# Time series modeling of circular data

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?

• 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. Dec 18, 2016 at 15:01
• Have you considered using Cartesian coordinates (that is, cosine and sine of the angle) for the directions?
– whuber
Dec 18, 2016 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)? Dec 18, 2016 at 16:34
• 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? Dec 21, 2016 at 8:07
• 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 Dec 22, 2016 at 7:50