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If the square of a time series is stationary, is the original time series stationary?


Downsampling stationary time series data, effect on varianceAutocorrelation vs Non-stationaryForecasting Time Series: Stationary vs Non-StationaryCross-correlation of two non-stationary time series?Compare stationary time seriesDetermining if a time series is covariance stationary or a random walkMean Square Convergence of a Linear Process Defined in Terms of a Stationary Time SeriesMaking a time series stationary by demeaningStationary vs. Trend-Stationary Time Series: Auto.Arima difference parameterDetect stationary section in an overall non-stationary time series






.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;








2












$begingroup$


I found a solution that stated that if the square of a time series is stationary, so is the original time series, and vice-versa.
However I don't seem able to prove it, anyone has an idea if this is true, and if it is how to derive it?










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$endgroup$











  • $begingroup$
    Have you tried starting from the definition of stationarity?
    $endgroup$
    – Matt P
    4 hours ago

















2












$begingroup$


I found a solution that stated that if the square of a time series is stationary, so is the original time series, and vice-versa.
However I don't seem able to prove it, anyone has an idea if this is true, and if it is how to derive it?










share|cite|improve this question









$endgroup$











  • $begingroup$
    Have you tried starting from the definition of stationarity?
    $endgroup$
    – Matt P
    4 hours ago













2












2








2





$begingroup$


I found a solution that stated that if the square of a time series is stationary, so is the original time series, and vice-versa.
However I don't seem able to prove it, anyone has an idea if this is true, and if it is how to derive it?










share|cite|improve this question









$endgroup$




I found a solution that stated that if the square of a time series is stationary, so is the original time series, and vice-versa.
However I don't seem able to prove it, anyone has an idea if this is true, and if it is how to derive it?







time-series self-study stationarity






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asked 5 hours ago









VictorVictor

586




586











  • $begingroup$
    Have you tried starting from the definition of stationarity?
    $endgroup$
    – Matt P
    4 hours ago
















  • $begingroup$
    Have you tried starting from the definition of stationarity?
    $endgroup$
    – Matt P
    4 hours ago















$begingroup$
Have you tried starting from the definition of stationarity?
$endgroup$
– Matt P
4 hours ago




$begingroup$
Have you tried starting from the definition of stationarity?
$endgroup$
– Matt P
4 hours ago










1 Answer
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$begingroup$

That conjecture is false. A simple counter-example is the deterministic time-series $X_t = (-1)^t$. This time series is not even mean stationary, but its square is strictly stationary.






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    $begingroup$

    That conjecture is false. A simple counter-example is the deterministic time-series $X_t = (-1)^t$. This time series is not even mean stationary, but its square is strictly stationary.






    share|cite|improve this answer









    $endgroup$

















      3












      $begingroup$

      That conjecture is false. A simple counter-example is the deterministic time-series $X_t = (-1)^t$. This time series is not even mean stationary, but its square is strictly stationary.






      share|cite|improve this answer









      $endgroup$















        3












        3








        3





        $begingroup$

        That conjecture is false. A simple counter-example is the deterministic time-series $X_t = (-1)^t$. This time series is not even mean stationary, but its square is strictly stationary.






        share|cite|improve this answer









        $endgroup$



        That conjecture is false. A simple counter-example is the deterministic time-series $X_t = (-1)^t$. This time series is not even mean stationary, but its square is strictly stationary.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered 4 hours ago









        BenBen

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