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TableForm[{#["ParameterConfidenceIntervalTable"] & /@ {nlm[
     xyAsOffset], nlm[xyAsAbsoluteTime]}}, 
 TableHeadings -> {{}, {"xyAsOffsets", "xyAsAbsoluteTime"}}]

compareCIResults[opts : OptionsPattern[NonlinearModelFit]] := 
 TableForm[{#["ParameterConfidenceIntervalTable"] & /@ {nlm[
      xyAsOffset, opts], nlm[xyAsAbsoluteTime, opts]}}, 
  TableHeadings -> {{opts}, {"xAsOffsetsFromTRef", 
     "xAsAbsoluteTime"}}];
compareCIResults[]

NOTE: At this point, the only difference between xAsOffsets and xAsAbsoluteTime is that the former are offset values from a TRef {0, 3600, ...} whereas the latter are AbsoluteTime values {3819830400, 3819832200, ...}. Both are monotonically increasing by 1800.

NOTE: At this point, the only difference between xAsOffsets and xAsAbsoluteTime is their IntegerLength[] size: the former are offset values from a TRef {0, 3600, ...} with IntegerLength[] <= 7 whereas the latter are AbsoluteTime values {3819830400, 3819832200, ...} whose IntegerLength[] == 10. Both are monotonically increasing by 1800.

1. Why does NLM ignore parameter constraints Abs[phi] <= 2Pi when AbsoluteTime units are utilized?
2. Is there an additional NLM tuning parameter to ensure Phi never steps outside its constrained param value?
3. Is there a two-pass strategy to get reasonable phaseCIs (e.g., estimate BestFitParameters in one pass with a specific NLM Method, and then run a second NLM passing with a Method that explicitly applies parameter constraints?
4. (More generally) What other issues does NLM have with respect to TimeSeries data with Circular and/or Directional Statistical models?

1. Why does NLM ignore parameter constraints Abs[phi] <= 2Pi when AbsoluteTime units are utilized?
2. Is there an additional NLM tuning parameter to ensure Phi never steps outside its constrained param value?
3. Is there a two-pass strategy to get reasonable phaseCIs (e.g., estimate BestFitParameters in one pass with a specific NLM Method, and then run a second NLM passing with a Method that explicitly applies parameter constraints)?
4. (More generally) What other issues does NLM have with respect to TimeSeries data with Circular Statistical models?