Principal components and iterative regression analysis of geophysical series: Application to Sunspot number (1750–2004)

We present here an implementation of a least squares iterative regression method applied to the sine functions embedded in the principal components extracted from geophysical time series. This method seems to represent a useful improvement for the non-stationary time series periodicity quantitative analysis. The principal components determination followed by the least squares iterative regression method was implemented in an algorithm written in the Scilab (2006) language. The main result of the method is to obtain the set of sine functions embedded in the series analyzed in decreasing order of significance, from the most important ones, likely to represent the physical processes involved in the generation of the series, to the less important ones that represent noise components. Taking into account the need of a deeper knowledge of the Sun's past history and its implication to global climate change, the method was applied to the Sunspot Number series (1750–2004). With the threshold and parameter values used here, the application of the method leads to a total of 441 explicit sine functions, among which 65 were considered as being significant and were used for a reconstruction that gave a normalized mean squared error of 0.146.