4. Semiparametric Estimation of Difference Parameter
These estimators are semiparametric estimators. The estimators involve the unknown
parameter of interest d, in the parametric relation
where L is the lag operator. The spectra density
) is estimated nonparametrically
imposing the condition that
, with mild regularity assumptions in a
neighbourhood of zero frequency, and its behaviour away from zero is unrestricted.
The three estimators of interest are:
Further discussions can be found in
the Tutorial on Long-Memory.
We shall use the default bandwidth
for estimation given by the quantlets.
Further discussions regarding bandwidth
selection can be found in Delgado and Robinson (1996).