Statistics Seminar: Professor Uwe Hassler -- Quantile Regression for Long Memory Testing

 In this paper we propose a quantile regression based test to detect long memory that
generalizes the Lagrange Multiplier test by Breitung and Hassler (2002, Journal of
Econometrics). The procedure is robust with respect to outliers or leptokurtic
distributions. Moreover, it allows to detect whether the degree of memory or fractional
integration varies at different quantiles, which is particularly useful when one is
interested in the tail-behaviour of the data. The limiting distribution is Gaussian or
χ2 and free of nuisance parameters. The validity in finite samples is established
through Monte Carlo experiments. The application to daily realized volatility produces
new insights into the widely accepted long-memory feature: The model with a constant
order of integration is rejected due to persistence that is growing with increasing
quantiles. This evidence suggest the existence of different regimes with different
degree of persistence in realized volatility.