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A Markov process for circular data. (English) Zbl 1411.62256
Summary: We propose a discrete time Markov process which takes values on the unit circle. Some properties of the process, including the limiting behaviour and ergodicity, are investigated. Many computations associated with this process are shown to be greatly simplified if the variables and parameters of the model are represented in terms of complex numbers. A further discussion is given on some submodels, in particular on the stationary process. The proposed model is compared with some existing Markov processes for circular data. Some statistical issues of the model, such as statistical inference, model selection and diagnostic checks, are considered. Finally, an application of the model to wind direction data is provided.

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
62P12 Applications of statistics to environmental and related topics
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