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Inference for Box–Cox Transformed Threshold GARCH Models with Nuisance Parameters
Author(s) -
LEE SANGYEOL,
LEE TAEWOOK
Publication year - 2012
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2012.00805.x
Subject(s) - mathematics , autoregressive conditional heteroskedasticity , heteroscedasticity , estimator , cauchy distribution , autoregressive model , indirect inference , series (stratigraphy) , statistics , econometrics , gaussian , volatility (finance) , paleontology , physics , quantum mechanics , biology
. Generalized autoregressive conditional heteroscedastic (GARCH) models have been widely used for analyzing financial time series with time‐varying volatilities. To overcome the defect of the Gaussian quasi‐maximum likelihood estimator (QMLE) when the innovations follow either heavy‐tailed or skewed distributions, Berkes & Horváth ( Ann. Statist. , 32, 633, 2004) and Lee & Lee ( Scand. J. Statist. 36, 157, 2009) considered likelihood methods that use two‐sided exponential, Cauchy and normal mixture distributions. In this paper, we extend their methods for Box–Cox transformed threshold GARCH model by allowing distributions used in the construction of likelihood functions to include parameters and employing the estimated quasi‐likelihood estimators (QELE) to handle those parameters. We also demonstrate that the proposed QMLE and QELE are consistent and asymptotically normal under regularity conditions. Simulation results are provided for illustration.