Erschienen in:

2000 | OriginalPaper | Buchkapitel

Reversibility and Identifiability

verfasst von : Murray Rosenblatt

Erschienen in: Gaussian and Non-Gaussian Linear Time Series and Random Fields

Verlag: Springer New York

Enthalten in: Professional Book Archive

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Let us first consider linear stationary sequences. A sequence of independent, identically distributed real random variables ξ_j, j = …, -1,0,1,… is given with Eξ_j = 0, 0 < Eξ_j2 = σ2 < ∞. The process x_j is obtained by passing this sequence through a linear filter characterized by the real weights, a_j, ∑a_j2 < ∞, 1.1.1$$ {x_{t}} = \sum\limits_{{j = - \infty }}^{\infty } {{a_{j}}\xi t - j.} $$

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