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Maximum likelihood estimation of a GARCH‐stable model
Author(s) -
Liu ShiMiin,
Brorsen B. Wade
Publication year - 1995
Publication title -
journal of applied econometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.878
H-Index - 99
eISSN - 1099-1255
pISSN - 0883-7252
DOI - 10.1002/jae.3950100305
Subject(s) - autoregressive conditional heteroskedasticity , heteroscedasticity , mathematics , econometrics , autoregressive model , financial models with long tailed distributions and volatility clustering , statistics , volatility (finance) , stochastic volatility , sabr volatility model
Maximum likelihood is used to estimate a generalized autoregressive conditional heteroskedastic (GARCH) process where the residuals have a conditional stable distribution (GARCH‐stable). The scale parameter is modelled such that a GARCH process with normally distributed residuals is a special case. The usual methods of estimating the parameters of the stable distribution assume constant scale and will underestimate the characteristic exponent when the scale parameter follows a GARCH process. The parameters of the GARCH‐stable model are estimated with daily foreign currency returns. Estimates of characteristic exponents are higher with the GARCH‐stable than when independence is assumed. Monte Carlo hypothesis testing procedures, however, reject our GARCH‐stable model at the 1% significance level in four out of five cases.