Nonparametric Regression on the Circle with Applications to Climate and Environmental Science

Overview & Synopsis

Two important indicators of climate change are the decline in Arctic sea ice area and the increase in average temperatures globally. Both sea ice and temperature exhibit seasonal patterns, making circular regression a natural approach for their analysis. In this paper, we construct computationally tractable Nadaraya-Watson type kernel regression estimators on the unit circle, using rate-optimal kernel density estimators. We introduce a leave-one-out cross-validation procedure for the data-driven selection of the smoothness parameter and evaluate the performance of the proposed estimators through a simulation study covering 48 scenarios, including comparisons with existing local polynomial estimators. We then apply our methodology to historical Arctic sea ice area data and daily temperature observations in Stockholm. The fitted regression functions and their derivatives or finite differences allow us to investigate changes in both the levels and seasonal dynamics of these environmental indicators. In particular, we observe a decline in fitted sea ice area and substantial changes in its seasonal rates of growth and retreat, together with higher fitted temperatures across most of the year in Stockholm during the more recent period in comparison to historical data.