Abstracts
Efficient prediction for nonlinear
autoregressive models
Wolfgang Wefelmeyer (University of Siegen)
Conditional expectations given past observations in stationary
time series are usually estimated directly by kernel estimators.
Such estimators do not converge at the (parametric) root n rate.
For nonlinear autoregressive models, we construct estimators
of conditional expectations that converge at the root n rate
and are asymptotically efficient in the sense of Hajek and Le Cam.
Our estimators exploit the independence of the innovations;
they are smoothed and weighted von Mises statistics based
on the residuals. The estimators are studied using two results
of independent interest: convergence rates for weitalksghted
residual-based innovation density estimators, and uniform
stochasic expansions of residual-based von Mises processes.
This is joint work with Ursula U. Mueller (Bremen) and
Anton Schick (Binghamton).
Semiparametric Time Series Models with Non-IID Errors
Feike C. Drost and Bas J.M. Werker (Tilburg University)
We study estimation of parametric components in general semiparametric time
series models. The time series models are not assumed to be driven by a
sequence of independent innovations with unknown distribution as is the case
in a more traditional semiparametric time series approach. We assume just
that the innovations are stationary and the dependence between the
innovations is seen as a nonparametric nuisance parameter in addition to the
marginal distribution of the innovations. We obtain a LAN result under quite
natural and economical conditions implying a lower bound on the asymptotic
performance of efficient estimators. We also study the influence of
additional knowledge on the conditional innovation distribution and discuss
the lower bounds obtained for several cases.
Mean-variance hedging in large financial markets
Luciano Campi
We consider a mean-variance hedging problem for an arbitrage-free large financial market, i.e. a financial market with countably many risky assets modelled by a sequence of continuous semimartingales. By using the stochastic integration theory for cylindrical martingales developed in Mikulevicius and Rozovskii (1998), we extend the results about a change of numeraire and mean-variance hedging of Gourieroux, Laurent and Pham (1998) to this setting. We also consider, for all n≥1, the market formed by the first n risky assets and study the solutions to the n-dimensional mean-variance hedging problem associated and their behaviour when n tends to infinity.
Integration and arbitrage in fractional Black-Scholes model
Tommi Sottinen
It has been proposed that the arbitrage possibility in the fractional
Black-Scholes model depends on the definition of the stochastic integral.
More precisely, if one uses the Wick-Ito-Skorohod integral one
obtains an arbitrage-free model. However, this integral does not allow
economical interpretation. On the other hand it is easy to give abrbitrage
examples in continuous time trading with self-financing strategies, if one
uses the Riemann-Stieltjes integral.
We study the connection between two different notions of self-financing
portfolios in the fractional Black-Scholes model by applying the
known connection between these two integrals. In particular, we give an
economical interpretation of the proposed arbitrage-free model in terms of
Riemann-Stieltjes integrals.
This is joint work with Esko Valkeila.