Abstract :
We study asymptotic properties of the local Whittle estimator of the long memory
parameter for a wide class of fractionally integrated nonlinear time series models+
In particular, we solve the conjecture posed by Phillips and Shimotsu ~2004,
Annals of Statistics 32, 656–692! for Type I processes under our framework, which
requires a global smoothness condition on the spectral density of the short memory
component+ The formulation allows the widely used fractional autoregressive
integrated moving average ~FARIMA! models with generalized autoregressive conditionally
heteroskedastic ~GARCH! innovations of various forms, and our asymptotic
results provide a theoretical justification of the findings in simulations that
the local Whittle estimator is robust to conditional heteroskedasticity+ Additionally,
our conditions are easily verifiable and are satisfied for many nonlinear time
series models+
