By ByoungSeon Choi (auth.)
During the final 20 years, huge growth has been made in statistical time sequence research. the purpose of this e-book is to give a survey of 1 of the main energetic parts during this box: the identity of autoregressive moving-average versions, i.e., deciding upon their orders. Readers are assumed to have already taken one direction on time sequence research as should be provided in a graduate direction, yet another way this account is self-contained. the most subject matters lined comprise: Box-Jenkins' strategy, inverse autocorrelation services, penalty functionality id comparable to AIC, BIC innovations and Hannan and Quinn's approach, instrumental regression, and a number trend identity tools. instead of hide the entire tools intimately, the emphasis is on exploring the basic principles underlying them. broad references are given to the examine literature and for that reason, all these engaged in examine during this topic will locate this a useful reduction to their work.
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Extra info for ARMA Model Identification
2. The Inverse Autocorrelation Method 41 McClave (1978b) and Bhansali (1983a) have utilized the IACF with some penalty functions, which will be discussed in Chapter 3, to identify MA processes. By analogy with the IACF, Hipel, McLeod, and Lennox (1977) have defined the inverse partial autocorrelation function (IPACF) of an ARMA(p, q) process by the PACF of its dual ARMA(q,p) process. Abraham and Ledolter (1984) have preferred the IPACF to the ACRF in detecting the orders of pure MA processes. Bhansali (1983b) has discussed the IPACF in detail.
3), and Brockwell and Davis (1987, Chapter 7). For derivations of their distributions, refer to R. L. Anderson (1942), Anderson and Rubin (1964), Ramasubban (1972), Hannan and Heyde (1972), Hannan (1976), Roy (1989), and the references therein. 3), and the references therein. Their results will be useful for studying asymptotic properties of the orders selected by penalty function methods, which will be discussed in Chapter 3. 4) For the lattice method, refer to Cybenko (1983) and Caines (1988, pp.
1) Some characteristics of the PACF have been discussed by Ramsey (1974) and Hamilton and Watts (1978). 1 was proven by Dixon (1944) and Quenouille (1949a, 1949b). Another simple proof can be found in Choi (1990b). 1 was presented by Bartlett and Rajalakshman (1953), Morf, Vieira, and Kailath (1978), and Sakai (1981). Yajima (1985) investigated the asymptotic properties of the sample ACVF and of the PACF estimate of a multiplicative ARIMA model. 2) For FFT algorithms, readers may refer to Runge (1903), Brigham and Morrow (1967), Cooley, Lewis, and Welch (1967, 1970a, 1970b), Bergland (1969), Brigham (1974), Silverman (1977), Brillinger (1981, pp.