By P. Sint (auth.), T. Havránek, Z. à idák, M. Novák (eds.)

ISBN-10: 3642518834

ISBN-13: 9783642518836

ISBN-10: 3705100076

ISBN-13: 9783705100077

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**Additional resources for Compstat 1984: Proceedings in Computational Statistics**

**Example text**

G. (1984), Estimating missing observations in economic time series, J. Am. Statist. Ass. 79, 125-131. H. (1980), Maximum likelihood fitting of ARMA models to time series with missing observations, Technometrics 22, 389-395. I. (1977), Derivation of the theoretical autocovariances of autoregressive moving average time series, Appl. Stat. 26, 194. 35 Parameter Estimation and Order Determination of a Multivariate Autoregressive Process M. Krzy~o, and D. Smoczyflski. : The least squares estimators of the parameters of t~e multlvar ate autoregressive process and the asymptotic properties of these estimators are investigated.

2) where X. ~:n denotes the i-th ascending order statistic associated to the sample (Xl' X2 ••••• Xn ) and Ql/2- {X[n/2]:n + X[n/2+1]:n}/2 seems to be the most simple. although powerful. test statistic (Gomes. Properties and asymptotic behaviour of W han ve been studied by Tiago de Oliveira and Gomes (1983). who have shown that log(logn) {W - [10g(n)+10g(10g2)]/[log(logn)-log(10g2)]} n + w Z (1. f. of X is Gumbel. v. f. Fm. ~1. n where F belongs to the domain of attraction of the Gumbel distribution (fact that we shall denote by F~~(A».

2 Ansley and Newbold (1980) and Wilson (1979) have recommended the use of a more exact method. It appears that a very ef- ficient method is given by the algorithm of Section 1, with the following modification (3) is replaced by (10) where the (atlht), t a 1, ••. , n, are generated by pseudo-random variables with a given arbitrary distribution. 4. THE LIKELIHOOD OF A TRANSFER FUNCTION MODEL The reader is referred to Liu (1983) for methods of estimation of transfer function models. •. , k). It is assumed that data for wt are available for t > 0 and that Xi,t is known for t > t i .

### Compstat 1984: Proceedings in Computational Statistics by P. Sint (auth.), T. Havránek, Z. à idák, M. Novák (eds.)

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