Nonparametric monitoring of sunspot number observations: a case study

Solar activity is a driver of long-term climate trends and must be accounted for in climate models. Unfortunately, direct measurements of this quantity over long periods do not exist. The only observation related to solar activity whose records reach back to the seventeenth century are sunspots. Surprisingly, determining the number of sunspots consistently over time remains a challenging statistical problem. It arises from the need of consolidating observations from multiple stations in a context of low signal-to-noise ratios, non-stationarity, missing data, non-standard distributions and many errors. In this paper, we propose a systematic and thorough statistical approach for monitoring these data. It consists of smoothing on multiple timescales, monitoring using block bootstrap calibrated CUSUM charts, and classifying of out-of-control situations by support vector techniques. This approach allows us to scan for a wide range of deviations many of which are observer or equipment related. Their detection and identification will help improve future observations, their elimination or correction in past data will lead to a more precise reconstruction of the International Sunspot Number, the world reference for solar activity. Our research provides a toolbox of statistical techniques of general use to monitor evolving panels of timeseries which occur in many disciplines.