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Can we compute temporal variograms just like spatial variograms? I know about spatio-temporal variograms but I am more interested in doing a comparison of separate spatial and temporal variograms and then comparing the results with spatio-temporal variograms to better understand the concepts. So far I have not gotten a straight answer from reading.

In my mind to calculate a temporal variogram we have to take 3 columns x, y and z. X and Y acting as coordinates and z being the value. If we have columns with x=zeros and y=date/time,

x y z
0 1/01/2004 0:00 15
0 1/04/2004 0:00 224
0 1/08/2004 0:00 34
0 1/12/2004 0:00 65

can I do that? If not, what should I do to calculate the spatio-temporal variogram with temporal variations.

kjetil b halvorsen
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user4405092
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    It would help to give an example. Do you mean, for example, finding gold nuggets in space and time? If so, these should be expressed by some multivariate linkage. For example, some rule or plan for finding gold nuggets. Please clarify your question, and without that clarification, the question itself is too broad to answer. – Carl Jan 20 '18 at 19:58
  • I have so2 data of 4 years. what i am confused about is that whether temporal variogram will give a new insight of data or the results are similar to time series analysis. – user4405092 Jan 20 '18 at 20:23
  • So, y is time. What are x and z? – Carl Jan 20 '18 at 20:27
  • z is the value of so2, and y is the time recorded for values. i am considering x as zero to see so2 behaviour over time. – user4405092 Jan 20 '18 at 20:28
  • Suggest you explain what x is and not use it as x=0. If you use, for example, x is some distance formula, then you can just make a 3D plot of distance, time, and concentration. – Carl Jan 20 '18 at 20:42

2 Answers2

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Of course you can use variograms also for time series data. The variogram has one advantage as compared to the autocorrelation function, it only needs the hypothesis of intrinsic stationarity, not stationarity (definitions can be found here: Intrinsic spatial stationarity: doesn't it only apply for small lags?). So it only assumes that the expectation of differences are zero, but the global mean, for instance, do not need to exist. So the variogram is defined even in cases where the variance do not exist, while the autocovariance function do need that the variance exists. So, potentially the variogram could be of interest for time series with long-range dependence. But I have never used it this way myself, nor seen it used.

But here is a relevant paper: https://rss.onlinelibrary.wiley.com/doi/abs/10.1111/1467-9884.00101

kjetil b halvorsen
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If I have understood you correctly, instead of a 2D "smearogram", make a 3D "blobogram." Making it somewhat transparent would help. That is, plot three coordinates, for example, difference in distance, at time, and versus difference in concentration.

Carl
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