# Tests statistiques sur le paramètre de longue mémoire d’un processus temporel

vendredi 24 mai 2013, 14h30 - 15h15

$We deal with detection of non-constant long memory parameter in time series.$
The null hypothesis presumes stationary or nonstationary time series with constant long memory parameter,
typically an \$I(d) \$ series with \$d > .5\$.
The alternative corresponds to an increase in persistence and includes in particular an abrupt or
gradual change from I\$(d_1)\$ to I\$(d_2)\$, \$-.5

We discuss several test statistics based on the ratio of forward and backward sample variances of the partial sums.

The consistency of the tests is proved under a very general setting.
We also study the behavior of these test statistics for some models with changing memory parameter.
A simulation study shows that our testing procedures have good finite sample properties and
turn out to be more powerful than the KPSS-based tests considered in some previous works.

The talk is based on the joint work with F. Lavancier, R. Leipus and D. Surgailis.