By Christian Gouriéroux (auth.)
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"Gourieroux deals a pleasant stability of conception and alertness during this e-book on ARCH modeling in finance…The booklet is easily written and has wide references. Its specialize in finance will entice monetary engineers and fiscal probability managers."
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Additional info for ARCH Models and Financial Applications
This test relies on the usual Fisher F -statistic for the null hypothesis Ho (C II = C 12 = 0), where the additional regressors c;_I' cr-l£r-2 are replaced by the corresponding residuals 8;_1' 8'-18,-2, and where 8, = Yr - pYr - 1 is computed under the null hypothesis. Such an approach based on Volterra's expansion was developed by Keenan (1985). ii) Independence of the White Noise Another way to proceed is based on a generalized Portmanteau statistic. Indeed, if £ = (£,) is a sequence of independent and identically distributed variables, the no correlation property holds for any nonlinear function of £: Vg, Vh 10, Cov[g(£,), g(c,-h)] = o.
Ii) Independence of the White Noise Another way to proceed is based on a generalized Portmanteau statistic. Indeed, if £ = (£,) is a sequence of independent and identically distributed variables, the no correlation property holds for any nonlinear function of £: Vg, Vh 10, Cov[g(£,), g(c,-h)] = o. 24 2. Linear and Nonlinear Processes A Portmanteau statistic may then be defined for each of these transformations. McLeod and Li (1983) have suggested a Portmanteau test based on the autocorrelations of the squared residuals.
Estimation and Tests It is known that in general the properties of this estimator, denoted OT and called pseudo maximum likelihood estimator (PML), both depend on the true underlying distribution and on the one used to compute the likelihood function (here the normal distribution). However, under standard regularity conditions (White 1981; Gourieroux et al. 1984; Gallant 1987; Gourieroux and Monfort 1989), this estimator is consistent even if the underlying distribution is not conditionally normal; that is, this property does not depend on the distribution that is used to build the likelihood function.
ARCH Models and Financial Applications by Christian Gouriéroux (auth.)