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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?

gung - Reinstate Monica
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krsnik93
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  • 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. – IrishStat Dec 18 '16 at 15:01
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    Have you considered using Cartesian coordinates (that is, cosine and sine of the angle) for the directions? – whuber Dec 18 '16 at 15:59
  • 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)? – krsnik93 Dec 18 '16 at 16:34
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    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? – MarkR Dec 21 '16 at 08:07
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    There are some papers on this subject, right now I'm looking at this one:http://link.springer.com/article/10.1007/s10463-008-0207-z – krsnik93 Dec 22 '16 at 07:50
  • They also use Cartesian coordinates (as suggested by whuber) to represent angles and then fit a VAR model... There are some additional interesting papers like: https://www1.maths.leeds.ac.uk/statistics/pgstats/theses/hughes.pdf, https://www.researchgate.net/publication/260161318_Time_Series_Analysis_of_Circular_Data and http://maths.dur.ac.uk/stats/people/psc/thesis.pdf... – krsnik93 Dec 22 '16 at 07:55
  • One important thing to realize here is that the distribution of error/noise cannot be assumed to be normally distributed because the support if the rv is restricted to 0-360. This may complicate estimation process also. You may probably find something in literature with non-normal distribution. – Dayne Jul 19 '19 at 04:06

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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?

Paul Hewson
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