Abstract
We consider nonparametric regression for bivariate circular time series with long-range dependence. Asymptotic results for circular Nadaraya–Watson estimators are derived. Due to long-range dependence, a range of asymptotically optimal bandwidths can be found where the asymptotic rate of convergence does not depend on the bandwidth. The result can be used for obtaining simple confidence bands for the regression function. The method is illustrated by an application to wind direction data.
Highlights
Directional or circular time series arise in many scientific fields such as meteorology, oceanography, biology, neuroscience, bioinformatics, geoscience and cosmology
An overview of directional data analysis can be found for instance in books by Mardia (1972), Fisher (1993), Mardia and Jupp (2000), Jammalamadaka and SenGupta (2001) and Ley and Verdebout (2017)
For cases where more than one circular variable is observed, parametric and nonparametric circular-circular regression with iid residuals is discussed for instance in Gould (1969), Fisher and Lee (1992), Johnson and Wehrly (1978), Mardia and Jupp (2000), Jammalamadaka and SenGupta (2001), Kato et al (2008), Kim and SenGupta (2016) and Polsen and Taylor (2015)
Summary
Directional or circular time series arise in many scientific fields such as meteorology, oceanography, biology, neuroscience, bioinformatics, geoscience and cosmology. For cases where more than one circular variable is observed, parametric and nonparametric circular-circular regression with iid residuals is discussed for instance in Gould (1969), Fisher and Lee (1992), Johnson and Wehrly (1978), Mardia and Jupp (2000), Jammalamadaka and SenGupta (2001), Kato et al (2008), Kim and SenGupta (2016) and Polsen and Taylor (2015). Ghosh (2019) define models with long-range dependence using Gaussian subordination, and derive asymptotic results for parametric estimators where the mean direction depends on deterministic explanatory variables. We consider asymptotic properties of circular kernel estimators of μ(w0). Limit theorems are derived using in particular general results in Mielniczuk and Wu (2004). 2. Limit theorems are discussed in Sect. An application to wind direction data is discussed in Sect.
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