Jennifer is correct — through phasing the maternal and paternal DNA, we can achieve reach to the parental generation. Even then, phasing isn’t error free and can be difficult if the parents are similar genetically.
The process is more akin to human ancestry testing, which compares to DNA from representative populations. For example, if someone tests as 20% Italian, then that means 20% of their DNA is similar to modern Italians. The Italians in that reference panel may or may not be relatives of the person testing their DNA.
Generation/lineage tracing is best achieved when samples from multiple relatives within a family are compared. Popular human DNA testing companies have this feature because a customer usually has some family members tested as well. The best results come from also testing parents and grandparents.
Our breed results, therefore, might not fully reflect the reality of a dog’s family history. Most dogs don’t have a known pedigree, nor samples available from multiple members of their family. But we do sometimes get enrolled dogs within a family (siblings or parent(s) with pup(s)), so we may be able to examine those families to improve phasing.
One of our partner projects, The Working Dog Project, might achieve lineage analysis, as many working dog organizations have breeding programs in which they track family history.