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We know that red noise is the same as a first-order autoregressive (AR(1)) stationary Gaussian process with a positive correlation at unit lag. Does there exist some formal statistical test for red noise process?

One way I can think of is to firstly fit an AR(1) model to the process, then perform white noise test on the model residuals to see whether the residuals follow a white noise process. If yes, the original process can be viewed as a red noise process...

Welcome any ideas and comments.

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Just interested, where can I read about why red noise is the same as AR(1) stationary Gaussian process with a positive correlation at unit lag? –  Dmitry Laptev Oct 12 '12 at 14:42
    
@DmitryLaptev Please refer to: H. von Storch and F. W. Zwiers (1999), Statistical Analysis in Climate Research, Cambridge, England: Cambridge University Press. –  Elaine Oct 13 '12 at 9:25

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