The HP "SmartClock" GPS Time & Frequency receivers have an internal metric called "predicted holdover uncertainty" which is shown in the SYST:STAT? display. As far as I can tell the prediction is a conservative measure of residual time error based on (drift-removed?) 1 day Allan Deviation frequency stability.
Now to be fair this metric has little to do with how stable the HP 58503A is in the short-term and it's probably useful only if one really anticipates keeping time during GPS loss (e.g., Telecom users). Still, it's a measure, I'm curious, and I've been looking for a HP 58503A (or HP 58503B, Z3801A, Z3816A, etc.) for years that would settle down well enough to display a predicted holdover stability of 1 us/day or better.
Two people I know have ones that get down to this level. I don't know if this is typical or not. I do know my two 58503A receivers don't get close and no matter what I do -- different cables, different antennas, different locations, days or months of warm-up -- I never see below about 5 us/day predicted holdover.
I now have a pile of surplus Z3801A receivers warming up and although they all meet spec the free-running oscillators vary considerably in their actual performance, from parts in ten to the 10th to parts in ten to the 13th. The very best one has an amazing short-term stability better than 5E-13 and is still 1E-12 at 10k seconds. So I'd expect that a few days after it locked to GPS that it would show a very good predicted holdover time. Sure enough, it is superb:
------------------------------- Receiver Status -------------------------------
SYNCHRONIZATION ............................................. [ Outputs Valid ]
SmartClock Mode ___________________________ Reference Outputs _______________
>> Locked to GPS TFOM 3 FFOM 0
Recovery 1PPS TI +200 ps relative to GPS
Holdover HOLD THR 1.000 us
Power-up Holdover Uncertainty ____________
Predict 300 ns/initial 24 hrs
ACQUISITION ............................................ [ GPS 1PPS CLK Valid ]
Satellite Status __________________________ Time ____________________________
Tracking: 5 Not Tracking: 3 GPS 06:05:28 14 May 2002
PRN El Az SS PRN El Az 1PPS CLK Synchronized to GPS Time
1 75 90 37 4 12 268 ANT DLY 0 ns
2 57 96 48 24 13 307 Position ________________________
13 70 309 43 *27 Acq . MODE Hold
20 27 176 32
22 41 63 42 LAT N 47:33:15.774
LON W 122:08:22.391
ELEV MASK 10 deg *attempting to track HGT +309.30 m (MSL)
HEALTH MONITOR ......................................................... [ OK ]
Self Test: OK Int Pwr: OK Oven Pwr: OK OCXO: OK EFC: OK GPS Rcv: OK
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