approximation and a truncation in the
dependency structure for the latent volatility. The procedure is implemented as
a package in the R computer language. Its performance is tested on synthetic
data and compared to an inference approach based on the generalized method of
moments. The method is applied to estimate parameters for various financial
stock indices.Comment: 8 pages, 3 figures, 2 table
Pareto Improving Social Security Reform when Financial Markets are Incomplete!?
While much of classical statistical analysis is based on Gaussian distributional assumptions, statistical modeling with the Laplace distribution has gained importance in many applied fields. This phenomenon is rooted in the fact that, like the Gaussian, the Laplace distribution has many attractive properties. This paper investigates two methods of combining them and their use in modeling and predicting financial risk. Based on 25 daily stock return series, the empirical results indicate that the new models offer a plausible description of the data. They are also shown to be competitive with, or superior to, use of the hyperbolic distribution, which has gained some popularity in asset-return modeling and, in fact, also nests the Gaussian and Laplace.GARCH, Hyperbolic Distribution, Kurtosis, Laplace Distribution, Mixture Distributions, Stock Market Returns
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