The purpose of this appendix is to provide a simple guide to the basic mathematics that underlies the search for weather cycles. As such it seeks to give only the most elementary features of what is a complex and wide-ranging subject. In addition, it is designed to reflect the fact that there has been a dramatic upsurge in the availability of computer power and statistical packages to carry out a wide range of highly sophisticated analyses on time series. So, it may help to assess the analysis presented in this book, and also provide a ‘health warning’ on the pitfalls of the uncritical use of powerful programs without looking closely at what can be achieved with what is frequently noisy data. This approach can, however, only go so far. Moreover, it is highly selective in focusing only on the essential elements of analysing time series. Anyone wishing to consider the analysis of time series in greater depth is advised to refer to the statistical section of the bibliography.