Additive vs Multiplicative model in Time Series Data The Next CEO of Stack Overflow2019 Community Moderator ElectionR lm(log(y)~x,data) models and predict, need to remember the exp. R2 differencesIdentifying trend and seasonality of time series dataTime Series prediction using LSTMs: Importance of making time series stationaryScaling multiple time series dataTime series finance -Correlation between a sector and MSCI ACWI returnsTime series forecasting using multiple time series as training dataAbout applying time series forecasting to problems better suited for reinforcement learning, like toy example “Jack's car rental”Estimation of hidden Markov Model from multiple time seriesAnalysis of Time Series data

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Additive vs Multiplicative model in Time Series Data



The Next CEO of Stack Overflow
2019 Community Moderator ElectionR lm(log(y)~x,data) models and predict, need to remember the exp. R2 differencesIdentifying trend and seasonality of time series dataTime Series prediction using LSTMs: Importance of making time series stationaryScaling multiple time series dataTime series finance -Correlation between a sector and MSCI ACWI returnsTime series forecasting using multiple time series as training dataAbout applying time series forecasting to problems better suited for reinforcement learning, like toy example “Jack's car rental”Estimation of hidden Markov Model from multiple time seriesAnalysis of Time Series data










2












$begingroup$


enter image description here
The above time series plot is a daily closing stock index of a company. I want to know which model between additive and multiplicative best suits the above data. I know what the two models are, but i haven't been able to figure out the correct model for the above data. Also, is there any way other than simple visualisation which can help me decide the correct model?










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    2












    $begingroup$


    enter image description here
    The above time series plot is a daily closing stock index of a company. I want to know which model between additive and multiplicative best suits the above data. I know what the two models are, but i haven't been able to figure out the correct model for the above data. Also, is there any way other than simple visualisation which can help me decide the correct model?










    share|improve this question











    $endgroup$




    bumped to the homepage by Community 40 mins ago


    This question has answers that may be good or bad; the system has marked it active so that they can be reviewed.

















      2












      2








      2





      $begingroup$


      enter image description here
      The above time series plot is a daily closing stock index of a company. I want to know which model between additive and multiplicative best suits the above data. I know what the two models are, but i haven't been able to figure out the correct model for the above data. Also, is there any way other than simple visualisation which can help me decide the correct model?










      share|improve this question











      $endgroup$




      enter image description here
      The above time series plot is a daily closing stock index of a company. I want to know which model between additive and multiplicative best suits the above data. I know what the two models are, but i haven't been able to figure out the correct model for the above data. Also, is there any way other than simple visualisation which can help me decide the correct model?







      r time-series forecast data-analysis






      share|improve this question















      share|improve this question













      share|improve this question




      share|improve this question








      edited Feb 25 at 8:27







      Jor_El

















      asked Feb 22 at 17:32









      Jor_ElJor_El

      312




      312





      bumped to the homepage by Community 40 mins ago


      This question has answers that may be good or bad; the system has marked it active so that they can be reviewed.







      bumped to the homepage by Community 40 mins ago


      This question has answers that may be good or bad; the system has marked it active so that they can be reviewed.






















          2 Answers
          2






          active

          oldest

          votes


















          0












          $begingroup$

          1. Calculate one day returns.

          2. Plot histogram of daily returns.

          3. Calculate $log(fracprice_i+1price_i)$.

          4. Plot histogram of above logarithm.

          5. If second plot is more likely to be normally distributed then choose multiplicative model. Else, choose additive model.

          You can also perform statistical test for normal distribution and check, which one has higher p-value.



          Explanation:



          Additive model is used when the variance of the time series doesn't change over different values of the time series.



          On the other hand, if the variance is higher when the time series is higher then it often means we should use a multiplicative models.



          Additive model:



          $return_i = price_i-price_i-1=trend_i-trend_i-1+seasonal_i-seasonal_i-1+error_i-error_i-1$



          If error's increments have normal iid distributions then $return_i$ has also a normal distribution with constant variance over time.



