2023/02/06 by Antoine Lejay, Lejay, Antoine, Sara Mazzonetto +1
Social Sciences · Economics, Econometrics and Finance · Mathematics · #Insurance, Mortality, Demography, Risk Management #Financial Risk and Volatility Modeling #Statistical Distribution Estimation and Applications
paper · pdf · doi:10.48550/arxiv.2302.02954
We give a thorough description of the asymptotic property of the maximum likelihood estimator (MLE) of the skewness parameter of a Skew Brownian Motion (SBM). Thanks to recent results on the Central Limit Theorem of the rate of convergence of estimators for the SBM, we prove a conjecture left open that the MLE has asymptotically a mixed normal distribution involving the local time with a rate of convergence of order 1/4. We also give a series expansion of the MLE and study the asymptotic behavior of the score and its derivatives, as well as their variation with the skewness parameter. In particular, we exhibit a specific behavior when the SBM is actually a Brownian motion, and quantify the explosion of the coefficients of the expansion when the skewness parameter is close to -1 or 1.