874 research outputs found
Nonparametric Estimation of Trend Function for Stochastic Differential Equations Driven by a Weighted Fractional Brownian Motion
In this paper, we consider the problem of nonparametric estimation of trend function for stochastic differential equations driven by a weighted fractional Brownian motion (weighted-fBm). Under some general conditions, the consistent uniform, the rate of convergence as well as the asymptotic normality of our estimator are established. In addition, a numerical example is provided to illustrate the validity of the considered estimator
Modelling and forecasting the kurtosis and returns distributions of financial markets: irrational fractional Brownian motion model approach
The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link. Open accessThis paper reports a new methodology and results on the forecast of the numerical value of the fat tail(s) in asset returns distributions using the irrational fractional Brownian motion model. Optimal model parameter values are obtained from fits to consecutive daily 2-year period returns of S&P500 index over [1950–2016], generating 33-time series estimations. Through an econometric model,the kurtosis of returns distributions is modelled as a function of these parameters. Subsequently an auto-regressive analysis on these parameters advances the modelling and forecasting of kurtosis and returns distributions, providing the accurate shape of returns distributions and measurement of Value at Risk
Lagrangian Time Series Models for Ocean Surface Drifter Trajectories
This paper proposes stochastic models for the analysis of ocean surface
trajectories obtained from freely-drifting satellite-tracked instruments. The
proposed time series models are used to summarise large multivariate datasets
and infer important physical parameters of inertial oscillations and other
ocean processes. Nonstationary time series methods are employed to account for
the spatiotemporal variability of each trajectory. Because the datasets are
large, we construct computationally efficient methods through the use of
frequency-domain modelling and estimation, with the data expressed as
complex-valued time series. We detail how practical issues related to sampling
and model misspecification may be addressed using semi-parametric techniques
for time series, and we demonstrate the effectiveness of our stochastic models
through application to both real-world data and to numerical model output.Comment: 21 pages, 10 figure
A statistical analysis of particle trajectories in living cells
Recent advances in molecular biology and fluorescence microscopy imaging have
made possible the inference of the dynamics of single molecules in living
cells. Such inference allows to determine the organization and function of the
cell. The trajectories of particles in the cells, computed with tracking
algorithms, can be modelled with diffusion processes. Three types of diffusion
are considered : (i) free diffusion; (ii) subdiffusion or (iii) superdiffusion.
The Mean Square Displacement (MSD) is generally used to determine the different
types of dynamics of the particles in living cells (Qian, Sheetz and Elson
1991). We propose here a non-parametric three-decision test as an alternative
to the MSD method. The rejection of the null hypothesis -- free diffusion -- is
accompanied by claims of the direction of the alternative (subdiffusion or a
superdiffusion). We study the asymptotic behaviour of the test statistic under
the null hypothesis, and under parametric alternatives which are currently
considered in the biophysics literature, (Monnier et al,2012) for example. In
addition, we adapt the procedure of Benjamini and Hochberg (2000) to fit with
the three-decision test setting, in order to apply the test procedure to a
collection of independent trajectories. The performance of our procedure is
much better than the MSD method as confirmed by Monte Carlo experiments. The
method is demonstrated on real data sets corresponding to protein dynamics
observed in fluorescence microscopy.Comment: Revised introduction. A clearer and shorter description of the model
(section 2
Recovering the Probability Density Function of Asset Prices Using GARCH as Diffusion Approximations
This paper uses Garch models to estimate the objective and risk-neutral density functions of financial asset prices and, by comparing their shapes, recover detailed information on economic agents' attitudes toward risk. It differs from recent papers investigating analogous issues because it uses Nelson's (1990) result that Garch schemes are approximations of the kind of differential equations typically employed in finance to describe the evolution of asset prices. This feature of Garch schemes usually has been overshadowed by their well-known role as simple econometric tools providing reliable estimates of unobserved conditional variances. We show instead that the diffusion approximation property of Garch gives good results and can be extended to situations with i) non-standard distributions for the innovations of a conditional mean equation of asset price changes and ii) volatility concepts different from the variance. The objective PDF of the asset price is recovered from the estimation of a nonlinear Garch fitted to the historical path of the asset price. The risk-neutral PDF is extracted from crosssections of bond option prices, after introducing a volatility risk premium function. The direct comparison of the shapes of the two PDFS reveals the price attached by economic agents to the different states of nature. Applications are carried out with regard to the futures written on the Italian 10-year bond.option pricing, stochastic volatility, ARCH, volatility risk premium
The History of the Quantitative Methods in Finance Conference Series. 1992-2007
This report charts the history of the Quantitative Methods in Finance (QMF) conference from its beginning in 1993 to the 15th conference in 2007. It lists alphabetically the 1037 speakers who presented at all 15 conferences and the titles of their papers.
Nonparametric statistical inference for drift vector fields of multi-dimensional diffusions
The problem of determining a periodic Lipschitz vector field from an observed trajectory of the solution of the
multi-dimensional stochastic differential equation \begin{equation*} dX_t =
b(X_t)dt + dW_t, \quad t \geq 0, \end{equation*} where is a standard
-dimensional Brownian motion, is considered. Convergence rates of a
penalised least squares estimator, which equals the maximum a posteriori (MAP)
estimate corresponding to a high-dimensional Gaussian product prior, are
derived. These results are deduced from corresponding contraction rates for the
associated posterior distributions. The rates obtained are optimal up to
log-factors in -loss in any dimension, and also for supremum norm loss
when . Further, when , nonparametric Bernstein-von Mises
theorems are proved for the posterior distributions of . From this we deduce
functional central limit theorems for the implied estimators of the invariant
measure . The limiting Gaussian process distributions have a covariance
structure that is asymptotically optimal from an information-theoretic point of
view.Comment: 55 pages, to appear in the Annals of Statistic
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