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View Submission - SDS2022
A0178
Title: Semiparametric estimation for time series: A frequency domain approach based on optimal transportation theory Authors:  Manon Felix - University of Geneva (Switzerland) [presenting]
Davide La Vecchia - University of Geneva (Switzerland)
Abstract: A novel approach is proposed for estimation in stationary ARMA processes. Our estimation is semi-parametric: we have a Euclidean parameter, but we do not assume any distribution for the innovation term. Working with the frequency domain approach, we use the Wasserstein distance (1-Wasserstein distance and 2-Wasserstein distance) to derive minimum distance estimators. To do this, we rely on the fact that the standardized periodogram ordinates are asymptotically independent and have an exponential distribution with rate one. We give heuristic arguments for their asymptotics and provide algorithms for their implementation. Monte-Carlo simulations illustrate the performance of our estimators, under different data generating mechanisms (e.g. leptokurtic underlying distributions, time domain additive outliers and frequency domain outliers). The numerical exercises highlight the improvements of our new estimators on the routinely-applied Whittles estimator.