ARMA Model Identification by ByoungSeon Choi (auth.)

By ByoungSeon Choi (auth.)

During the final twenty years, significant development has been made in statistical time sequence research. the purpose of this ebook is to give a survey of 1 of the main lively parts during this box: the id of autoregressive moving-average versions, i.e., identifying their orders. Readers are assumed to have already taken one path on time sequence research as will be provided in a graduate direction, yet another way this account is self-contained. the most subject matters coated contain: Box-Jenkins' process, inverse autocorrelation features, penalty functionality id akin to AIC, BIC strategies and Hannan and Quinn's process, instrumental regression, and more than a few development id tools. instead of disguise the entire tools intimately, the emphasis is on exploring the basic principles underlying them. vast references are given to the examine literature and for this reason, all these engaged in examine during this topic will locate this a useful reduction to their work.

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Sample text

Kendall and Stuart [1979, p. 446)) that 2I(f; g) is approximate to f {f(x) - g(x)P dx f(x) , which is similar to Pearson's X 2 statistic. Also, refer to Larimore (1983). All of the above theorems show that the larger 1(f;g) is, the more different 9 is from f. Thus, the Kullback-Leibler information number is a good measure of statistical distances. Because an estimated probability density function j(x) should be close to the true probability density function f(x), it is reasonable to choose j(x) minimizing the Kullback-Leibler information number 1 (f; j).

Cleveland's method is not useful for identifying mixed ARMA models by the same reason as Box-Jenkins'. It should be noted that the covariance of (;i(k 1 ) and (;i(k 2 ) may be nonnegligible compared with the variance of (;i(k). Thus, the selection rule based on the simultaneous confidence region should be applied. Some statisticians prefer the IACF to the PACF in ARMA model identification. One of the reasons is that no new body of knowledge regarding the relationship between a time series and its IACF needs to be developed due to the duality between the IACF and the ACRF of ARMA models.

Nowadays the procedure is called 46 3. Penalty Function Methods Akaike's FPE criterion because it has been popular since his publications. The FPE procedure has been applied to more general statistical modeling than AR order selection. 9. In practice it is impossible to calculate the FPE for all orders. Usually an integer K is preassigned as an upper bound of possible orders. Clearly, the integer K should be large enough to contain the true order. Several subjective benchmarks about the upper bound K have been proposed.

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