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This question is not as obvious as it might seem. Consider this, concerning Rubidium clocks:
All commercial rubidium frequency standards operate by disciplining a crystal oscillator to the rubidium hyperfine transition...
So at a fixed temperature, and over a few seconds (say 10 seconds), is a regular crystal oscillator stable to part per billion accuracy?
Your question is addressed by Allan variance. Yes, a decent crystal oscillator is quite stable over a time frame of a few seconds, but not as stable as one disciplined by a rubidium cell. The long-term stability of a quartz oscillator suffers from aging. From one to ten seconds, a good quartz oscillator can be stable to about one part in 10^11:
There are several types of 'regular crystal oscillator'. SC cut is quieter than the more pullable and cheaper AT cut, overtone operation, even at 10MHz, is quieter than fundamental, which has more pulling range.
If you are building a rubidium stabilised clock, then you'd start with an ovened overtone SC crystal. This will be quieter at most frequency offsets than the rubidium or caesium reference. It's only when you get down to mHz offsets, or stability over minutes of operation, that the rubidium reference becomes quiet enough to be worth correcting the crystal.
This timescale implies that a good crystal disciplined from GPS can be every bit as quiet as a rubidium source.
That's a surprisingly involved question and depends on what kind of oscillator you operate how, and what model you apply to assess the stability.
What you probably want to read up on is "Allan Variance", which describes the distribution of phase error (and a frequency error is a linear-in-time phase error) when observing one clock with another clock. Whether or not you interpret random phase fluctuations as frequency error is up to your oscillator model!
The practical problem here really is finding a clock that's significantly better within a 10 s observational window.
Experience, however, tells us that practical communication systems that would require such a ppb stability for their receivers "waste" a lot of channel capacity for periodic synchronization. That's often more of an result of accomodating changing channels (especially in wireless mobile comms), but if you think about fibreoptics, which do have billions of symbols per second, you'll find that extensive clock recovery is done all the time, taking away bandwidth for actual payload data.
That points out that even for datacenter-grade electronics, you can't just plug in an oscillator and hope it runs stable enough for seconds after you initially estimated frequency. So, I'd argue, that even without looking at Allan Deviation in oscillator datasheet, the answer is "no, PPB stabilities are the domain of atomic clocks, very expensive oven controlled oscillators, or GPS-disciplined oscillators".
If by "regular" you mean something from Digi-Key for under $5, then no. 1 ppb works out to +/-0.01 Hz at 10 MHz. A $2 part will move more than that in one second, let alone 10.
0.5 ppb = $760
1.5 ppb = $119
1.0 ppm = $13 - temperature compensated
10 ppm = $1.27 - normal
