Seasonal process by an example of cyclic fluctuations of solar activity

Abstract

A method is proposed for estimating non-multiple seasonal periods by an example of data on cyclic solar activity in the form of Wolf numbers. The values of the periods obtained are used to construct a multiplicative seasonal model in which the number of periods cannot exceed five in practice. Two possible variants of the algorithm for choosing the initial approximations of the model parameters with the use of a pseudorandom number generator are described. A modification of the two-stage steepest descent algorithm with improved performance and stability is given. For incomplete inadequate autoregressive moving average models, an additional criterion of proximity of the trajectory formed by the model to actual data is proposed, which can improve the forecast quality.