| Summary: | 碩士 === 逢甲大學 === 統計與精算所 === 95 === This paper proposed a simple test of the hypothesis that either the mean or the variance are nonlinear in a heteroskedastic model. We estimated the parameters under Bayesian Markov chain Monte Carlo methods and fit a general double threshold ARX-GARCH model with exogenous threshold variables. The posterior credible intervals on model parameters specify threshold nonlinearity in the mean and volatility equations. Simulation experiments demonstrate that the method works favorably in identifying model specifications varying in complexity from the conventional GARCH up to the full double-threshold
nonlinear GARCH model and is robust to over-specification in model orders. We considered nine international financial market indices including FTSE 100 of United Kingdom, CAC 40 of France, Milan MIBTel Index of Italy, ADX 30 of Germany, Toronto SE 300 of Canada, Nikkei 225 Index of Japan, Heng Seng Index of Hong Kong, Weight Stock Index of Taiwan, and AORD of Australia and employed the daily return on US Standard and Poor’s 500 Index (S&P 500) as an exogenous variable. Evidence supports the hypothesis of threshold nonlinearity in mean and/or volatility.
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