Sucarrat, Genaro and Grønneberg, Steffen and Escribano, Alvaro (2013): Estimation and Inference in Univariate and Multivariate LogGARCHX Models When the Conditional Density is Unknown.
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Abstract
Exponential models of Autoregressive Conditional Heteroscedasticity (ARCH) are of special interest, since they enable richer dynamics (e.g. contrarian or cyclical), provide greater robustness to jumps and outliers, and guarantee the positivity of volatility. The latter is not guaranteed in ordinary ARCH models, in particular when additional exogenous and/or predetermined variables ("X") are included in the volatility specification. Here, we propose estimation and inference methods for univariate and multivariate Generalised logARCHX (i.e. logGARCHX) models when the conditional density is not known. The methods employ (V)ARMAX representations and relies on a biasadjustment in the logvolatility intercept. The bias is induced by (V)ARMA estimators, but the remaining parameters are consistently estimated by (V)ARMA methods. We derive a simple formula for the biasadjustment, and a closedform expression for its asymptotic variance. Next, we show that adding exogenous or predetermined variables and/or increasing the dimension of the model does not change the structure of the problem. Accordingly, the univariate biasadjustment result is likely to hold not only for univariate logGARCHX models, but also for multivariate logGARCHX models equationbyequation. Extensive simulation evidence verify our results, and an empirical application show that they are particularly useful when the Xvector is highdimensional.
Item Type:  MPRA Paper 

Original Title:  Estimation and Inference in Univariate and Multivariate LogGARCHX Models When the Conditional Density is Unknown 
English Title:  Estimation and Inference in Univariate and Multivariate LogGARCHX Models When the Conditional Density is Unknown 
Language:  English 
Keywords:  ARCH, exponential GARCH, LogGARCHX, ARMAX, multivariate logGARCHX, VARMAX 
Subjects:  C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C22  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables > C32  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C51  Model Construction and Estimation C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C52  Model Evaluation, Validation, and Selection 
Item ID:  57238 
Depositing User:  Dr. Genaro Sucarrat 
Date Deposited:  11. Jul 2014 03:37 
Last Modified:  11. Jul 2014 04:15 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/57238 
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Estimation and Inference in Univariate and Multivariate LogGARCHX Models When the Conditional Density is Unknown. (deposited 29. Aug 2013 14:30)

Estimation and Inference in Univariate and Multivariate LogGARCHX Models When the Conditional Density is Unknown. (deposited 10. Jul 2014 20:12)
 Estimation and Inference in Univariate and Multivariate LogGARCHX Models When the Conditional Density is Unknown. (deposited 11. Jul 2014 03:37) [Currently Displayed]

Estimation and Inference in Univariate and Multivariate LogGARCHX Models When the Conditional Density is Unknown. (deposited 10. Jul 2014 20:12)