158 research outputs found
Asymptotic results for sample autocovariance functions and extremes of integrated generalized Ornstein-Uhlenbeck processes
We consider a positive stationary generalized Ornstein--Uhlenbeck process
V_t=\mathrm{e}^{-\xi_t}\biggl(\int_0^t\mathrm{e}^{\xi_{s-}}\
,\mathrm{d}\eta_s+V_0\biggr)\qquadfor t\geq0, and the increments of the
integrated generalized Ornstein--Uhlenbeck process
, , where
is a three-dimensional L\'{e}vy process
independent of the starting random variable . The genOU model is a
continuous-time version of a stochastic recurrence equation. Hence, our models
include, in particular, continuous-time versions of
and processes. In this paper we investigate the
asymptotic behavior of extremes and the sample autocovariance function of
and . Furthermore, we present a
central limit result for . Regular variation and point
process convergence play a crucial role in establishing the statistics of
and . The theory can be applied to the
and the Nelson diffusion model.Comment: Published in at http://dx.doi.org/10.3150/08-BEJ174 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Dependence Estimation for High Frequency Sampled Multivariate CARMA Models
The paper considers high frequency sampled multivariate continuous-time ARMA
(MCARMA) models, and derives the asymptotic behavior of the sample
autocovariance function to a normal random matrix. Moreover, we obtain the
asymptotic behavior of the cross-covariances between different components of
the model. We will see that the limit distribution of the sample autocovariance
function has a similar structure in the continuous-time and in the
discrete-time model. As special case we consider a CARMA (one-dimensional
MCARMA) process. For a CARMA process we prove Bartlett's formula for the sample
autocorrelation function. Bartlett's formula has the same form in both models,
only the sums in the discrete-time model are exchanged by integrals in the
continuous-time model. Finally, we present limit results for multivariate MA
processes as well which are not known in this generality in the multivariate
setting yet
Inclusive Art Education as a Tool for Art Museum Experiences
This Thesis looks at art education as a tool for meaningful art museum experiences. The study follows students on field trips at the High Art Museum as a process to develop a fully inclusive art educational program. The focus of the process of inclusivity evaluates the personal, socio-cultural, and physical aspects of the learning environment within the museum. The research questions that guide the study are 1) how the inclusive strategies I have found in my art classroom can be utilized to create an inclusive art museum setting, 2) how we can approach inclusive student learning an art museum environment, and 3) how the art museum field trip experience can be designed to create an engaging and worthwhile experience for students on the autism spectrum. This study offers a model of inclusion to an artistic learning environment
Extremal behavior of stochastic volatility models
Empirical volatility changes in time and exhibits tails, which are heavier than normal. Moreover, empirical volatility has - sometimes quite substantial - upwards jumps and clusters on high levels. We investigate classical and non-classical stochastic volatility models with respect to their extreme behavior. We show that classical stochastic volatility models driven by Brownian motion can model heavy tails, but obviously they are not able to model volatility jumps. Such phenomena can be modelled by Levy driven volatility processes as, for instance, by Levy driven Ornstein-Uhlenbeck models. They can capture heavy tails and volatility jumps. Also volatility clusters can be found in such models, provided the driving Levy process has regularly varying tails. This results then in a volatility model with similarly heavy tails. As the last class of stochastic volatility models, we investigate a continuous time GARCH(1,1) model. Driven by an arbitrary Levy process it exhibits regularly varying tails, volatility upwards jumps and clusters on high levels
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