On nonparametric regression for bivariate circular long-memory time series - Jan Beran; Britta Steffens; Sucharita Ghosh (Statistical Papers, 2021)
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.
Keywords: 510; Circular time series; Circular circular kernel regression; Long-range dependence; Gaussian subordination; Confidence interval