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Factorizing multivariate time series operators

Author

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  • Stensholt, Eivind
  • Tjøstheim, Dag

Abstract

Motivated by problems occurring in the empirical identification and modelling of a n-dimensional ARMA time series X(t) we study the possibility of obtaining a factorization (I + a1B + ... + apBp) X(t) = [[Pi]i=1p (I - [alpha]iB)] X(t), where B is the backward shift operator. Using a result in [3] we conclude that as in the univariate case such a factorization always exists, but unlike the univariate case in general the factorization is not unique for given a1, a2,..., ap. In fact the number of possibilities is limited upwards by (np)!/(n!)p, there being cases, however, where this maximum is not reached. Implications for the existence and possible use of transformations which removes nonstationarity (or almost nonstationarity) of X(t) are mentioned.

Suggested Citation

  • Stensholt, Eivind & Tjøstheim, Dag, 1981. "Factorizing multivariate time series operators," Journal of Multivariate Analysis, Elsevier, vol. 11(2), pages 244-249, June.
    • Handle: RePEc:eee:jmvana:v:11:y:1981:i:2:p:244-249
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