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On the identification of ARMA echelon‐form models
Author(s) -
Nsiri Said,
Roy Roch
Publication year - 1992
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315608
Subject(s) - autoregressive–moving average model , mathematics , autoregressive model , series (stratigraphy) , statistic , autocorrelation , representation (politics) , test statistic , canonical form , statistical hypothesis testing , moving average , algorithm , statistics , biology , paleontology , politics , political science , pure mathematics , law
An identification procedure for multivariate autoregressive moving average (ARMA) echelon‐form models is proposed. It is based on the study of the linear dependence between rows of the Hankel matrix of serial correlations. To that end, we define a statistical test for checking the linear dependence between vectors of serial correlations. It is shown that the test statistic t̃ n considered is distributed asymptotically as a finite linear combination of independent chi‐square random variables with one degree of freedom under the null hypothesis, whereas under the alternative hypothesis, t̃ N /N converges in probability to a positive constant. These results allow us, in particular, to compute the asymptotic probability of making a specification error with the proposed procedure. Links to other methods based on the application of canonical analysis are discussed. A simulation experiment was done in order to study the performance of the procedure. It is seen that the graphical representation of t̃ N , as a function of N, can be very useful in identifying the dynamic structure of ARMA models. Furthermore, for the model considered, the proposed identification procedure performs very well for series of 100 observations or more and reasonably well with short series of 50 observations.