39 research outputs found
Pathwise stability of likelihood estimators for diffusions via rough paths
We consider the classical estimation problem of an unknown drift parameter
within classes of nondegenerate diffusion processes. Using rough path theory
(in the sense of T. Lyons), we analyze the Maximum Likelihood Estimator (MLE)
with regard to its pathwise stability properties as well as robustness toward
misspecification in volatility and even the very nature of the noise. Two
numerical examples demonstrate the practical relevance of our results.Comment: Published at http://dx.doi.org/10.1214/15-AAP1143 in the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
The expected signature of Brownian motion stopped on the boundary of a circle has finite radius of convergence
The expected signature is an analogue of the Laplace transform for rough
paths. Chevyrev and Lyons showed that, under certain moment conditions, the
expected signature determines the laws of signatures. Lyons and Ni posed the
question of whether the expected signature of Brownian motion up to the exit
time of a domain satisfies Chevyrev and Lyons' moment condition. We provide the
first example where the answer is negative
Invariants of multidimensional time series based on their iterated-integral signature
We introduce a novel class of features for multidimensional time series, that
are invariant with respect to transformations of the ambient space. The general
linear group, the group of rotations and the group of permutations of the axes
are considered. The starting point for their construction is Chen's
iterated-integral signature.Comment: complete rewrite of Section 3.
Pathwise stability of likelihood estimators for diffusions via rough paths
We consider the estimation problem of an unknown drift parameter within classes of non-degenerate diffusion processes. The Maximum Likelihood Estimator (MLE) is analyzed with regard to its pathwise stability properties and robustness towards misspecification in volatility and even the very nature of noise. We construct a version of the estimator based on rough integrals (in the sense of T. Lyons) and present strong evidence that this construction resolves a number of stability issues inherent to the standard MLEs