Turbocharger compressors are limited in their operating range at low mass flows by compressor surge, thus restricting internal combustion engine operation at low engine speeds and high mean effective pressures. Since the exact location of the surge line in the compressor map depends on the whole gas exchange system, a safety margin towards surge must be provided. Accurate early surge detection could reduce this margin. During surge, the compressor outlet pressure fluctuates periodically. The Hurst exponent of the compressor outlet pressure is applied in this paper as an indicator to evaluate how close to the surge limit the compressor operates. It is a measure of the time-series memory that approaches zero for anti-persistence of the time series. That is, a Hurst exponent close to zero means a high statistical preference that a high value is followed by a low value, as during surge. Maps of a passenger-car sized turbocharger compressor with inlet geometries that result in different surge lines are measured on a cold gas stand. It is demonstrated that the Hurst exponent in fact decreases as the compressor moves towards surge, and that a constant value of the Hurst exponent can be used as a threshold for stable operation. Transient pressure signals of the compressor entering surge are analyzed in order to evaluate the time lag until surge can be detected using the Hurst exponent. Two surge cycles are usually needed to detect unstable operation. However, since the amplitude of these oscillations is relatively small for the first cycles, detection is possible before the oscillations grow into deep surge.