A general class of SemiGARCH models based on the Box-Cox transformation
Xuehai Zhang (),
Yuanhua Feng () and
Christian Peitz ()
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Xuehai Zhang: Paderborn University
Yuanhua Feng: Paderborn University
Christian Peitz: Paderborn University
No 104, Working Papers CIE from Paderborn University, CIE Center for International Economics
The paper proposes a wide class of semiparametric GARCH models by introducing a scale function into a GARCH class model for featuring long-run volatility dynamics, which can be thought of as an MEM (multiplicative error model) with a varying scale function. Our focus is to estimate the scale function under suitable weak moment conditions by means of the Box-Cox transformation of the absolute returns. The estimation of the scale function is independent of any GARCH specification. To overcome the drawbacks of the kernel and the local linear approaches, a non-negatively constrained local linear estimator of the scale function is considered, which is then proposed to fit a suitable parametric GARCH model to the standardized residuals, is used. Asymptotic properties of the proposed nonpara- metric and parametric estimators are studied in detail and iterative plug-in algorithms are developed for selecting the bandwidth and transformation parameters, which are selected by MLE and JB statistic. The algorithms are also carried out independently without any parametric specification in the stationary part. Application to real data sets show that the proposals work very well in practice.
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