From short to long memory: Aggregation and estimation

Jan Beran, Martin Schützner and Sucharita Ghosh

Computational Statistics & Data Analysis, 2010, vol. 54, issue 11, 2432-2442

Abstract: Contemporaneous aggregation of asymptotically stationary AR(1) processes is considered where the squared random coefficients are beta-distributed. Based on the sample correlation coefficients for the individual AR(1) processes, an estimator for the parameters of the underlying beta distribution, and thus for the long memory parameter of the aggregated process, is introduced. Consistency and asymptotic normality are derived and the new estimator is shown to be asymptotically equivalent to the maximum likelihood estimator of the beta distribution.

Date: 2010
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