On a double-threshold autoregressive heteroscedastic time series model

C. W. LI, Wai Keung LI

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151 Citations (Scopus)

Abstract

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
Volume11
Issue number3
DOIs
Publication statusPublished - May 1996

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time series
business cycle
Time series models
Autoregressive conditional heteroscedasticity
Threshold model
Modeling
diagnostic
statistics
market
Model checking
Nonlinearity
Adequacy
Maximum likelihood estimation
Statistics
Weighted least squares
Business cycles
Financial data
Conditional variance
Diagnostics

Citation

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