I'm building ARIMA models for some wind/waves data. I'm building a separate model for each variable.

Two of the variables that I need to model are wave and wind direction. The values are in degrees (0-360°). Is it possible to model this type of data where the value interval is circular? If not, which class of models is best for this kind of data?

  • $\begingroup$ I don't see why not . Perhaps if you post your actual data I may be able to see better. The term "value interval" is somewhat vague to me. $\endgroup$
    – IrishStat
    Dec 18, 2016 at 15:01
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    $\begingroup$ Have you considered using Cartesian coordinates (that is, cosine and sine of the angle) for the directions? $\endgroup$
    – whuber
    Dec 18, 2016 at 15:59
  • $\begingroup$ The data goes from 0 to 359°59'59'' (converted to float)... When I say value interval, I mean the range of possible values, it's continuous but also circular... For example, when I forecast and the values get close to 360, the confidence interval goes well over 360... The model doesn't realize that the interval should be circular, so that 359°59'59'' is the maximal possible value and the next one is 0 again... Haven't tried Cartesian coordinates, that would require a VAR model then (2 series, one for cosine and another for sine value)? $\endgroup$
    – krsnik93
    Dec 18, 2016 at 16:34
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    $\begingroup$ Do you have more specifics about what you are trying to understand through the modelling? Additional informaton on the reason/purpose would be good. I would imagine modelling the change in direction, for instance, would be easier (e.g. change in degrees could result in a cyclic or sinusoidal model). Your questions seems to be hinting at whether the model is good enough - that will be determined by your technical experience and fit? $\endgroup$
    – MarkR
    Dec 21, 2016 at 8:07
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    $\begingroup$ There are some papers on this subject, right now I'm looking at this one:link.springer.com/article/10.1007/s10463-008-0207-z $\endgroup$
    – krsnik93
    Dec 22, 2016 at 7:50

1 Answer 1


Is the von Mises distribution a good model for wind direction. It has support over 0 to 2\pi (or -pi to +pi) https://www.statisticshowto.datasciencecentral.com/von-mises-distribution/

If so, there are examples (https://iris.unipa.it/retrieve/handle/10447/94147/118553/basile_et_al_icrera_2013.pdf) who use a von Mises distribution with a time series. It's hooked up to a Hidden Markov Model rather than ARIMA, but I think the key thing is the von Mises (Tikhonov) distribution?


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