51,502 research outputs found
A unified approach to nonlinearity, structural change and outliers
This paper demonstrates that the class of conditionally linear and Gaussian
state-space models offers a general and convenient framework for simultaneously
handling nonlinearity, structural change and outliers in time series. Many
popular nonlinear time series models, including threshold, smooth transition
and Markov-Switching models, can be written in state-space form. It is then
straightforward to add components that capture parameter instability and
intervention effects. We advocate a Bayesian approach to estimation and
inference, using an efficient implementation of Markov Chain Monte Carlo
sampling schemes for such linear dynamic mixture models. The general modelling
framework and the Bayesian methodology are illustrated by means of several
examples. An application to quarterly industrial production growth rates for
the G7 countries demonstrates the empirical usefulness of the approach
Mean Field Limit of a Behavioral Financial Market Model
In the past decade there has been a growing interest in agent-based
econophysical financial market models. The goal of these models is to gain
further insights into stylized facts of financial data. We derive the mean
field limit of the econophysical model by Cross, Grinfeld, Lamba and Seaman
(Physica A, 354) and show that the kinetic limit is a good approximation of the
original model. Our kinetic model is able to replicate some of the most
prominent stylized facts, namely fat-tails of asset returns, uncorrelated stock
price returns and volatility clustering. Interestingly, psychological
misperceptions of investors can be accounted to be the origin of the appearance
of stylized facts. The mesoscopic model allows us to study the model
analytically. We derive steady state solutions and entropy bounds of the
deterministic skeleton. These first analytical results already guide us to
explanations for the complex dynamics of the model
Efficient Gibbs Sampling for Markov Switching GARCH Models
We develop efficient simulation techniques for Bayesian inference on
switching GARCH models. Our contribution to existing literature is manifold.
First, we discuss different multi-move sampling techniques for Markov Switching
(MS) state space models with particular attention to MS-GARCH models. Our
multi-move sampling strategy is based on the Forward Filtering Backward
Sampling (FFBS) applied to an approximation of MS-GARCH. Another important
contribution is the use of multi-point samplers, such as the Multiple-Try
Metropolis (MTM) and the Multiple trial Metropolize Independent Sampler, in
combination with FFBS for the MS-GARCH process. In this sense we ex- tend to
the MS state space models the work of So [2006] on efficient MTM sampler for
continuous state space models. Finally, we suggest to further improve the
sampler efficiency by introducing the antithetic sampling of Craiu and Meng
[2005] and Craiu and Lemieux [2007] within the FFBS. Our simulation experiments
on MS-GARCH model show that our multi-point and multi-move strategies allow the
sampler to gain efficiency when compared with single-move Gibbs sampling.Comment: 38 pages, 7 figure
Asymptotic properties of the maximum likelihood estimator in autoregressive models with Markov regime
An autoregressive process with Markov regime is an autoregressive process for
which the regression function at each time point is given by a nonobservable
Markov chain. In this paper we consider the asymptotic properties of the
maximum likelihood estimator in a possibly nonstationary process of this kind
for which the hidden state space is compact but not necessarily finite.
Consistency and asymptotic normality are shown to follow from uniform
exponential forgetting of the initial distribution for the hidden Markov chain
conditional on the observations.Comment: Published at http://dx.doi.org/10.1214/009053604000000021 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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