# Earthquake Magnitude and Frequency Forecasting in Northeastern Algeria using Time Series Analysis
## 6 Discussion and Conclusions  
The SSA technique is a well-known and effective time series analysis tool. On the studied earthquake magnitude time series, the forecasting capabilities of the SSA method were evaluated and compared with those of the standard ARIMA one, which is recognized to have a more suitable structure for forecasting. The results of this study show that the SSA technique could be effectively applied as an algorithm for forecasting earthquake number and sizes. According to [PERSON] et al. [61], the seismicity in the studied area is continuous and moderate. Several swarm sequences occurred in the recent past, showing intense activity with low magnitudes and limited time. An analysis of the series covering the years 1910 to 2015 is performed in order to validate the method employed in the current study by forecasting for the years 2016 to 2019. The forecasting values agree very well with the observed events both for the frequency and the annual maximum magnitude. Moreover, according to the recent recorded seismicity in the studied area, the forecasted magnitudes computed in the current study agree very well with the recorded seismicity during the years 2020 and 2021. The recorded magnitude events during these two years are lower than the maximum forecasted magnitudes, equal to 4.9 and 5.1, respectively. These results should to be considered as the maximum magnitude that is not exceeded. Figure 11: N-test values for (**a**) \(\delta_{1}\) index and (**b**) \(\delta_{2}\) index. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Year** & **N Observed** & **N Forecasted** & **N-Test \(\delta_{1}\)** & **N-Test \(\delta_{2}\)** \\ \hline
2016 & 2 & 3.0 & 0.8506 & 0.2240 \\
2017 & 2 & 3.2 & 0.8705 & 0.2079 \\
2018 & 0 & 3.5 & 1 & 0.0302 \\
2019 & 2 & 3.4 & 0.8865 & 0.1929 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Observed and forecasted earthquake number using the selected SSA model quantile score \(\delta_{1}\) and \(\delta_{2}\). The SSA model successfully modelled the considered data file and provided an accurate forecast of future earthquake magnitudes. Furthermore, the SSA model's trend component is a clear deterministic component for estimating earthquake magnitude. The N-test was employed in this study to assess the consistency between the observation and forecasting in terms of the total number of events. The results were given in terms of quantile scores \(\delta_{1}\) and \(\delta_{2}\). According to the results, the test is passed, which validates the suggested model. The results also show that, while significant parts of the variability in those seismological time series do not appear to have an adequate time structure to be forecasted, the key components may still be identified and forecasted using the SSA model. It is worth noting that the data file used in this study, which spans the years 1910 to the end of 2019, including events with magnitudes greater than Mw 4.0, could be modelled by an inhomogeneous Poisson process with a variable activity rate (Figure 2). A future study could forecast the number of earthquakes using such an inhomogeneous Poisson process, while the annual maximum magnitude could also be forecasted using, for instance, the extreme probability statistics [25]. An issue that appears to be a weakness of these procedures, and deserves special attention in the future, is the assessment of uncertainties of the forecasted values. Conceptualization, M.M., M.H. and J.A.P. ; methodology, M.H., M.M. and J.A.P. ; validation, M.H., M.M., J.A.P., and J.H. ; formal analysis, M.H., M.M. and J.A.P. and T.M. ; investigation, M.H., M.M., J.A.P., J.H. and T.M. ; resources, M.H. ; data curation, M.H., M.M., and J.A.P. ; writing-original draft preparation, M.H., M.M., and J.A.P. ; writing-review and editing, M.H., M.M., J.A.P., J.H. and T.M. ; visualization, M.H., M.M., J.A.P., J.H., and T.M; supervision, M.H., M.M., J.A.P., J.H. and T.M. ; project administration, M.H. All authors have read and agreed to the published version of the manuscript.