Justifying the trend component in a time series?

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I am working on a time series forecasting problem ,I used Dickey–Fuller test to check the stationary of the time series and the p value is 0.000835 , hense I rejected the null hypothesis and assumed that it's a stationary time series.



I decomposed the time series and the trend component does not have any particular pattern.plot-enter image description here



I want to ask how can we justify that a time series has any particular trend, Is this decomposition enough to ensure and guarantee that this time series has no trend ?



Plot of rolling mean-



enter image description here



Plot of rolling variance-



enter image description here










share|cite|improve this question











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    2












    $begingroup$


    I am working on a time series forecasting problem ,I used Dickey–Fuller test to check the stationary of the time series and the p value is 0.000835 , hense I rejected the null hypothesis and assumed that it's a stationary time series.



    I decomposed the time series and the trend component does not have any particular pattern.plot-enter image description here



    I want to ask how can we justify that a time series has any particular trend, Is this decomposition enough to ensure and guarantee that this time series has no trend ?



    Plot of rolling mean-



    enter image description here



    Plot of rolling variance-



    enter image description here










    share|cite|improve this question











    $endgroup$














      2












      2








      2





      $begingroup$


      I am working on a time series forecasting problem ,I used Dickey–Fuller test to check the stationary of the time series and the p value is 0.000835 , hense I rejected the null hypothesis and assumed that it's a stationary time series.



      I decomposed the time series and the trend component does not have any particular pattern.plot-enter image description here



      I want to ask how can we justify that a time series has any particular trend, Is this decomposition enough to ensure and guarantee that this time series has no trend ?



      Plot of rolling mean-



      enter image description here



      Plot of rolling variance-



      enter image description here










      share|cite|improve this question











      $endgroup$




      I am working on a time series forecasting problem ,I used Dickey–Fuller test to check the stationary of the time series and the p value is 0.000835 , hense I rejected the null hypothesis and assumed that it's a stationary time series.



      I decomposed the time series and the trend component does not have any particular pattern.plot-enter image description here



      I want to ask how can we justify that a time series has any particular trend, Is this decomposition enough to ensure and guarantee that this time series has no trend ?



      Plot of rolling mean-



      enter image description here



      Plot of rolling variance-



      enter image description here







      time-series statistical-significance






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Mar 16 at 7:30







      A.kumar

















      asked Mar 14 at 10:01









      A.kumarA.kumar

      354




      354




















          2 Answers
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          $begingroup$

          The Augmented Dickey–Fuller test is UNIT ROOT test - NOT a stationarity test. The null-hypothesis on this test is that the data have been generated by a restricted AR model containing a unit-root. Rejecting this hypothesis DOES NOT mean the series is stationary. It just means that there is enough evidence to allow you rejecting the hypothesis of a very specific form of NON-stationarity (i.e. unit root). Evidence is assessed contrastively i.e. v.s. an unrestricted AR model. Rejecting the hypothesis that an animal is a chicken with an alternative being a pig doesn't mean the animal might not be a horse! The examined animal might contrastively not look like a chicken (e.g. because it has 4 legs) but that doesn't make it a pig.



          Now look at your decomposition. You could see with a bare eye data don't look stationary. Trend as well as variance change with time. The decomposition does not support your conclusion. It supports the opposite view. There both parametric as well as non-parametric ways to check changes in the trend of the series. For example (see following poster about Detecting Changes in the Mean ):



          test






          share|cite|improve this answer











          $endgroup$












          • $begingroup$
            Thanks for the clarification regarding the Dickey–Fuller test.I have added the plots of rolling mean and variance of the time series with a window of 10.It's observed that the variance is almost constant with some fluctuations while the mean has many change points. I am using R package changepoint to detect the change points ,but I want to ask is there any method to forecast the future change points/ give a probability to the future points that they may be change points.
            $endgroup$
            – A.kumar
            Mar 16 at 7:42



