          Multiplicative model:



          If log of the time series is an additive model then the original time series is a multiplicative model, because:



          $log(price_i)=log(trend_i cdot seasonal_i cdot error_i)=log(trend_i)+log(seasonal_i)+log(error_i)$



          So the return of logarithms:



          $log(price_i)-log(price_i-1)= log(fracprice_iprice_i-1)$



          must be normal with constant variance.






          share|improve this answer











          $endgroup$












          • $begingroup$
            Could you please explain the logic behind the algorithm?
            $endgroup$
            – Jor_El
            Feb 25 at 16:03










          • $begingroup$
            I've added some explanations in my post above.
            $endgroup$
            – Michał Kardach
            Feb 25 at 17:39


















          0












          $begingroup$


          I want to know which model between additive and multiplicative best suits the above data.




          It is hard to tell just by looking at it.



          A multiplicative decomposition roughly corresponds to an additive decomposition of the logarithms.
          The additive decomposition is the most appropriate if the magnitude of the seasonal fluctuations, or the variation around the trend-cycle, does not vary with the level of the time series. When the variation in the seasonal pattern, or the variation around the trend-cycle, appears to be proportional to the level of the time series, then a multiplicative decomposition is more appropriate. Multiplicative decompositions are common with economic time series.



          An alternative to using a multiplicative decomposition is to first transform the data until the variation in the series appears to be stable over time, then use an additive decomposition. So, basically you need to check for heteroskedasticity, eliminate that if it is there by transformations and do an additive decomposition of the transformed series.



          Most common transformations are log or square root of the series and are special cases of Power transform.



          Reference:
          Forecasting principles and practice






          share|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









            0












            $begingroup$

            1. Calculate one day returns.

            2. Plot histogram of daily returns.

            3. Calculate $log(fracprice_i+1price_i)$.

            4. Plot histogram of above logarithm.

            5. If second plot is more likely to be normally distributed then choose multiplicative model. Else, choose additive model.

            You can also perform statistical test for normal distribution and check, which one has higher p-value.



            Explanation:



            Additive model is used when the variance of the time series doesn't change over different values of the time series.



            On the other hand, if the variance is higher when the time series is higher then it often means we should use a multiplicative models.



            Additive model:



            $return_i = price_i-price_i-1=trend_i-trend_i-1+seasonal_i-seasonal_i-1+error_i-error_i-1$



            If error's increments have normal iid distributions then $return_i$ has also a normal distribution with constant variance over time.



            Multiplicative model:



            If log of the time series is an additive model then the original time series is a multiplicative model, because:



            $log(price_i)=log(trend_i cdot seasonal_i cdot error_i)=log(trend_i)+log(seasonal_i)+log(error_i)$



            So the return of logarithms:



            $log(price_i)-log(price_i-1)= log(fracprice_iprice_i-1)$



            must be normal with constant variance.






            share|improve this answer











            $endgroup$












            • $begingroup$
              Could you please explain the logic behind the algorithm?
              $endgroup$
              – Jor_El
              Feb 25 at 16:03










            • $begingroup$
              I've added some explanations in my post above.
              $endgroup$
              – Michał Kardach
              Feb 25 at 17:39















            0












            $begingroup$

            1. Calculate one day returns.

            2. Plot histogram of daily returns.

            3. Calculate $log(fracprice_i+1price_i)$.

            4. Plot histogram of above logarithm.

            5. If second plot is more likely to be normally distributed then choose multiplicative model. Else, choose additive model.

            You can also perform statistical test for normal distribution and check, which one has higher p-value.



            Explanation:



            Additive model is used when the variance of the time series doesn't change over different values of the time series.



            On the other hand, if the variance is higher when the time series is higher then it often means we should use a multiplicative models.



            Additive model:



            $return_i = price_i-price_i-1=trend_i-trend_i-1+seasonal_i-seasonal_i-1+error_i-error_i-1$



            If error's increments have normal iid distributions then $return_i$ has also a normal distribution with constant variance over time.



            Multiplicative model:



            If log of the time series is an additive model then the original time series is a multiplicative model, because:



            $log(price_i)=log(trend_i cdot seasonal_i cdot error_i)=log(trend_i)+log(seasonal_i)+log(error_i)$



            So the return of logarithms:



            $log(price_i)-log(price_i-1)= log(fracprice_iprice_i-1)$



            must be normal with constant variance.






            share|improve this answer











            $endgroup$












            • $begingroup$
              Could you please explain the logic behind the algorithm?
              $endgroup$
              – Jor_El
              Feb 25 at 16:03










            • $begingroup$
              I've added some explanations in my post above.
              $endgroup$
              – Michał Kardach
              Feb 25 at 17:39













            0












            0








            0





            $begingroup$

            1. Calculate one day returns.

            2. Plot histogram of daily returns.

            3. Calculate $log(fracprice_i+1price_i)$.

            4. Plot histogram of above logarithm.

            5. If second plot is more likely to be normally distributed then choose multiplicative model. Else, choose additive model.

