1. A method for automatic detection of unstable oxygen saturation of a patient using a pulse oximeter, the method performed with a processor and comprising: receiving at least a single time series input of oxygen saturation values; computing at least two statistical metrics based on statistical properties of the single time series input of oxygen saturation values, wherein the at least two statistical metrics in combination are sensitive to both magnitude and frequency range of oxygen saturation variations; and determining if an unstable oxygen saturation condition exists based on the at least two statistical metrics.