Through its magnetic activity and bursts of electromagnetic radiation and energetic particles, the Sun influences the flux of cosmic ray particles reaching Earth in terms of magnitude and energy spectrum. The resulting effect on space weather has practical importance for human activities in space, in the air and on the Earth’s surface. In this thesis, two cosmic ray related events in the year 2021, namely a Ground Level Enhancement (GLE) and a Forbush decrease (FD), were studied based on data generated by two mini neutron monitors (NM) located at a research station in Antarctica. In particular, the distribution of waiting times, i.e. the difference between the arrival times of two subsequent counts registered by the NM, was analysed using different proxy variables aiming to reflect the energy spectrum of the incident particles. While low-energy neutrons lead to single detection events, neutrons with higher energies produce additional neutrons through interactions with the lead of the NM. This means a single incident neutron with sufficient energy (i.e. a leader count) results in multiple detection events with shorter waiting times (i.e. follower counts), which is referred to as multiplicity. The different proxy variables are based on the ratio of leader to follower counts (i.e. the leader fraction) and were compared in terms of meaningfulness and applicability for the study of GLEs and FDs. The study accounted for atmospheric pressure effects on the spectra of neutrons in air. The five main results of this thesis are: 1. The initially observed spikes in the long waiting time tail of the waiting time distribution (WTD) were found to be caused by the data acquisition system of the NM. If instead of the timestamp of the Raspberry Pi micro-computer the timestamp of the PIC32 microcontroller is used for calculating the waiting time, the spikes in the WTD disappear and the long waiting time tail follows the expected exponential shape. 2. A new method to calculate a proxy variable for the multiplicity and the energy spectrum of the incident particles was developed based on the WTD and the statistical properties of leader counts. 3. DOMB is not a perfect bare NM, as was found from the WTD analysis. The neutrons produced in the lead of DOMC can reach the neighbouring DOMB and lead to the registration of multiplicity counts. 4. The barometric correction coefficients for the DOMC NM for the total count rate, leader count rate and three different proxy variables were determined. 5. From a numerical and graphical comparison of the different proxies for the energy spectrum of incident atmospheric particles, the new proxy variable appears to better reflect the expected trends during the GLE and FD. Considering the underlying variability, however, the changes during the GLE and FD cannot be judged statistically significant.