O MySQL não suporta funções analíticas, mas você pode emular tal comportamento com user- variáveis 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
Veja em sqlfiddle .
