Gaussian estimation of parametric spectral density with unknown pole
Open Access
- 1 August 2001
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Statistics
- Vol. 29 (4), 987-1023
- https://doi.org/10.1214/aos/1013699989
Abstract
We consider a parametric spectral density with power-law behavior about a fractional pole at the unknown frequency $\omega$. The case of known $\omega$, especially $\omega =0$, is standard in the long memory literature. When $omega$ is unknown, asymptotic distribution theory for estimates of parameters, including the (long) memory parameter, is significantly harder. We study a form of Gaussian estimate. We establish $n$-consistency of the estimate of $\omega$, and discuss its (non-standard) limiting distributional behavior. For the remaining parameter estimates,we establish $\sqrt{n}$-consistency and asymptotic normality.
Keywords
This publication has 12 references indexed in Scilit:
- A limit theory for long-range dependence and statistical inference on related modelsThe Annals of Statistics, 1997
- A GENERALIZED FRACTIONALLY INTEGRATED AUTOREGRESSIVE MOVING‐AVERAGE PROCESSJournal of Time Series Analysis, 1996
- Efficient Tests of Nonstationary HypothesesJournal of the American Statistical Association, 1994
- A central limit theorem for quadratic forms in strongly dependent linear variables and its application to asymptotical normality of Whittle's estimateProbability Theory and Related Fields, 1990
- Efficient Parameter Estimation for Self-Similar ProcessesThe Annals of Statistics, 1989
- ON GENERALIZED FRACTIONAL PROCESSESJournal of Time Series Analysis, 1989
- Large-Sample Properties of Parameter Estimates for Strongly Dependent Stationary Gaussian Time SeriesThe Annals of Statistics, 1986
- Fractional differencingBiometrika, 1981
- Alternative models for stationary stochastic processesStochastic Processes and their Applications, 1978
- An exponential model for the spectrum of a scalar time seriesBiometrika, 1973