Cómo agrupar rangos continuos usando MySQL

MySQL no admite funciones analíticas, pero puede emular dicho comportamiento con user- variables definidas :

SELECT   CatID, Begin, MAX(Date) AS End, Rate
FROM (
  SELECT   my_table.*,
           @f:=CONVERT(
             IF(@c<=>CatId AND @r<=>Rate AND DATEDIFF(Date, @d)=1, @f, Date), DATE
           ) AS Begin,
           @c:=CatId, @d:=Date, @r:=Rate
  FROM     my_table JOIN (SELECT @c:=NULL) AS init
  ORDER BY CatId, Rate, Date
) AS t
GROUP BY CatID, Begin, Rate

Véalo en sqlfiddle .