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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.

Change Point and Trend Analyses of Annual Expectile Curves of Tropical Storms