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I want to claim the time series in figure 1 is more stationary than figure 2. However, [Augmented Dickey-Fuller test asserts http://en.wikipedia.org/wiki/Augmented_Dickey%E2%80%93Fuller_test asserts they are both stationary, at least at 90% confidence. But intuition, the distribution of figure 2 seems to be changing over time. Is there any statistic to measure the degree of stationary of a time series? Or any other way to support (or even refute) my claim? Thanks in advance.

Time series 1

Time series 2

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My understanding is that time-frequency methods are useful here. See if this helps: Measuring the degree of non-stationarity by using the Wigner-Ville spectrum

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