Editado com os requisitos mais recentes.
Seu problema é que você está tentando obter o previous_avg tentando manipular QTR e YEAR. Estou usando a função RANK, ordenando a maneira como quero que os dados sejam classificados. Nas junções estou me certificando de que Região Média =Região Anterior e desconsiderando o ano desde o trimestre anterior poderia ser Q4 do ano anterior para o ano Médio Q1; é mais limpo assim.
--Build the test table
IF OBJECT_ID('SALES','U') IS NOT NULL
DROP TABLE SALES
CREATE TABLE SALES
(
Region VARCHAR(255)
, Product VARCHAR(10)
, [Year] INT
, QTR INT
, [Month] VARCHAR(19)
, Sales DECIMAL(19,4)
);
INSERT SALES
VALUES
('NORTH', 'P1', 2015, 1, 'JAN', 1000)
,('NORTH', 'P1', 2015, 1, 'FEB', 2000)
,('NORTH', 'P1', 2015, 1, 'MAR', 3000)
,('NORTH', 'P1', 2015, 2, 'APR', 4000)
,('NORTH', 'P1', 2015, 2, 'MAY', 5000)
,('NORTH', 'P1', 2015, 2, 'JUN', 6000)
,('NORTH', 'P1', 2015, 3, 'JUL', 7000)
,('NORTH', 'P1', 2015, 3, 'AUG', 8000)
,('NORTH', 'P1', 2015, 3, 'SEP', 9000)
,('NORTH', 'P1', 2015, 4, 'OCT', 1000)
,('NORTH', 'P1', 2015, 4, 'DEC', 4000)
,('NORTH', 'P1', 2015, 4, 'NOV', 2000)
,('NORTH', 'P3', 2015, 1, 'FEB', 1000)
,('NORTH', 'P3', 2015, 1, 'FEB', 9000)
,('NORTH', 'P3', 2015, 2, 'APR', 2000)
,('NORTH', 'P3', 2015, 3, 'JUL', 8000)
,('NORTH', 'P1', 2016, 1, 'MAR', 3000)
,('NORTH', 'P1', 2016, 1, 'FEB', 1000)
,('NORTH', 'P1', 2016, 1, 'JAN', 2000)
,('SOUTH', 'P1', 2015, 1, 'JAN', 2000)
,('SOUTH', 'P1', 2015, 1, 'FEB', 3000)
,('SOUTH', 'P1', 2015, 1, 'JAN', 4000)
,('SOUTH', 'P2', 2015, 1, 'MAR', 1000)
,('SOUTH', 'P2', 2015, 1, 'JAN', 8000)
,('SOUTH', 'P2', 2015, 1, 'FEB', 9000)
,('SOUTH', 'P2', 2015, 2, 'JUN', 9000)
,('SOUTH', 'P2', 2015, 2, 'MAY', 8000)
,('SOUTH', 'P2', 2015, 2, 'APR', 2000)
,('SOUTH', 'P2', 2015, 3, 'SEP', 4000)
,('SOUTH', 'P2', 2015, 3, 'AUG', 2000)
,('SOUTH', 'P2', 2015, 3, 'JUL', 1000)
,('SOUTH', 'P2', 2015, 4, 'NOV', 2000)
,('SOUTH', 'P2', 2015, 4, 'DEC', 1000)
,('SOUTH', 'P2', 2015, 4, 'OCT', 5000)
,('SOUTH', 'P3', 2015, 3, 'AUG', 9000)
,('SOUTH', 'P3', 2015, 4, 'OCT', 1000)
,('SOUTH', 'P3', 2015, 4, 'NOV', 3000)
,('SOUTH', 'P2', 2016, 1, 'JAN', 2000)
,('SOUTH', 'P2', 2016, 1, 'JAN', 4000);
--CTE TO CAPTURE AVG SALES BY REGION, PRODCUT, YEAR, QTR; OMIT PRODUCT IF YOU WANT STRAIGHT UP QUARTER AVG, REGARDLESS OF PRODCUCT
WITH cteAvgSales AS
(
SELECT Region, Product, [Year], QTR, AVG(Sales) current_avg
, RANK() OVER(ORDER BY Region, Product, [Year], QTR) AS RNK
FROM SALES
GROUP BY Region, Product, [Year], QTR
)
SELECT s.Region, s.Product, s.[Year] AS [year], s.QTR AS [quarter], s.[Month], s.Sales, a.current_avg, p.current_avg AS previous_avg
FROM SALES s
INNER JOIN cteAvgSales a ON a.Region = s.Region
AND a.Product = s.Product
AND a.[Year] = s.[Year]
AND a.QTR = s.QTR
LEFT JOIN cteAvgSales p ON p.Region = a.Region
AND p.Product = s.Product
AND p.RNK=a.RNK-1
ORDER BY s.Region, s.Product, s.[Year], s.QTR
