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Aug 9, 2013 9:27 AM
(1519 views)

Hello,

I have different variables (Y1, Y2,) spaced evenly with time (X). I suspect that there is a delay time between the two responses Y1 and Y2 based on the process involved and would like to estimate by how much I must timeshift the data (i.e. what is the delay time) so as to compare Y1 and Y2 at the same row number?

I tried to use the auto-correlation function to determine the periodicity in each variable Y1 and Y2 to extract this information, but did not get very far.

Can anybody provide any suggestions?

Thank you

Anoop

3 REPLIES

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Aug 13, 2013 3:47 PM
(1289 views)

Hi Anoop,

I'm not sure I understand you fully.

So, is your data like this?

Time (x) | Y1 | Y2 |
---|---|---|

1 | .23 | .56 |

2 | .3 | .45 |

3 | .21 | .35 |

4 | .3 | .34 |

And, do you want to model Y2 as a function of Time and Y1?

If so, you can use the Time Series platform and use Y2 as your Time Series, Y1 as your Input List and Time as your Time ID.

If I've misunderstood, please give us some more details so we can understand your question more clearly.

Thanks!

-Jeff

-Jeff

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Aug 14, 2013 9:31 AM
(1289 views)

Hello Jeff,

Thank you very much for your reply.

You are correct about the form of the data. What I want to do, though, is to determine by how much time I should shift Y2 (say, by 4 time units) so that Y1 and the new time-shifted Y2 variable can be analyzed together as a pair i.e. Y1(t) and Y2(t+delta) are now on the same rows and I can then do correlations, partition etc.. I believe that Y2 will be delayed from Y1 because of the time taken for any event to go through the process and want to find out what "delta" should be. An example would be a chemical concentration change that travels through a large tank volume to get from where Y1 is measured to where Y2 is measured.

I used the Time Series platform as you suggested and would like to know how to analyze the results. I tried the ARIMA model fit but do not really know how to use it e.g. what to specify for the (p.d.q) values etc. I am not even sure if that is the right approach to get the answer ("delta") I am looking for.

Any help will be greatly appreciated.

Thank you

Anoop

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Aug 15, 2013 6:40 AM
(1289 views)

Hello, Anoop --

Maybe this might help with your problem. Here is a simple example where we have two periodic signals, one with a delay of 5 samples:

If we launch the Time Series platform with Series 1 as our Y, Series 2 as the Input List and Time as the X, Time ID like this (as Jeff had suggested):

We can run a cross-corrleation on the signals, by selecting it from under the red triangle:

This will create our Cross Correlation Plots for the Output Series - Series 1. If I right click on the plot, I can select 'Make Into Data Table':

I can see the max cross correlation is at 5 samples, which happens to be the amount that the second signal is delayed. If I plot these data in Graph Builder, I can also visualize this delay as the max of the cross correlation.

So I would conclude my delta between the two signals is 5 samples. From there I would lag my series 2 by 5 samples so that we can perform subsequent analyses. This is a very simple example, but try this workflow with your data and see how it works.

Check out the JMP blog: jmp.com/blog