ABSTRACT
This chapter shows how monofractal long-term correlated records can be generated numerically and how they can also be detected in the presence of external trends. It gives examples for long-term correlated hydroclimate records. The chapter discusses how the formalism to detect monofractal correlations can be generalized to also detect nonlinear long-term correlations. It also discusses the consequences of both linear and nonlinear correlations for the temporal arrangements of extreme events. The chapter also shows how external trends can be detected in data with long-term memory. It considers the consequences of linear and non-linear long-term memory on the occurrence of rare extreme events and their predictability. The stretched exponential behaviour is quite universal and does not seem to depend on the way the original data are distributed. The chapter examines fractals and multifractals in climate and hydrological time series and quantified their relation to linear and nonlinear long-term memory.
