Abstract for:

Semiparametric Estimation for Stationary Processes whose Spectra have an Unknown Pole

Javier Hidalgo, January 2005
Paper No' EM/2005/481: | Full paper

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Keywords: spectral density estimation; long memory processes, Gaussian processes

JEL Classification: C14; G22

Is hard copy/paper copy available? YES - Paper Copy Still In Print.

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This Paper is published under the following series: Econometrics

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Abstract:

We consider the estimation of the location of the pole and memory parameter, λ⁰ and α respectively, of covariance stationary linear processes whose spectral density function f(λ) satisfies f(λ) ∼ C|λ − λ⁰|^−α in a neighbourhood of λ⁰. We define a consistent estimator of λ⁰ and derive its limit distribution Z_λ⁰ . As in related optimization problems, when the true parameter value can lie on the boundary of the parameter space, we show that Z_λ⁰ is distributed as a normal random variable when λ⁰ ∈ (0, π), whereas for λ⁰ = 0 or π, Z_λ⁰ is a mixture of discrete and continuous random variables with weights equal to 1/2. More specifically, when λ⁰ = 0, Z_λ⁰ is distributed as a normal random variable truncated at zero. Moreover, we describe and examine a two-step estimator of the memory parameter α, showing that neither its limit distribution nor its rate of convergence is affected by the estimation of λ⁰. Thus, we reinforce and extend previous results with respect to the estimation of α when λ⁰ is assumed to be known a priori. A small Monte Carlo study is included to illustrate the finite sample performance of our estimators.