On Estimating the Cumulant Generating Function of Linear Processes

Ghosh, Sucharita; Beran, Jan

On Estimating the Cumulant Generating Function of Linear Processes

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Datum

2006

Autor:innen

Ghosh, Sucharita

Beran, Jan

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

Annals of the Institute of Statistical Mathematics. 2006, 58(1), pp. 53-71. ISSN 0020-3157. eISSN 1572-9052. Available under: doi: 10.1007/s10463-005-0009-5

Zusammenfassung

We compare two estimates of the cumulant generating function of a stationary linear process. The first estimate is based on the empirical moment generating function. The second estimate uses the linear representation of the process and the empirical moment generating function of the innovations. Asymptotic expressions for the mean square errors are derived under short- and long-range dependence. For long-memory processes, the estimate based on the linear representation turns out to have a better rate of convergence. Thus, exploiting the linear structure of the process leads to an infinite gain in asymptotic efficiency.

Fachgebiet (DDC)

510 Mathematik

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ISO 690

GHOSH, Sucharita, Jan BERAN, 2006. On Estimating the Cumulant Generating Function of Linear Processes. In: Annals of the Institute of Statistical Mathematics. 2006, 58(1), pp. 53-71. ISSN 0020-3157. eISSN 1572-9052. Available under: doi: 10.1007/s10463-005-0009-5

BibTex

@article{Ghosh2006Estim-27577,
  year={2006},
  doi={10.1007/s10463-005-0009-5},
  title={On Estimating the Cumulant Generating Function of Linear Processes},
  number={1},
  volume={58},
  issn={0020-3157},
  journal={Annals of the Institute of Statistical Mathematics},
  pages={53--71},
  author={Ghosh, Sucharita and Beran, Jan}
}

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