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Two-dimensional long memory models. (English) Zbl 0649.62086
The paper investigates the two-dimensional model \((I-AB)^{\delta}X_ t=\epsilon_ t\), \(0<\delta <\), where B is the back-shift operator and A is a matrix with eigenvalues \(| \lambda_ j| \leq 1\). Exact formulae for the spectral density and the covariance function R(t) are derived and the corresponding AR(\(\infty)\) and MA(\(\infty)\) representations are given. The cases of long memory dependence \(\sum_{t}\sum_{j,k}| R_{jk}(t)| =\infty\) are described.
Reviewer: I.G.Zhurbenko
MSC:
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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