A hybrid model for the time series of complex structure (HMTS) was proposed. It is based on the combination of function expansions in a wavelet series with ARIMA models. HMTS has regular and anomalous components. The time series components, obtained after expansion, have a simpler structure that makes it possible to identify the ARIMA model if the components are stationary. This allows us to obtain a more accurate ARIMA model for a time series of complicated structure and to extend the area for application. To identify the HMTS anomalous component, threshold functions are applied. This paper describes a technique to identify HMTS and proposes operations to detect anomalies. With the example of an ionospheric parameter time series, we show the HMTS efficiency, describe the results and their application in detecting ionospheric anomalies. The HMTS was compared with the nonlinear autoregression neural network NARX, which confirmed HMTS efficiency.

In spite of significant progress in the development of new devices for magnetic measurements, mathematical and computational technologies for data processing and means of communication, the quality of magnetic data accessible through the data centres (for example, World Data Centres or INTERMAGNET) still largely depends on the actual conditions in which observation of the Earth's magnetic field is performed at observatories. Processing of raw data of magnetic measurements by observatory staff plays an important role. It includes effective identification of noise and elimination of its influence on final data. In this paper, on the basis of the experience gained during long-term magnetic monitoring carried out at the observatories of IKIR FEB RAS (Russia) and CSIR-NGRI (India), we present a review of methods commonly encountered in actual practice for noise identification and the possibility of reducing noise influence.

In the present paper, we propose a wavelet-based method of describing variations in the Earth’s magnetic field, such as the horizontal component of the geomagnetic field, in addition to methods for evaluating changes in the energy characteristics of the field and for isolating the periods of increased geomagnetic activity. Based on a combination of multiresolution wavelet decompositions with neural networks, we propose a method of approximation of the cosmic ray time course and the allocation of anomalous variations (Forbush effects) that occur during periods of high solar activity. During the realization of the method, an algorithm was created for selecting the level of the wavelet decomposition and adaptive construction of the neural network. By using the proposed methods, we performed a joint analysis of the geomagnetic field and cosmic rays during periods of strong magnetic storms. The strongest geomagnetic field perturbations were observed in periods of abnormal changes in cosmic ray level. Assessment of the intensity of geomagnetic disturbances on the eve of and during magnetic storm development allowed us to highlight local increases in intensity of the geomagnetic field occurring at different frequency ranges prior to the development of the storm’s main phase. Implementation of the proposed method with theoretical tools in combination with other methods will improve the estimation accuracy of the geomagnetic field state during space weather forecasting.

In this study, a new multicomponent model (MCM) to determine the time variation of ionospheric parameters is suggested. The model was based on the combination of wavelets with autoregressive-integrated moving average model classes and allowed the study of the seasonal and diurnal variations of ionospheric parameters and the determination of anomalies occurring during ionospheric disturbances. To investigate in detail anomalous changes in the ionosphere, new computational solutions to detect anomalies of different scales and estimate their parameters (e.g., time of occurrence, duration, scale, and intensity) were developed based on a continuous wavelet transform. The MCM construction for different seasons and periods of solar activity was described using ionosphere critical frequency f o F2 data from Kamchatka (Paratunka Station, 52° 58′ N, 158° 15′ E, Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS). A comparison of the MCM with the empiric International Reference Ionosphere (IRI) model and the moving median method for the analyzed region showed that the suggested method was promising for future research, since it had the advantage of providing quantitative estimates for the occurrence time, duration, and intensity of the anomalies, characterizing the ionospheric state and disturbance degree with a higher accuracy. Geomagnetic storms from 17 March and 2 October 2013 were analyzed using the suggested method, and it was shown that the ionospheric disturbances were at maximum during the strongest geomagnetic disturbances. An increase in the electron concentration in comparison with the background level, under calm or weakly disturbed geomagnetic field conditions, was identified before the analyzed magnetic storms.

We propose a method of the modeling and analysis of ionospheric parameters by combining wavelet transform with autoregression models (integrated moving average). The method makes it possible to reveal regularities in ionospheric parameters and to make forecasts on variations. Also, this method can be used to fill the gaps in ionospheric parameters, with consideration of their diurnal and seasonal variations. The method was tested on foF2 data and data on the total electron content for the regions of Kamchatka and Magadan. The models constructed for the natural variation in ionospheric parameters allowed us to analyze its dynamical mode and build a forecast with a step of up to five hours. Based on estimates for model errors, we revealed anomalies arising during periods of increased solar activity and strong earthquakes in Kamchatka.