Consumer-grade economical radon monitors are becoming increasingly popular in private and institutional use, both in the context of Citizen Science and traditional research. Although originally designed for screening indoor radon levels in view of radon regulation and decisions about mitigation or remediation - motivated by the health hazard posed by high radon concentrations - researchers are increasingly exploring their potential in some environmental studies. For long time, radon has been used as a tracer for investigating atmospheric transport processes. This paper focuses on the RadonEye, currently the most sensitive among low-cost monitors available on the market, and specifically, its potential use for monitoring very low radon concentrations. It has two objectives: firstly, discussing issues of statistics of low count rates and secondly, analyzing radon concentration time series acquired with RadonEyes outdoors and in low-radon indoor spaces. Regarding the first objective, among other things, the inference of reported to expected true radon concentration is discussed. The second objective includes the application of autoregressive methods and fractal statistics to time series analysis. The overall result is that radon dynamics can be well captured using this "low-tech" approach. Statistical results are plausible; however, few results are available in the literature for comparison, particularly concerning fractal methods. The paper may therefore be seen as an incentive for further research in this direction.