On a double-threshold autoregressive heteroscedastic time series model

C. W. LI, Wai Keung LI

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167 Citations (Scopus)


Tong's threshold models have been found useful in modelling nonlinearities in the conditional mean of a time series. The threshold model is extended to the so-called double-threshold ARCH(DTARCH) model, which can handle the situation where both the conditional mean and the conditional variance specifications are piecewise linear given previous information. Potential applications of such models include financial data with different (asymmetric) behaviour in a rising versus a falling market and business cycle modelling. Model identification, estimation and diagnostic checking techniques are developed. Maximum likelihood estimation can be achieved via an easy-to-use iteratively weighted least squares algorithm. Portmanteau-type statistics are also derived for checking model adequacy. An illustrative example demonstrates that asymmetric behaviour in the mean and the variance could be present in financial series and that the DTARCH model is capable of capturing these phenomena. Copyright © 1996 John Wiley & Sons, Ltd.
Original languageEnglish
Pages (from-to)253-274
JournalJournal of Applied Econometrics
Issue number3
Publication statusPublished - May 1996


Li, C. W., & Li, W. K. (1996). On a double-threshold autoregressive heteroscedastic time series model. Journal of Applied Econometrics, 11(3), 253-274. doi: 10.1002/(SICI)1099-1255(199605)11:3<253::AID-JAE393>3.0.CO;2-8


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