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GARCH Models
book

GARCH Models

by Christian Francq, Jean-Michel Zakoian
August 2010
Intermediate to advanced content levelIntermediate to advanced
504 pages
12h 59m
English
Wiley
Content preview from GARCH Models

5

Identification

In this chapter, we consider the problem of selecting an appropriate GARCH or ARMA-GARCH model for given observations X1, …, Xn of a centered stationary process. A large part of the theory of finance rests on the assumption that prices follow a random walk. The price variation process, X = (Xt), should thus constitute a martingale difference sequence, and should coincide with its innovation process, 2208_fmt = (2208_fmtt). The first question addressed in this chapter, in Section 5.1, will be the test of this property, at least a consequence of it: absence of correlation. The problem is far from trivial because standard tests for noncorrelation are actually valid under an independence assumption. Such an assumption is too strong for GARCH processes which are dependent though uncorrelated.

If significant sample autocorrelations are detected in the price variations - in other words, if the random walk assumption cannot be sustained - the practitioner will try to fit an ARMA(P, Q) model to the data before using a GARCH(p, q) model for the residuals. Identification of the orders (P, Q) will be treated in Section 5.2, identification of the orders (p,q) in Section 5.3. Tests of the ARCH effect (and, more generally, Lagrange multiplier tests) will be considered in Section 5.4.

5.1 Autocorrelation ...

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Publisher Resources

ISBN: 9780470683910