Root-T consistent density estimation in GARCH models
Aurore Delaigle, Alexander Meister, Jeroen Rombouts
JOURNAL OF ECONOMETRICS | ELSEVIER SCIENCE SA | Published : 2016
We consider a new nonparametric estimator of the stationary density of the logarithm of the volatility of the GARCH(1, 1) model. This problem is particularly challenging since this density is still unknown, even in cases where the model parameters are given. Although the volatility variables are only observed with multiplicative independent innovation errors with unknown density, we manage to construct a nonparametric procedure which estimates the log volatility density consistently. By carefully exploiting the specific GARCH dependence structure of the data, our iterative procedure even attains the striking parametric root-T convergence rate. As a by-product of our main results, we also der..View full abstract
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Awarded by Australian Research Council
Delaigle's research was supported by a grant (DP140100125) and a fellowship (FT130100098) from the Australian Research Council.