B1184
Title: The adaptive Lasso estimator of AR(p) time series with applications to INAR(p) and Hawkes processes
Authors: Daniela De Canditiis - CNR (Italy) [presenting]
Abstract: The consistency and the oracle properties of the adaptive Lasso estimator for the coefficients of AR(p) time series with a strictly stationary white noise, not necessarily ergodic, are investigated. Roughly speaking, it is proven that (i) if the white noise has a finite second moment, then the adaptive Lasso estimator is almost sure consistent; (ii) if the white noise has a finite fourth moment, then the error estimate converges to zero with the same rate as the regularizing parameters of the adaptive Lasso estimator; (iii) if the white noise has a finite fourth moment and the regularizing parameters are weighted by a reverse power of the Conditional Least Squares estimates of the coefficients, then the adaptive Lasso estimator has the oracle properties. Such theoretical findings are applied $(i)$ to estimate the coefficients of a new class of time series, which includes INAR(p) time series $(ii)$ to estimate the fertility function of Hawkes processes. The results are validated by some numerical simulations, which show that the adaptive Lasso estimator allows for a better balancing between bias and variance with respect to the Conditional Least Square estimator and the classical Lasso estimator.
