A quantification of variation for a time series, aggregated over various time intervals.

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This question has been bugging me for quite a while, and I did not manage to find an answer online.



I have a time series of integer flow data (a flow of cyclists, per second, average 0.3 bicycles/s), and I want to report a mean and a (sample) standard deviation of the flow. That is straightforward. Now, I want to calculate the the same, but for the flow over a bigger time interval, for example 10 seconds or a minute. I was expecting to calculate the new standard deviation with the formula $ sigma_T
=sigma_1sec/sqrtT$ with T the interval size. In the graph that should be visible when clicking the link, I show the difference. My goal is to find a measure of variance that is independent of the interval size.



I suspect that this might have something to do with auto correlation of the flow, but I don't know how to check or compensate for that. Can someone help me understand the difference between the two lines in the graph, and which formula I should use?



Graph of expected relationship and real calculated relationship between standard deviation and interval size




standard-deviation time-series




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    up vote
    0
    down vote

    favorite












    This question has been bugging me for quite a while, and I did not manage to find an answer online.



    I have a time series of integer flow data (a flow of cyclists, per second, average 0.3 bicycles/s), and I want to report a mean and a (sample) standard deviation of the flow. That is straightforward. Now, I want to calculate the the same, but for the flow over a bigger time interval, for example 10 seconds or a minute. I was expecting to calculate the new standard deviation with the formula $ sigma_T
    =sigma_1sec/sqrtT$ with T the interval size. In the graph that should be visible when clicking the link, I show the difference. My goal is to find a measure of variance that is independent of the interval size.



    I suspect that this might have something to do with auto correlation of the flow, but I don't know how to check or compensate for that. Can someone help me understand the difference between the two lines in the graph, and which formula I should use?



    Graph of expected relationship and real calculated relationship between standard deviation and interval size




    standard-deviation time-series




    share|cite|improve this question
























      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      This question has been bugging me for quite a while, and I did not manage to find an answer online.



      I have a time series of integer flow data (a flow of cyclists, per second, average 0.3 bicycles/s), and I want to report a mean and a (sample) standard deviation of the flow. That is straightforward. Now, I want to calculate the the same, but for the flow over a bigger time interval, for example 10 seconds or a minute. I was expecting to calculate the new standard deviation with the formula $ sigma_T
      =sigma_1sec/sqrtT$ with T the interval size. In the graph that should be visible when clicking the link, I show the difference. My goal is to find a measure of variance that is independent of the interval size.



      I suspect that this might have something to do with auto correlation of the flow, but I don't know how to check or compensate for that. Can someone help me understand the difference between the two lines in the graph, and which formula I should use?



      Graph of expected relationship and real calculated relationship between standard deviation and interval size




      standard-deviation time-series




      share|cite|improve this question














      This question has been bugging me for quite a while, and I did not manage to find an answer online.



      I have a time series of integer flow data (a flow of cyclists, per second, average 0.3 bicycles/s), and I want to report a mean and a (sample) standard deviation of the flow. That is straightforward. Now, I want to calculate the the same, but for the flow over a bigger time interval, for example 10 seconds or a minute. I was expecting to calculate the new standard deviation with the formula $ sigma_T
      =sigma_1sec/sqrtT$ with T the interval size. In the graph that should be visible when clicking the link, I show the difference. My goal is to find a measure of variance that is independent of the interval size.



      I suspect that this might have something to do with auto correlation of the flow, but I don't know how to check or compensate for that. Can someone help me understand the difference between the two lines in the graph, and which formula I should use?



      Graph of expected relationship and real calculated relationship between standard deviation and interval size





      standard-deviation time-series





      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Aug 23 at 16:32









      Jendrik Stelzner

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      asked Aug 20 at 8:46









      Cyclist

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