Abstract :
Recently, Shimotsu and Phillips (2005, Annals of Statistics 33, 1890–1933) developed
a new semiparametric estimator, the exact local Whittle (ELW) estimator, of the
memory parameter (d) in fractionally integrated processes. The ELW estimator has
been shown to be consistent, and it has the same N(0, 14
) asymptotic distribution for
all values of d, if the optimization covers an interval of width less than 9/2 and the
mean of the process is known.With the intent to provide a semiparametric estimator
suitable for economic data, we extend the ELW estimator so that it accommodates
an unknown mean and a polynomial time trend. We show that the two-step ELW
estimator, which is based on a modified ELW objective function using a tapered
local Whittle estimator in the first stage, has an N(0, 14
) asymptotic distribution for
d ∈ (−12
,2) (or d ∈ (−12
, 74
) when the data have a polynomial trend). Our simulation
study illustrates that the two-step ELW estimator inherits the desirable properties of
the ELW estimator.
