Estimation of the location and exponent of the spectral singularity of a long memory process

Javier Hidalgo (1) , Philippe Soulier (2)

1 Department of Economics
2 MODAL'X - Modélisation aléatoire de Paris X

We consider the estimation of the location of the pole and memory parameter $\omega_0$ and $d$ of a covariance stationary process with spectral density $f(x) = |1-e^{i(x-\omega_0)}|^{-d} |1-e^{i(x+\omega_0)}|^{-d}f^*(x)$. We investigate optimal rates of convergence for the estimators of $\omega_0$ and $d$, and the consequence that the lack of knowledge of $\omega_0$ has on the estimation of the memory parameter $d$. We present estimators which achieve the optimal rates.

Keywords: Long Memory; Fractionally differenced processes; Gegenbauer processes; Periodogram; Semiparametric estimation

Domains: Statistics [math.ST]

Javier Hidalgo, Philippe Soulier. Estimation of the location and exponent of the spectral singularity of a long memory process. Journal of Time Series Analysis, 2004, 25 (1), pp.55-81. ⟨10.1111/j.1467-9892.2004.00337.x⟩. ⟨hal-00147620⟩