2016/09/26 by Salwa Bajja, Bajja, Salwa, Khalifa Es-Sebaiy +3
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Advanced Statistical Process Monitoring #Financial Risk and Volatility Modeling #Stochastic processes and financial applications #math.PR #math.ST #stat.TH
paper · pdf · doi:10.48550/arxiv.1609.08199
arxiv created 2016/09/26 · arxiv updated 2016/09/28
We first study the drift parameter estimation of the fractional Ornstein-Uhlenbeck process (fOU) with periodic mean for every (1)/(2)<H<1. More precisely, we extend the consistency proved in \citeDFW for (1)/(2)<H<(3)/(4) to the strong consistency for any (1)/(2)<H<1 on the one hand, and on the other, we also discuss the asymptotic normality given in \citeDFW. In the second main part of the paper, we study the strong consistency and the asymptotic normality of the fOU of the second kind with periodic mean for any (1)/(2)<H<1.