2,913 research outputs found
Nonparametric sequential prediction for stationary processes
We study the problem of finding an universal estimation scheme
, which will satisfy
\lim_{t\rightarrow\infty}{\frac{1}{t}}\sum_{i=1}^t|h_
i(X_0,X_1,...,X_{i-1})-E(X_i|X_0,X_1,...,X_{i-1})|^p=0 a.s. for all real valued
stationary and ergodic processes that are in . We will construct a single
such scheme for all , and show that for mere integrability
does not suffice but does.Comment: Published in at http://dx.doi.org/10.1214/10-AOP576 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Statistical inference for time-varying ARCH processes
In this paper the class of ARCH models is generalized to the
nonstationary class of ARCH models with time-varying coefficients.
For fixed time points, a stationary approximation is given leading to the
notation ``locally stationary ARCH process.'' The asymptotic
properties of weighted quasi-likelihood estimators of time-varying ARCH
processes () are studied, including asymptotic normality. In
particular, the extra bias due to nonstationarity of the process is
investigated. Moreover, a Taylor expansion of the nonstationary ARCH process in
terms of stationary processes is given and it is proved that the time-varying
ARCH process can be written as a time-varying Volterra series.Comment: Published at http://dx.doi.org/10.1214/009053606000000227 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Nonparametric inference for fractional diffusion
A non-parametric diffusion model with an additive fractional Brownian motion
noise is considered in this work. The drift is a non-parametric function that
will be estimated by two methods. On one hand, we propose a locally linear
estimator based on the local approximation of the drift by a linear function.
On the other hand, a Nadaraya-Watson kernel type estimator is studied. In both
cases, some non-asymptotic results are proposed by means of deviation
probability bound. The consistency property of the estimators are obtained
under a one sided dissipative Lipschitz condition on the drift that insures the
ergodic property for the stochastic differential equation. Our estimators are
first constructed under continuous observations. The drift function is then
estimated with discrete time observations that is of the most importance for
practical applications.Comment: Published in at http://dx.doi.org/10.3150/13-BEJ509 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
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