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UNIT ROOT TESTING IN THE PRESENCE OF HEAVY‐TAILED GARCH ERRORS
Author(s) -
Wang Gaowen,
Mao WeiLin
Publication year - 2008
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2008.00517.x
Subject(s) - mathematics , autoregressive conditional heteroskedasticity , unit root , heteroscedasticity , autoregressive model , unit root test , moment (physics) , independent and identically distributed random variables , statistics , gaussian , econometrics , volatility (finance) , random variable , cointegration , quantum mechanics , physics , classical mechanics
Summary We derive the asymptotic distributions of the Dickey–Fuller (DF) and augmented DF (ADF) tests for unit root processes with Generalized Autoregressive Conditional Heteroscedastic (GARCH) errors under fairly mild conditions. We show that the asymptotic distributions of the DF tests and ADF t ‐type test are the same as those obtained in the independent and identically distributed Gaussian cases, regardless of whether the fourth moment of the underlying GARCH process is finite or not. Our results go beyond earlier ones by showing that the fourth moment condition on the scaled conditional errors is totally unnecessary. Some Monte Carlo simulations are provided to illustrate the finite‐sample‐size properties of the tests.