CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST 2011, 27(6) 642-656 DOI:      ISSN: 1001-4268 CN: 31-1256

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State Space Estimation for Long Memory ARFIMA-GARCH Models

Wang Lihong,Gu Chengzu

Nanjing University

Abstract��

This paper considers the state space representation
for the ARFIMA-GARCH model, which combines both the long memory time
series and the conditional heteroscedastic processes. Although this
state space representation is infinite dimensional, an exact maximum
likelihood (ML) estimator based on this kind of representation can
be computed in a finite number of iterations. Quasi ML estimators
based on the autoregressive approximation for the likelihood
function are proposed. Due to the facility of the state space
representation, these estimation approaches can be easily applied to
the missing data case. Simulation results of both the non-missing
data case and the missing data case are reported. A real data
example from stock market illustrates the proposed method.

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