Time Series 101

[Arnold Rots]

Following up on yesterday's time series session, I thought it might be
helpful to summarize the basics on time information.
It really isn't that complicated.
For reference and more information than you really want, you can turn
to FITS WCS Paper IV: A&A 574, 36 (2015).

1. Required:
1.1 Record time stamps in JD, MJD, ISO-8601, or elapsed time
(if in elapsed time, you need to give a zero point in a time stamp that is
not
provided in elapsed time, of course)
1.2 Provide the time scale used (TT, TDB, TAI, GPS, ET, UTC, TCG, TCB)
1.3 Provide the reference position (place where the time is measured)

2. Note the following:
JD and MJD do not imply a time scale; it needs to be provided separately.
JD and MJD are dimensionless, though a unit of "day" is implied.
It's a bad idea to mix UTC with JD or MJD, since not all UTC days are the
same length.
Use the restricted form of ISO-8601:
[[+|-]c]ccyy-mm-dd[Thh[:mm[:ss[.ss...]]]]
No time zone characters.
TDB runs on average synchronously with TT, but corrects for the relativistic
effects caused by deviations in the earth's orbit from perfect circularity
and
constant gravitational potential.

3. Recommendations:
Also provide an estimate of the uncertainty in your timestamps.
Avoid UTC. It is trivial to convert the times provided by, e.g., space
agencies
to TT immediately when you get them and it will save headaches later on.
We do it for Chandra (and RXTE).
Use TT: it's the official IAU time scale, continuous with ET and the one
solar
system ephemerides are based on.
TAI and GPS are acceptable alternatives, with constant offsets from TT.
Use the same reference position for time and space and make sure it is
commensurate with your time scale. For instance, when you convert to
the barycenter, also convert to TDB.
Beware that the barycenter is not the heliocenter.
Be specific in labeling the time axis; e.g.: JD(TT;GEOCENTER)
or MJD(TDB;BARYCENTER).
Use proleptic Gregorian dates for ISO-8601.

4. Do never use:
TJD, HJD, BJD, etc.
These are not officially recognized and suggest certain metadata values, but
leave considerable ambiguity as to what those metadata values actually are.
Instead, specify your metadata explicitly. It avoids confusion later on and
isn't
much more work.

5. What if you deal with incomplete data?
If you don't know the time scale and/or reference position, you can provide
them
as UNKNOWN and set the systematic error/uncertainty to, say, 1000 s.
100 s will do if only the time scale is unknown.

6. What else is there to know?
Quit a lot, especially the so-called coordinate time scales (TCG and TCB).
Because TDB runs on average synchronously with TT, but in a very different
potential
well, you may have realized that this requires different values for
fundamental
physical constants in the barycenter. That's awkward and the coordinate
time scales
fix that by running at different rates. Eventually these may come into more
common
use, but at least for my lifetime I assume we will be sticking with TT and
TDB.
More in the cited A&A paper.

Hope this is helpful,

Cheers,

  - Arnold

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Arnold H. Rots                                          Chandra X-ray
Science Center
Smithsonian Astrophysical Observatory                   tel:  +1 617 496
7701
60 Garden Street, MS 67                                      fax:  +1 617
495 7356
Cambridge, MA 02138
arots at cfa.harvard.edu
USA
http://hea-www.harvard.edu/~arots/
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