SQL to Extract Continuous Timestamp Ranges

Table Device_Status

Expected Output (Need SQL query to generate):

Basically, for each ID get min (timestamp) and max (timestamp) but over continuous records for that ID. If there is only one record, then min=max as is the case with the second and third record in the sample result set.

I have tried this (and various subquery variants thereof)

SELECT Id, min(Timestamp) AS Fail_Begin, max(Timestamp) AS Fail_EndFROM Device_StatusGROUP BY Id

but need to group by only continuously occurring records,

So perhaps by adding a notion of status change first would help? Starting with zero as initial status and then incrementing the change code by 1 every time the next record is different in order to thereby generate an intermediate result like so...

Table Device_Status_With_Change_Column

And then doing

SELECT Id, Change, min(Timestamp) AS Fail_Begin, max(Timestamp) AS Fail_EndFROM Device_Status_With_Change_ColumnGROUP BY Id, Change

Other than looping over the result set in a programming language, I do not yet see a direct SQL statement that would do this in one fell swoop without the intermediate table and I do not see how to compute the column Change (in SQL).