SQL Serverの不特定多数のアイテム間にピアソン相関テーブルを作成する方法

Question

特定の日に一連のリターン（ret）の間にピアソン相関テーブルを作成しようとしました。比較したいアイテムの数は毎日異なります。それは50から200の間で変わります。

：私は分析する特定の日に

は、私はこのような項目ごとにすべてのリターンが含まれている1台RetTableを持っている、（ここでは9月1日に私は過去3日間の相関関係を見てみたいです）そのテーブルから

Id RetDate  Ret 
1 2017-08-31 -0.062720 
1 2017-08-30 0.032650 
1 2017-08-29 -0.086360 
2 2017-08-31 -0.033100 
2 2017-08-30 0.032900 
2 2017-08-29 -0.032400 
3 2017-08-31 -0.017900 
3 2017-08-30 -0.018300 
3 2017-08-29 -0.015200 

私はこのような各項目の平均値と別のテーブル（MeanTable）を作成した：次の段階は、私にそのテーブルDiffRetAvgTableを与える各リターンの平均リターンを減算することである

Id MeanRet 
1 -0.038810 
2 -0.010866 
3 -0.017133 

。

ID RetDate DiffRetAvg 
1 2017-08-31 -0.023910 
1 2017-08-30 0.071460 
1 2017-08-29 -0.047550 
2 2017-08-31 -0.022234 
2 2017-08-30 0.043766 
2 2017-08-29 -0.021534 
3 2017-08-31 -0.000767 
3 2017-08-30 -0.001167 
3 2017-08-29 0.001933 

次のステップでは、各項目に対応する各DiffRetAvgの結果を掛けることになります。それは私が立ち往生している場所です。私が2,3のアイテムしか持っていなかった場合は、単純な算術を使うことができましたが、私はある日から何回まで持っているのか分かりません。

ピボットの相関表は次のようになります。

ID 1 2 3 
1 1 ? ? 
2 ? 1 ? 
3 ? ? 1 

（自身との項目の相関関係は常に1になります）

をここで私が持っているコードは、これまで

DECLARE @MeanTable AS TABLE (Id INT, AvgRet NUMERIC(10,6)) 
DECLARE @SquareTable AS TABLE (Id INT, SqRoot NUMERIC(10,6)) 
DECLARE @RetTable AS TABLE (Id INT,RetDate DATE, Ret NUMERIC(10,6)) 
DECLARE @DiffRetAvgTable AS TABLE (Id INT, RetDate DATE, DiffRetAVG NUMERIC(10,6)) 
DECLARE @PairMultiTable AS TABLE (ID1 int, ID2 int,Exp2 NUMERIC(10,6)) 
DECLARE @PairMultiTable2 AS TABLE (ID1 int, ID2 int,SumPairMulti NUMERIC(10,6)) 

INSERT INTO @RetTable VALUES 
(1,'2017-08-31' ,-0.06272), 
(1,'2017-08-30' , 0.03265), 
(1,'2017-08-29' , -0.08636), 
(2,'2017-08-31' , -0.0331), 
(2,'2017-08-30' , 0.0329), 
(2,'2017-08-29' , -0.0324), 
(3,'2017-08-31' , -0.0179), 
(3,'2017-08-30' , -0.0183), 
(3,'2017-08-29' , -0.0152) 

--Step 1 : Get all the average by Items 
INSERT INTO @MeanTable SELECT ID, avg(Ret) AS avgRet FROM @RetTable GROUP BY ID 

--Step 2 : Substract the average from every occurence in each Item and call it DiffRetAvg 
INSERT INTO @DiffRetAvgTable SELECT a.ID,RetDate, ret-AvgRet AS DiffRetAvg FROM @RetTable a INNER JOIN @MeanTable b on a.Id = b.Id 

-- Step 3 Multiply each DiffRetAvg for each occurence by its correspondant for another occurence and call it SumPairMulti 
INSERT INTO @PairMultiTable2 
SELECT ID1 , ID2, sum(Multi) AS SumPairMulti FROM (
SELECT a.ID AS ID1, b.ID AS ID2, cast(a.ID AS NVARCHAR(3)) + '_' + cast(b.id AS NVARCHAR(3)) AS Pair_ID, a.Retdate , a.diffRetAvg*b.DiffRetAVG AS Multi FROM @DiffRetAvgTable a 
INNER JOIN @DiffRetAvgTable b on a.RetDate =b.RetDate) c 
GROUP BY ID1, ID2 

