Change point and trend analyses of annual expectile curves of tropical storms

Motivated by the conjectured existence of trends in the intensity of tropical storms, new inferential methodology to detect a trend in the annual pattern of environmental data is developed. It can be applied to any data which form a time series of functions. Other examples include annual temperature or daily pollution curves at specific locations. Within a framework of a functional regression model, two tests of significance of the slope function are derived. One of the tests relies on a Monte Carlo distribution to compute the critical values, the other is pivotal with the chi-square limit distribution. Full asymptotic justification of both tests is provided. Their finite sample properties are investigated by a simulation study. Applied to tropical storm data, these tests show that there is a significant trend in the shape of the annual pattern of upper wind speed levels of hurricanes.