No. 1086

Title:

A Markov process for circular data

Author(s):

KATO, Shogo (Institute of Statistical Mathematics, Japan)

Key words:

Circular autocorrelation; Circular time series; Mobius transformation; Robustness; Wrapped Cauchy distribution

Abstract:

    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, especially, on the stationary process. The proposed model is compared with some existing Markov processes for circular data. Statistical inference for the process is considered. Finally, an application of the model to wind direction data is provided.