出版社：Suntory Toyota International Centres for Economics and Related Disciplines
摘要：We consider the estimation of the location of the pole and memory parameter, λ0and α respectively, of covariance stationary linear processes whose spectral density function f(λ) satisfies f(λ) ～ C|λ . λ0|.αin a neighbourhood of λ0. We define a consistent estimator of λ0and derive its limit distribution 0λZ . As in related optimization problems, when the true parameter value can lie on the boundary of the parameter space, we show that 0λZ is distributed as a normal random variable when λ0∈ (0, π), whereas for λ0= 0 or π, 0λZ is a mixture of discrete and continuous random variables with weights equal to 1/2. More specifically, when λ0= 0, 0λZ 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 λ0is assumed to be known a priori. A small Monte Carlo study is included to illustrate the finite sample performance of our estimators
关键词：Spectral density estimation; long memory processes; Gaussian ;Processes.
