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.

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.

The paper proposes an automated method for analyzing ionospheric parameters and detecting ionospheric anomalies. The method is based on a generalized multicomponent model of ionospheric parameters (GMCM) developed by the authors. The model identification is based on an integrated approach combining the wavelet-transform methods with the autoregressive-integrated moving average models (ARIMA models). The paper provides estimates of the method efficiency, describes the operations of detecting ionospheric anomalies and evaluating their parameters. On the example of ionospheric parameter processing (the ionospheric critical frequency (foF2)) for the Kamchatka region, we demonstrate the possibility of applying the method in on-line mode (as data become available to system). On the basis of the method, we detected shot-period anomalous changes proceeding magnetic storms and characterizing the occurrences of oscillatory processes in the ionosphere at the background of increased solar activity. The method has been implemented in the “Aurora” system for complex geophysical data analysis (http://lsaoperanalysis.ikir.ru/lsaoperanalysis.html).