The Annals of Statistics

Log-Periodogram Regression of Time Series with Long Range Dependence

P. M. Robinson

Full-text: Open access


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.

Article information

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

Long range dependence $\log$-periodogram regression least squares generalized least squares limiting distribution theory


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.

Export citation