  We analyze noise properties of time series of frequency data from different
counting modes of a Keysight 53230A frequency counter. We use a 10 MHz
reference signal from a passive hydrogen maser connected via phase-stable
Huber+Suhner Sucoflex 104 cables to the reference and input connectors of the
counter. We find that the high resolution gap-free (CONT) frequency counting
process imposes long-term correlations in the output data, resulting in a
modified Allan deviation that is characteristic of random walk phase noise.
Equally important, the CONT mode results in a frequency bias. In contrast, the
counter's undocumented raw continuous mode (RCON) yields unbiased frequency
stability estimates with white phase noise characteristics, and of a magnitude
consistent with the counter's 20 ps single-shot resolution. Furthermore, we
demonstrate that a 100-point running average filter in conjunction with the
RCON mode yields resolution enhanced frequency estimates with flicker phase
noise characteristics. For instance, the counter's built-in moving-average
function can be used. The improved noise characteristics of the averaged RCON
mode versus the CONT mode imply that the former mode yields frequency estimates
with improved confidence for a given measurement time.
