• Journal of the Korean Statistical Society
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• v.35 no.4
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• pp.409-417
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• 2006

This article is concerned with threshold modeling of the bifurcating autoregressive model (BAR) originally suggested by Cowan and Staudte (1986) for tree structured data of cell lineage study where each individual $(X_t)$ gives rise to two off-spring $(X_{2t},\;X_{2t+1})$ in the next generation. The triplet $(X_t,\;X_{2t},\;X_{2t+1})$ refers to mother-daughter relationship. In this paper we propose a threshold model incorporating the difference of 'fertility' of the mother for the first and second off-springs, and thereby extending BAR to threshold-BAR (TBAR, for short). We derive a sufficient condition of stationarity for the suggested TBAR model. Also various inferential methods such as least squares (LS), maximum likelihood (ML) and quasi-likelihood (QL) methods are discussed and relevant limiting distributions are obtained.

• The Korean Journal of Applied Statistics
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• v.13 no.2
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• pp.437-445
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• 2000

The present paper is introducing a new model so called TAR-GARCH in the context of stock price analysis Conventional models such as AR(l), TAR(l), ARCH(I) and GARCH( 1,1) are briefly reviewed and TAR-GARCH is suggested in analyizing domestic stock prices. Also, relevant iterative estimation procedure is developed. It is seen that TAR-GARCH provides the better fit relative to traditional first order models for stock prices data in Korea.