          2












          $begingroup$

          visually there is an apparent autoregressive process and a change in model error variance .. thus non-stationarity is the call.






          share|cite|improve this answer









          $endgroup$













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            2 Answers
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            active

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            2 Answers
            2






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            3












            $begingroup$

            The Augmented Dickey–Fuller test is UNIT ROOT test - NOT a stationarity test. The null-hypothesis on this test is that the data have been generated by a restricted AR model containing a unit-root. Rejecting this hypothesis DOES NOT mean the series is stationary. It just means that there is enough evidence to allow you rejecting the hypothesis of a very specific form of NON-stationarity (i.e. unit root). Evidence is assessed contrastively i.e. v.s. an unrestricted AR model. Rejecting the hypothesis that an animal is a chicken with an alternative being a pig doesn't mean the animal might not be a horse! The examined animal might contrastively not look like a chicken (e.g. because it has 4 legs) but that doesn't make it a pig.



            Now look at your decomposition. You could see with a bare eye data don't look stationary. Trend as well as variance change with time. The decomposition does not support your conclusion. It supports the opposite view. There both parametric as well as non-parametric ways to check changes in the trend of the series. For example (see following poster about Detecting Changes in the Mean ):



            test






            share|cite|improve this answer











            $endgroup$












            • $begingroup$
              Thanks for the clarification regarding the Dickey–Fuller test.I have added the plots of rolling mean and variance of the time series with a window of 10.It's observed that the variance is almost constant with some fluctuations while the mean has many change points. I am using R package changepoint to detect the change points ,but I want to ask is there any method to forecast the future change points/ give a probability to the future points that they may be change points.
              $endgroup$
              – A.kumar
              Mar 16 at 7:42
















            3












            $begingroup$

            The Augmented Dickey–Fuller test is UNIT ROOT test - NOT a stationarity test. The null-hypothesis on this test is that the data have been generated by a restricted AR model containing a unit-root. Rejecting this hypothesis DOES NOT mean the series is stationary. It just means that there is enough evidence to allow you rejecting the hypothesis of a very specific form of NON-stationarity (i.e. unit root). Evidence is assessed contrastively i.e. v.s. an unrestricted AR model. Rejecting the hypothesis that an animal is a chicken with an alternative being a pig doesn't mean the animal might not be a horse! The examined animal might contrastively not look like a chicken (e.g. because it has 4 legs) but that doesn't make it a pig.



            Now look at your decomposition. You could see with a bare eye data don't look stationary. Trend as well as variance change with time. The decomposition does not support your conclusion. It supports the opposite view. There both parametric as well as non-parametric ways to check changes in the trend of the series. For example (see following poster about Detecting Changes in the Mean ):



            test






            share|cite|improve this answer











            $endgroup$












            • $begingroup$
              Thanks for the clarification regarding the Dickey–Fuller test.I have added the plots of rolling mean and variance of the time series with a window of 10.It's observed that the variance is almost constant with some fluctuations while the mean has many change points. I am using R package changepoint to detect the change points ,but I want to ask is there any method to forecast the future change points/ give a probability to the future points that they may be change points.
              $endgroup$
              – A.kumar
              Mar 16 at 7:42














            3












            3








            3





            $begingroup$

            The Augmented Dickey–Fuller test is UNIT ROOT test - NOT a stationarity test. The null-hypothesis on this test is that the data have been generated by a restricted AR model containing a unit-root. Rejecting this hypothesis DOES NOT mean the series is stationary. It just means that there is enough evidence to allow you rejecting the hypothesis of a very specific form of NON-stationarity (i.e. unit root). Evidence is assessed contrastively i.e. v.s. an unrestricted AR model. Rejecting the hypothesis that an animal is a chicken with an alternative being a pig doesn't mean the animal might not be a horse! The examined animal might contrastively not look like a chicken (e.g. because it has 4 legs) but that doesn't make it a pig.