            You can also perform statistical test for normal distribution and check, which one has higher p-value.



            Explanation:



            Additive model is used when the variance of the time series doesn't change over different values of the time series.



            On the other hand, if the variance is higher when the time series is higher then it often means we should use a multiplicative models.



            Additive model:



            $return_i = price_i-price_i-1=trend_i-trend_i-1+seasonal_i-seasonal_i-1+error_i-error_i-1$



            If error's increments have normal iid distributions then $return_i$ has also a normal distribution with constant variance over time.



            Multiplicative model:



            If log of the time series is an additive model then the original time series is a multiplicative model, because:



            $log(price_i)=log(trend_i cdot seasonal_i cdot error_i)=log(trend_i)+log(seasonal_i)+log(error_i)$



            So the return of logarithms:



            $log(price_i)-log(price_i-1)= log(fracprice_iprice_i-1)$



            must be normal with constant variance.






            share|improve this answer











            $endgroup$



            1. Calculate one day returns.

            2. Plot histogram of daily returns.

            3. Calculate $log(fracprice_i+1price_i)$.

            4. Plot histogram of above logarithm.

            5. If second plot is more likely to be normally distributed then choose multiplicative model. Else, choose additive model.

            You can also perform statistical test for normal distribution and check, which one has higher p-value.



            Explanation:



            Additive model is used when the variance of the time series doesn't change over different values of the time series.



            On the other hand, if the variance is higher when the time series is higher then it often means we should use a multiplicative models.



            Additive model:



            $return_i = price_i-price_i-1=trend_i-trend_i-1+seasonal_i-seasonal_i-1+error_i-error_i-1$



            If error's increments have normal iid distributions then $return_i$ has also a normal distribution with constant variance over time.



            Multiplicative model:



            If log of the time series is an additive model then the original time series is a multiplicative model, because:



            $log(price_i)=log(trend_i cdot seasonal_i cdot error_i)=log(trend_i)+log(seasonal_i)+log(error_i)$



            So the return of logarithms:



            $log(price_i)-log(price_i-1)= log(fracprice_iprice_i-1)$



            must be normal with constant variance.







            share|improve this answer














            share|improve this answer



            share|improve this answer








            edited Feb 25 at 20:12

























            answered Feb 25 at 10:39









            Michał KardachMichał Kardach

            716




            716











            • $begingroup$
              Could you please explain the logic behind the algorithm?
              $endgroup$
              – Jor_El
              Feb 25 at 16:03










            • $begingroup$
              I've added some explanations in my post above.
              $endgroup$
              – Michał Kardach
              Feb 25 at 17:39
















            • $begingroup$
              Could you please explain the logic behind the algorithm?
              $endgroup$
              – Jor_El
              Feb 25 at 16:03










            • $begingroup$
              I've added some explanations in my post above.
              $endgroup$
              – Michał Kardach
              Feb 25 at 17:39















            $begingroup$
            Could you please explain the logic behind the algorithm?
            $endgroup$
            – Jor_El
            Feb 25 at 16:03




            $begingroup$
            Could you please explain the logic behind the algorithm?
            $endgroup$
            – Jor_El
            Feb 25 at 16:03












            $begingroup$
            I've added some explanations in my post above.
            $endgroup$
            – Michał Kardach
            Feb 25 at 17:39




            $begingroup$
            I've added some explanations in my post above.
            $endgroup$
            – Michał Kardach
            Feb 25 at 17:39











            0












            $begingroup$


            I want to know which model between additive and multiplicative best suits the above data.




            It is hard to tell just by looking at it.



            A multiplicative decomposition roughly corresponds to an additive decomposition of the logarithms.
            The additive decomposition is the most appropriate if the magnitude of the seasonal fluctuations, or the variation around the trend-cycle, does not vary with the level of the time series. When the variation in the seasonal pattern, or the variation around the trend-cycle, appears to be proportional to the level of the time series, then a multiplicative decomposition is more appropriate. Multiplicative decompositions are common with economic time series.



