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Let $x[n]$ be some time series in 1D or $x[m,n]$ in 2D, of length $N$ (resp. $N^2$) How can I assess whether it is stationary? At least in the weak sense. I can check whether the stdev remains constant, but this is only a necessary condition.

Kyle.
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yoki
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  • http://lojze.lugos.si/~darja/software/r/library/tseries/html/adf.test.html The Augmented Dickey Fuller is a test that is often used. here is the R package for the test. – Eric Peterson Feb 26 '14 at 16:11
  • I have tried to use adftest on my own series of an antipersistent fractional Brownian motion (i.e., H<0.5) and the ADFtest rejected the null hypotheses, i.e. identified it as stationary. While it is short-range dependent -- it is definitely not stationary. – yoki Feb 26 '14 at 16:39
  • if it isn't stationary, have you considered first differencing the time series and checking again for stationarity? – Eric Peterson Feb 26 '14 at 16:55
  • I am only doing this by simulation; with my real x[n], I do not know whether it is stationary or not. Let us say I am given (unknowingly) an fBm with H<0.5, a nonstationary series, then the test will fail... – yoki Feb 26 '14 at 16:59

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