Estimation risk in conditional expectiles

Marcelo Fernandes (FGV-EESP), joint work with Victor Henriques (Argus Media), Duda Mendes (FGV-EESP)

Abstract: We establish the consistency and asymptotic normality of a two-step estimator of conditional expectiles in the context of location-scale models. We first estimate the parameters of the conditional mean and variance by quasi-maximum likelihood and then compute the unconditional expectile of the innovations using the empirical quantiles of the standardized residuals. We show how replacing true innovations with standardized residuals affects the asymptotic variance of the expectile estimator. In addition, we also obtain asymptotic-valid bootstrap-based confidence intervals. Finally, our empirical analysis reveals that conditional expectiles are very interesting alternatives to assess tail risk in cryptomarkets, relative to traditional quantile-based risk measures, such as value at risk and expected shortfall.