            An alternative to using a multiplicative decomposition is to first transform the data until the variation in the series appears to be stable over time, then use an additive decomposition. So, basically you need to check for heteroskedasticity, eliminate that if it is there by transformations and do an additive decomposition of the transformed series.



            Most common transformations are log or square root of the series and are special cases of Power transform.



            Reference:
            Forecasting principles and practice






            share|improve this answer











            $endgroup$

















              0












              $begingroup$


              I want to know which model between additive and multiplicative best suits the above data.




              It is hard to tell just by looking at it.



              A multiplicative decomposition roughly corresponds to an additive decomposition of the logarithms.
              The additive decomposition is the most appropriate if the magnitude of the seasonal fluctuations, or the variation around the trend-cycle, does not vary with the level of the time series. When the variation in the seasonal pattern, or the variation around the trend-cycle, appears to be proportional to the level of the time series, then a multiplicative decomposition is more appropriate. Multiplicative decompositions are common with economic time series.



              An alternative to using a multiplicative decomposition is to first transform the data until the variation in the series appears to be stable over time, then use an additive decomposition. So, basically you need to check for heteroskedasticity, eliminate that if it is there by transformations and do an additive decomposition of the transformed series.



              Most common transformations are log or square root of the series and are special cases of Power transform.



              Reference:
              Forecasting principles and practice






              share|improve this answer











              $endgroup$















                0












                0








                0





                $begingroup$


                I want to know which model between additive and multiplicative best suits the above data.




                It is hard to tell just by looking at it.



                A multiplicative decomposition roughly corresponds to an additive decomposition of the logarithms.
                The additive decomposition is the most appropriate if the magnitude of the seasonal fluctuations, or the variation around the trend-cycle, does not vary with the level of the time series. When the variation in the seasonal pattern, or the variation around the trend-cycle, appears to be proportional to the level of the time series, then a multiplicative decomposition is more appropriate. Multiplicative decompositions are common with economic time series.



                An alternative to using a multiplicative decomposition is to first transform the data until the variation in the series appears to be stable over time, then use an additive decomposition. So, basically you need to check for heteroskedasticity, eliminate that if it is there by transformations and do an additive decomposition of the transformed series.



                Most common transformations are log or square root of the series and are special cases of Power transform.



                Reference:
                Forecasting principles and practice






                share|improve this answer











                $endgroup$




                I want to know which model between additive and multiplicative best suits the above data.




                It is hard to tell just by looking at it.



                A multiplicative decomposition roughly corresponds to an additive decomposition of the logarithms.
                The additive decomposition is the most appropriate if the magnitude of the seasonal fluctuations, or the variation around the trend-cycle, does not vary with the level of the time series. When the variation in the seasonal pattern, or the variation around the trend-cycle, appears to be proportional to the level of the time series, then a multiplicative decomposition is more appropriate. Multiplicative decompositions are common with economic time series.



                An alternative to using a multiplicative decomposition is to first transform the data until the variation in the series appears to be stable over time, then use an additive decomposition. So, basically you need to check for heteroskedasticity, eliminate that if it is there by transformations and do an additive decomposition of the transformed series.



                Most common transformations are log or square root of the series and are special cases of Power transform.



                Reference:
                Forecasting principles and practice







                share|improve this answer














                share|improve this answer



                share|improve this answer








                edited Feb 26 at 19:15

























                answered Feb 25 at 16:23









                naivenaive

                2766




                2766



























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                    ValueError: Expected n_neighbors <= n_samples, but n_samples = 1, n_neighbors = 6 (SMOTE) The 2019 Stack Overflow Developer Survey Results Are InCan SMOTE be applied over sequence of words (sentences)?ValueError when doing validation with random forestsSMOTE and multi class oversamplingLogic behind SMOTE-NC?ValueError: Error when checking target: expected dense_1 to have shape (7,) but got array with shape (1,)SmoteBoost: Should SMOTE be ran individually for each iteration/tree in the boosting?solving multi-class imbalance classification using smote and OSSUsing SMOTE for Synthetic Data generation to improve performance on unbalanced dataproblem of entry format for a simple model in KerasSVM SMOTE fit_resample() function runs forever with no result