## 2 Description of the Method
### Identification of the Model Disturbed Component  
Geomagnetic field disturbance degree is the quantity that, according to the paper [41], can be estimated by finding the difference between the highest and the least deviations of signal values from the corresponding values of a quiet diurnal variation. In the proposed model (1), geomagnetic disturbances are described by the component \(D(t)=\sum_{\rho}\tau_{\rho}{}^{pert}(t)\). Following the paper [31] and considering the significant nonstationarity \(D(t)\), we shall use the continuous wavelet transform and adaptive threshold functions to identify it. Continuous wavelet transform is determined as [29; 30]  
\[W_{b,s}=|s|^{\frac{-1}{2}}\int_{-\infty}^{+\infty}f(t)\Psi\bigg{(}\frac{t-b}{ s}\bigg{)}dt;s,b\in R,s\
eq 0.\]  
Then for \(D(t)\) we obtain the representation:  
\[D(t)=\sum_{b,s}E_{1,s}(W_{b,s})\Psi_{b,s}(t)+\sum_{b,s}E_{2,s}(W_{b,s})\Psi_{b,s}(t),\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Wavelet**} & **Losses \(P_{\text{m}}\) of the** & \multirow{2}{*}{**Losses \(P\) of the** **************} & **Errors \(U_{\text{m}}\) of the** **Suggested** & **Errors \(U\) of the** **Optimal Basis** \\  & **Suggested** & **Optimal Basis** & **Method** & **Optimal Basis** \\ \hline Db1 & 396.09 & 165.05 & 21.05 & 74.06 \\ Db2 & 349.63 & 141.32 & 21.37 & 53.99 \\ Db3 & 331.57 & 131.04 & 20.99 & 51.76 \\ Db4 & 330.26 & 130.85 & 21.26 & 50.54 \\ Db5 & 329.77 & 130.82 & 21.31 & 50.80 \\ Db6 & 327.42 & 130.91 & 21.06 & 51.55 \\ Db7 & 326.31 & 130.87 & 21.22 & 51.28 \\ Db8 & 329.35 & 131.02 & 21.32 & 50.06 \\ Db9 & 324.30 & 130.90 & 21.14 & 50.89 \\ Db10 & 324.20 & 130.96 & 21.17 & 51.20 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Method efficiency estimate results, obtained from the data for January 2021. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Wavelet**} & **Losses \(P_{\text{m}}\) of the** **Suggested** & **Losses \(P\) of the** **Optimal Basis** & **Errors \(U_{\text{m}}\) of the** **Suggested** & **Errors \(U\) of the** **Optimal Basis** \\  & **Method** & **Method** & **Method** & **Optimal Basis** \\ \hline Db1 & 495.86 & 185.22 & 21.52 & 126.27 \\ Db2 & 459.81 & 170.22 & 21.34 & 68.39 \\ Db3 & 439.88 & 156.99 & 21.52 & 74.70 \\ Db4 & 438.27 & 155.61 & 21.57 & 63.92 \\ Db5  
\(E_{1,s}(\cdot)\), \(E_{2,s}(\cdot)\) are the threshold functions determining the respectively weak (of \(i=1\) class) and strong (of \(i=2\) class) geomagnetic disturbances  
\[E_{1,s}(W_{b,s})=\left\{ \begin{array}{c}0,\ if\ \big{|}W_{b,s}\big{|}\leq T_{1,s} \ or\ \big{|}W_{b,s}\big{|}>T_{2,s}\\ W_{b,s},\ if\ T_{1,s}<\big{|}W_{b,s}\big{|}\leq T_{2,s}\end{array} \right. ; \tag{8}\]  
\[E_{2,s}(W_{b,s})=\left\{ \begin{array}{c}0,\ if\ \big{|}W_{b,s}\big{|}\leq T_{2,s} \\ W_{b,s},\ if\ \big{|}W_{b,s}\big{|}>T_{2,s}\end{array} \right.,\]  
\(T_{i,s}=U_{i}\times St_{s}\), \(i=1,2\), \(U_{i}\) is the threshold coefficient, \(St_{s}=\sqrt{\frac{1}{I-1}\sum_{k}^{l}\big{(}W_{b,s}-\overline{W_{b,s}}\big{)} ^{2}}\), \(\overline{W_{b,s}}\) is the wavelet coefficient average calculated in a moving time window of length \(l\). Taking into account the equivalence of the discrete and continuous wavelet transform [29; 30], when selecting the wavelet \(\Psi\) we can use the estimates obtained for discrete decompositions (Tables 1 and 2, Section 2.1). The intensity of positive and negative disturbances of the geomagnetic field of each class \(i\) at the time \(t=k\) can be estimated as  
\[I_{k}{}^{i\pm}(k)=\sum_{s}\Big{|}W_{b,s}^{\pm}\Big{|}. \tag{9}\]  
The thresholds \(T_{i,s}\) in (8) are determined by the root-mean-square deviation (\(St_{s}\)), which is estimated dynamically in a moving time window of duration \(l\). That provides adaptation of thresholds \(T_{i,s}\) to signal properties change. The coefficients of the thresholds \(U_{i}\) (see (8)) can be determined by minimizing the posterior risk [44].