Circular–circular Regression Model, with Application to Meteorological Data
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Abstract
The purpose of this paper is to investigate the four–parameter circular regression model of Taylor in which the angular error is distributed as a wrapped Cauchy distribution. The study is also extended to a polynomial circular model, including parameter estimation using a method of maximum likelihood. The estimations of regression parameters are examined through simulations. In addition, an application of the model considered here is illustrated using a real dataset of wind directions measured at a weather station in Texas and its fit is compared with some existing regression models. The results of the simulation show that the proposed parameter estimations perform favorably since the biases of estimators are close to zero and root mean square errors of estimators are small. Furthermore, the findings from this real application show that the circular–circular regression model of Taylor in which the angular error is distributed as a wrapped Cauchy distribution represents the relationship between the wind directions reasonably well.
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