The Annals of Statistics
- Ann. Statist.
- Volume 23, Number 3 (1995), 1048-1072.
Log-Periodogram Regression of Time Series with Long Range Dependence
This paper discusses the estimation of multiple time series models which allow elements of the spectral density matrix to tend to infinity or zero at zero frequency and be unrestricted elsewhere. A form of log-periodogram regression estimate of differencing and scale parameters is proposed, which can provide modest efficiency improvements over a previously proposed method (for which no satisfactory theoretical justification seems previously available) and further improvements in a multivariate context when differencing parameters are a priori equal. Assuming Gaussianity and additional conditions which seem mild, asymptotic normality of the parameter estimates is established.
Ann. Statist., Volume 23, Number 3 (1995), 1048-1072.
First available in Project Euclid: 11 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 60G18: Self-similar processes 62G05: Estimation
Robinson, P. M. Log-Periodogram Regression of Time Series with Long Range Dependence. Ann. Statist. 23 (1995), no. 3, 1048--1072. doi:10.1214/aos/1176324636. https://projecteuclid.org/euclid.aos/1176324636