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Hypothesis Test

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  • #30681

    Fonseca
    Participant

    I am search of a hypothesis test that I can use to confirm if time series changed their means. Tha data I am working with show seasonality and dependence therefore I can´t use the parametric or non-parametric traditional alternatives for sample location (ANOVA, Kruskal-Wallis, etc.). Is there any special test for checking for mean shifting in time series ?
    Thanks,
    Marcelo

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    #80305

    Carl H
    Participant

    Marcelo,
    Your quiestion is timely as I will post a similar question today.
    In your time series (with seasonality and dependance or autocorrelation?), you may wish to try the following things:

    Compare current month to 12 months ago and do this for last 12 months.  This is 12 point data set of differences year over year with seasonality removed. If data is fairly normal, try a paired t-test with Ho = 0 or no change.
    If there is dependance/autocorrelation, try subgrouping by 3 month quarters or sampling less frequently (3+ months) if this gets you out of dependance/auto corrlation.  The you may be able to proceeed with a 2 sample t or non parametric test on two groups of sampled data.
     
    I may be way off and look forward to other ideas.
     
    Carl
     

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    #80312

    Mike Carnell
    Participant

    Marcelo,
    Have you tried setting it up in a control chart and run the tests for trends, runs, shifts and cycles?
    Good luck.

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    #80315

    Fonseca
    Participant

    Carl,
    Thank you for your quick answer.
    I intended to use Wilcoxon Paired Test since it is a non parametric procedure. What I really had forgotten is to remove the seasonality through differences method. I think I can do that using Minitab. Another problem is that I don´t have monthly data. I have daily data. I will have a larger sample but on the other side I will have to select the points to compare carefully.
    If you have other ideas I will be waiting, ok ?
    Marcelo
     
     

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    #80328

    Leung
    Participant

    You might want to try a technique called change point analysis. Wayne A. Taylor has posted a 19-page article on his website.
    Ben

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    #80329

    Fonseca
    Participant

    Thank you, Ben.
    I have just found the article (and a thousand of other references…) in Internet. I hope that it is applicable to my problem.
    Marcelo
     

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    #80330

    Erik L
    Participant

    Reducing the sampling frequency, ad hoc, should not be a technique that you apply to this scenario.  However, I do have some recommendations about how you could potentially do this through a more analytical technique.  The main problem with  reducing the sampling interval is that it could leave you wide open to significant shifts upstream that could impact the process. 
    If you are using control charts as a method to montior the process you could (and it sounds like you think you are being impacted by this) be violating one of the core assumptions that’s making the charts work effectively-namely independence.  the autocorrelation plot that I recommend below could provide you with insight into what lag coefficient needs to be used so that the data that you are looking at is providing you with independent pieces of information. 
    If you have Minitab I’d recommend that you go into Stat>time series>autocorrelation.  Once there, I’d input the column that has your data.  That graph that you will see will have, typically, 95% CIs around autoregressive factors for the data.  I’d also recommend that you look at the Partial Autocorrelation Function (PACF) as an add-on analysis.  If you see graphs for the ACF and PACF that have initially large spikes that tail off then you have some indication that you have an autoregressive process.  The ACF with large initial spikes that tails to 0 indicates a moving average process and a combination of the ACF and PACF with a pattern tailing to 0 indicates a combination of autoregressive factors and a process that is exhibiting moving average. 
    With the potential lag factors identified from ACF or PACF I’d next recommend that you go to ARIMA as a way of validating that this is the appropriate autoregressive factor.  The path within Minitab would be Stat>Timeseries>ARIMA.   Once you establish the autoregressive factor you would look to the resulting residuals as substantiation that you have the appropriate factor.  A NPP of the residuals and a IX-MR chart of the residuals should help with reinforcement.
    Another technique would be to go to Stat>timeseries>lag.  The rule of thumb is to choose the autocorrelation factor be that which has a correlation of 0.5.
    Once you establish the lag factor, now you have some insight into reduction of sampling frequency.
    Well, hope this has helped some.  Good luck with the analysis.
    Regards,
    Erik

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    #80331

    Fonseca
    Participant

    Erik,
    This would be the firts ARIMA model fitting that I would do in my life. Therefore there is a high probability to make mistakes (I have never found a friendly Time Series textbook. Just like you said to me: “go to Minitab and do this…”).
    No, I am not using Shewart charts in this process. Generally I follow the Control Charts assumptions very rigidly.
    From what I could understand, the main idea is to find the lag factor, ok ? After that, what should I do ? For example, if the lag factor is seven, I need to pick up samples from six to six or from five to five ?
    I should not forget the main question: how to confirm that there was a statiscally significant mean change ?
    I would appreciate very much if you could tell me some details of this procedure.
    Thanks,
    Marcelo 

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    #80348

    Erik L
    Participant

    Marcelo,
    If you are interested in testing whether time series (or autocorrelation) is impacting the process then a way to test that would be through the Autocorrelation Function.  If there is an initial spike, or subsequent spikes at 2,3, or 4, that trails off to 0 then this typically is interpreted as a process functioning under autocorrelation and would substantiate your hypothesis that there are factors influencing the data. 
    The lag factor that is identified through the analysis can help you dependent on how the data is structured that went into it.  Is it minutes, hours, months, or quarters?  If for arguments sake, it is in hours, and you substantiate a lag of 4 then that means that you should be sampling every 4 hours. 
    Unless you identify the absence, or presence, of autocorrelation any of the other hypothesis tests that you’ve mantioned are going to be suspect.  One of their key assumptions is also independence of the data.  All else considered your precedence of concern should go:  independence, homogeneity of variance, and normality.
    Has this helped any?
    Regards,
    Erik

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    #80394

    Fonseca
    Participant

    Erik,
    Would you mind to send me your email in order I could show you some results I got from Minitab ?
    Thank you very much,
    Marcelo
     
     

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    #80673

    Kevin C
    Participant

    You might consider fitting an ARIMA model to both peroids then testing for differences in the coefficients. This might provide a better insight into what is really changing.

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    #80688

    Erik L
    Participant

    Marcelo,
    I can be reached at [email protected]
     
    Regards,
    Erik

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    #80699

    Ovidiu Contras
    Participant

    Eric ,
    autocorrelation was not explained during the 6S training I had .I would be interested to learn more about it . Can you suggest some articles / books ?
    Thank you .

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    #80702

    Erik L
    Participant

    Ovidiu,
    Wow!  Nothing about autocorrelation!  That’s kind of scary when one of the assumptions that’s repeatedly mentioned through the battery of BB tools is independence.  No worries though.  You can always sharpen the saw on your own.  I guarantee you after really thinking about the issue of autocorrelation that you’ll look back on some of your past recommendations and the pucker factor will jump exponentially. 
    There is some introductory stuff within Statistics for Experimenters, BHH.  I’d highly recommend Box and Jenkins’ Time Series Analysis:  Forecasting and Control.  It’s been a little outdated by some of the more recent advances in analysis, but it’s a great text for establishing a solid base.  That should definitely get you on your way.  Best of luck.
    Regards,
    Erik 

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    #80704

    Ovidiu Contras
    Participant

    Thank you very much…..you guys really add value to this forum…

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