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Empirical likelihood test for the application of swqmele in fitting an arma‐garch model
Author(s) -
Zhou Mo,
Peng Liang,
Zhang Rongmao
Publication year - 2021
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12563
Subject(s) - mathematics , autoregressive conditional heteroskedasticity , econometrics , moment (physics) , zero (linguistics) , empirical likelihood , asymptotic distribution , statistics , exponential function , conditional expectation , volatility (finance) , estimator , mathematical analysis , linguistics , philosophy , physics , classical mechanics
Fitting an ARMA‐GARCH model has become a common practice in financial econometrics. Because the asymptotic normality of the quasi maximum likelihood estimation (QMLE) requires finite fourth moment for both errors and the sequence itself, self‐weighted quasi maximum exponential likelihood estimation (SWQMELE) has been proposed to reduce the moment constraints but requires the errors to have zero median instead of zero mean. Because changing zero mean to zero median destroys the ARMA‐GARCH structure and has a serious effect on skewed data, this article proposes an efficient empirical likelihood test for zero mean of errors in the application of SWQMELE to ensure that the model still concerns conditional mean. A simulation study confirms the good finite sample performance before applying the test to the US housing price indexes and financial returns for the study of comovement.