            Now look at your decomposition. You could see with a bare eye data don't look stationary. Trend as well as variance change with time. The decomposition does not support your conclusion. It supports the opposite view. There both parametric as well as non-parametric ways to check changes in the trend of the series. For example (see following poster about Detecting Changes in the Mean ):



            test






            share|cite|improve this answer











            $endgroup$



            The Augmented Dickey–Fuller test is UNIT ROOT test - NOT a stationarity test. The null-hypothesis on this test is that the data have been generated by a restricted AR model containing a unit-root. Rejecting this hypothesis DOES NOT mean the series is stationary. It just means that there is enough evidence to allow you rejecting the hypothesis of a very specific form of NON-stationarity (i.e. unit root). Evidence is assessed contrastively i.e. v.s. an unrestricted AR model. Rejecting the hypothesis that an animal is a chicken with an alternative being a pig doesn't mean the animal might not be a horse! The examined animal might contrastively not look like a chicken (e.g. because it has 4 legs) but that doesn't make it a pig.



            Now look at your decomposition. You could see with a bare eye data don't look stationary. Trend as well as variance change with time. The decomposition does not support your conclusion. It supports the opposite view. There both parametric as well as non-parametric ways to check changes in the trend of the series. For example (see following poster about Detecting Changes in the Mean ):



            test







            share|cite|improve this answer














            share|cite|improve this answer



            share|cite|improve this answer








            edited Mar 14 at 13:20

























            answered Mar 14 at 13:06









            StatsStats

            728210




            728210











            • $begingroup$
              Thanks for the clarification regarding the Dickey–Fuller test.I have added the plots of rolling mean and variance of the time series with a window of 10.It's observed that the variance is almost constant with some fluctuations while the mean has many change points. I am using R package changepoint to detect the change points ,but I want to ask is there any method to forecast the future change points/ give a probability to the future points that they may be change points.
              $endgroup$
              – A.kumar
              Mar 16 at 7:42

















            • $begingroup$
              Thanks for the clarification regarding the Dickey–Fuller test.I have added the plots of rolling mean and variance of the time series with a window of 10.It's observed that the variance is almost constant with some fluctuations while the mean has many change points. I am using R package changepoint to detect the change points ,but I want to ask is there any method to forecast the future change points/ give a probability to the future points that they may be change points.
              $endgroup$
              – A.kumar
              Mar 16 at 7:42
















            $begingroup$
            Thanks for the clarification regarding the Dickey–Fuller test.I have added the plots of rolling mean and variance of the time series with a window of 10.It's observed that the variance is almost constant with some fluctuations while the mean has many change points. I am using R package changepoint to detect the change points ,but I want to ask is there any method to forecast the future change points/ give a probability to the future points that they may be change points.
            $endgroup$
            – A.kumar
            Mar 16 at 7:42





            $begingroup$
            Thanks for the clarification regarding the Dickey–Fuller test.I have added the plots of rolling mean and variance of the time series with a window of 10.It's observed that the variance is almost constant with some fluctuations while the mean has many change points. I am using R package changepoint to detect the change points ,but I want to ask is there any method to forecast the future change points/ give a probability to the future points that they may be change points.
            $endgroup$
            – A.kumar
            Mar 16 at 7:42














            2












            $begingroup$

            visually there is an apparent autoregressive process and a change in model error variance .. thus non-stationarity is the call.






            share|cite|improve this answer









            $endgroup$

















              2












              $begingroup$

              visually there is an apparent autoregressive process and a change in model error variance .. thus non-stationarity is the call.






              share|cite|improve this answer









              $endgroup$















                2












                2








                2





                $begingroup$

                visually there is an apparent autoregressive process and a change in model error variance .. thus non-stationarity is the call.






                share|cite|improve this answer









                $endgroup$



                visually there is an apparent autoregressive process and a change in model error variance .. thus non-stationarity is the call.







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered Mar 14 at 13:14









                IrishStatIrishStat

                21.4k42342




                21.4k42342



























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