[__init]

Intel x86 cores have had Last Branch Records (LBRs) and Branch Trace Store (BTS) since at least Merom in 2006 [1][2]. Nowadays, there's Processor Trace (PT) or Precise Event-Based Sampling (PEBS) which can provide even more information. PT in particular is almost purpose-built to enable this kind of trace reconstruction.

[1] https://stackoverflow.com/questions/14670586/what-is-the-ove...

[2] The MSRs for LBRs (MSR_LASTBRANCH_*_{TO,FROM}_IP) and BTS (IA32_DS_AREA) are described in Volume 4, Section 2.2 of the SDM: "MSRS IN THE INTEL® CORE™ 2 PROCESSOR FAMILY". Core 2 was launched in 2006.

[Veserv]

Those are only sufficient to produce a execution trace rather than a full data trace which is needed for time-travel debugging.

Though they are sufficient to do what the person you responded to asked for which is just execution trace.