We work on the statistical inference for several classes of stochastic processes.
Long memory processes are stationary processes whose the autocorrelation function exhibits persistence. , They play an important role in fields as diverse as econometry, finance, hydrology, physical sciences… We study long memory processes to understand probabilistic foundations and statistical principles.
The aggregation provides a class of models for which we propose new techniques of estimation. We also build testing procedures for detecting the presence of long memory in time series or for comparing the intensity of the memory of two time series.
Self-regulating processes are stochastic processes whose the pointwise Hölder exponent is a function of amplitude. We propose an estimator of this function using non parametric approach. Asymptotic properties validate our inference method.
The multistable processes generalize stable processes in the sense that the intensity of jumps varies in time. We study the problem of discriminate between stable and multistable processes.