Long memory in surface air temperature: detection, modeling, and application to weather derivative valuation

Three multidecadal daily time series of mid-latitude near-surface air temperature are analysed. Long-range dependence can be detected in all 3 time series with 95% statistical significance. It is shown that fractionally integrated time-series models can accurately and parsimoniously reproduce the autocovariance structure of the observed data, The concept of weather derivatives is introduced and problems surrounding their pricing are discussed. It is shown that the fractionally integrated time-series models provide much more accurate pricing as compared with traditional autoregressive models employing a similar number of parameters. Finally, it is suggested that a simple explanation for the presence of long memory in the time series may be given in terms of aggregation of several short-memory processes.