The Annals of Statistics

Bartlett Type Identities for Martingales

Per Aslak Mykland

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Abstract

Bartlett type identities are shown to exist for martingales. As applications, we give a cumulant-based proof of the martingale central limit theorem, and we give an algorithm for calculating approximate cumulants of the least squares estimator in the AR(1) process.

Article information

Source
Ann. Statist., Volume 22, Number 1 (1994), 21-38.

Dates
First available in Project Euclid: 11 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176325355

Digital Object Identifier
doi:10.1214/aos/1176325355

Mathematical Reviews number (MathSciNet)
MR1272073

Zentralblatt MATH identifier
0808.62030

JSTOR
links.jstor.org

Subjects
Primary: 60G42: Martingales with discrete parameter
Secondary: 60G44: Martingales with continuous parameter 62E99: None of the above, but in this section 60F99: None of the above, but in this section 62E20: Asymptotic distribution theory 62M09: Non-Markovian processes: estimation 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]

Keywords
Bartlett identities central limit theorem Edgeworth expansions martingales time series

Citation

Mykland, Per Aslak. Bartlett Type Identities for Martingales. Ann. Statist. 22 (1994), no. 1, 21--38. doi:10.1214/aos/1176325355. https://projecteuclid.org/euclid.aos/1176325355


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