Asymptotic behavior of mixed power variations and statistical estimation in mixed models

Marco Dozzi (1) , Yuliya Mishura (2) , Georgiy Shevchenko (2)

1 IECL - Institut Élie Cartan de Lorraine
2 Taras Shevchenko National University of Kyiv

In this paper we study asymptotic behaviour of power variations of a linear combination of independent Wiener process and fractional Brownian motion. These results are applied to construct consistent parameter estimators and approximate confidence intervals in mixed models.

Mots clés: asymptotic confidence interval; consistent estimator; power variation; fractional Brownian motion; Hurst parameter; Wiener process

Domaines: Probabilités [math.PR]

Marco Dozzi, Yuliya Mishura, Georgiy Shevchenko. Asymptotic behavior of mixed power variations and statistical estimation in mixed models. Statistical Inference for Stochastic Processes, 2015, 18 (2), pp.151-175. ⟨10.1007/s11203-014-9106-5⟩. ⟨hal-01095611⟩