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I am a little confused about whether this graph shows stationary or non-stationary time series:

AC graph

PAC graph

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4 Answers 4

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The autocorrelation graphs show nothing about stationarity. In fact, they rely on the assumption that your time series is covariance stationary (otherwise you wouldn't have a single autocorrelation coefficient).

A time series can be non-stationary for two reasons: it follows a deterministic trend (which would make its mean non-constant) or it has a unit root (ie. it follows a random walk). For the first case looking at a graph is probably the easiest way to tell is probably by plotting or to think of a model which would justify a particular trend. For the second, the Augmented Dickey Fuller test is the easiest way to approach it.

PS:I know this answer comes quite late but I was having similar issues and this might help someone else.

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Impossible to make a determination as there my be level shifts ( causing npn-nob-staionarity ) , time trends (causing non-stationarity ) , chnages in paramters over time ( causing non-stationarity ) , changes in the variance of the errors over time ( causing no,-statioanarity ) etc.... Please post you data as that will disclose whether or not your data is stationary or non-stationary.

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Looking at the pictures it seems to be stationary, nevertheless I suggest you to run Dickey–Fuller or Augmented Dickey–Fuller test in order to have a definitive answer.

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    $\begingroup$ Could you explain what it is about the graphics that suggests stationarity? It looks like one ought to draw the opposite conclusion, especially from the consistent trend in the acf and the extraordinarily high partial autocorrelation at lag 40. $\endgroup$
    – whuber
    Commented Feb 22, 2018 at 19:27
  • $\begingroup$ Graphs only can give you intuitions or clues, there is no way other than statistical tests to evaluate it. $\endgroup$
    – Nemo4t
    Commented Feb 28, 2018 at 9:51
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    $\begingroup$ The graph seems to a trend down or possibly the start of a cyclic pattern. Nothing to indicate stationarity. $\endgroup$ Commented Mar 10, 2018 at 3:42
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The structure of this serie is that of linear trend and circle. A single straight line can run through the centre of the series to the end. Implying that it has a single mean through the whole length of time and therefore stationary. This circles sorrounding the mean imply that the signal has stationary trend and circles

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    $\begingroup$ As it’s currently written, your answer is unclear. Please edit to add additional details that will help others understand how this addresses the question asked. You can find more information on how to write good answers in the help center. $\endgroup$
    – Community Bot
    Commented Oct 1, 2023 at 18:42
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    $\begingroup$ This answer seems not to recognize that the plots in the question are an autocorrelation function (ACF) and partial autocorrelation function (PACF). In that context this answer makes no sense. $\endgroup$
    – whuber
    Commented Oct 1, 2023 at 19:36

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