Actuarial pricing methods for weather derivatives depend on statistical modelling of stationary time series of historical meteorological data. This is described in chapters 3 to 6 for single contracts, and chapters 7 and 8 for portfolios. However, historical meteorological data is anything but stationary, and we must process it in a number of ways before the pricing methods can be applied. Firstly, we must clean the data to remove absurd values and fill gaps. Secondly, we must identify (and perhaps attempt to remove) jumps in the data that occur as a result of station changes. Finally, we may need to remove gradual trends from the data. Our discussion of the methods used for identifying and replacing absurd values, filling gaps and identifying and removing jumps will be rather cursory; a more thorough explanation is given in Boissonnade et al., 2002. We will, however, discuss the identification and removal of trends in some detail.

Data cleaning

Meteorological data measurements are usually made by national meteorological services (NMSs), and occasionally by universities, private companies or military organisations. We will restrict ourselves to a discussion of the data measured by the NMSs since this is what is generally used in the weather market. In many parts of the world measurements exist that go back at least fifty years, and in some cases much longer. However, as we shall discuss below, even very recent data already has significant problems with reliability and homogeneity, and earlier data is usually significantly worse.