-- Step 4 Calculate the square of each DiffRetAvg for each occurence 
INSERT INTO @PairMultiTable 
SELECT ID1 , ID2, sum(Multi) AS Exp2 FROM (
SELECT a.ID AS ID1, b.ID AS ID2, a.Retdate , a.diffRetAvg*b.DiffRetAVG AS Multi FROM @DiffRetAvgTable a 
INNER JOIN @DiffRetAvgTable b ON a.RetDate =b.RetDate) c 
WHERE ID1=ID2 
GROUP BY ID1, ID2 

--Step 5 Calculate the correlation between each Item with this formula : SumPairMulti/sqrt(ID1_Exp2*ID2_EXP2) 

SELECT c.ID1, c.ID2, d.SumPairMulti/SQRTProd AS Correlation FROM (
SELECT a.ID1, b.ID2, sqrt(a.Exp2*b.Exp2) AS SQRTProd FROM @PairMultiTable a 
CROSS JOIN @PairMultiTable b) c 
INNER JOIN @PairMultiTable2 d ON d.ID1 = c.ID1 and d.id2 = c.id2 

です

これは私にこのテーブルを与える：

ID1 ID2 Correlation 
1 1 1 
2 1 0.980387747360583 
3 1 -0.71935145479392 
1 2 0.980387747360583 
2 2 1 
3 2 -0.578754772354275 
1 3 -0.71935145479392 
2 3 -0.578754772354275 
3 3 1` 

今、私はこのような出力がしたい：

ID 1  2  3 
1 1 0.98 -0.72 
2 0.98 1 -0.58 
3 -0.72 -0.58 1 

Answer 1

DECLARE @MeanTable AS TABLE (Id INT, AvgRet NUMERIC(10,6)) 
DECLARE @SquareTable AS TABLE (Id INT, SqRoot NUMERIC(10,6)) 
DECLARE @RetTable AS TABLE (Id INT,RetDate DATE, Ret NUMERIC(10,6)) 
DECLARE @DiffRetAvgTable AS TABLE (Id INT, RetDate DATE, DiffRetAVG NUMERIC(10,6)) 
DECLARE @PairMultiTable AS TABLE (ID1 int, ID2 int,Exp2 NUMERIC(10,6)) 
DECLARE @PairMultiTable2 AS TABLE (ID1 int, ID2 int,SumPairMulti NUMERIC(10,6)) 
DECLARE @CorrTable AS TABLE (ID1 INT, ID2 INT, Correlation NUMERIC(10,6)) 

INSERT INTO @RetTable VALUES 
(1,'2017-08-31' ,-0.06272), 
(1,'2017-08-30' , 0.03265), 
(1,'2017-08-29' , -0.08636), 
(2,'2017-08-31' , -0.0331), 
(2,'2017-08-30' , 0.0329), 
(2,'2017-08-29' , -0.0324), 
(3,'2017-08-31' , -0.0179), 
(3,'2017-08-30' , -0.0183), 
(3,'2017-08-29' , -0.0152) 

--Step 1 : Get all the average by Items 
INSERT INTO @MeanTable SELECT ID, avg(Ret) AS avgRet FROM @RetTable GROUP BY ID 

--Step 2 : Substract the average from every occurence in each Item and call it DiffRetAvg 
INSERT INTO @DiffRetAvgTable SELECT a.ID,RetDate, ret-AvgRet AS DiffRetAvg FROM @RetTable a INNER JOIN @MeanTable b on a.Id = b.Id 

-- Step 3 Multiply each DiffRetAvg for each occurence by its correspondant for another occurence and call it SumPairMulti 
INSERT INTO @PairMultiTable2 
SELECT ID1 , ID2, sum(Multi) AS SumPairMulti FROM (
SELECT a.ID AS ID1, b.ID AS ID2, cast(a.ID AS NVARCHAR(3)) + '_' + cast(b.id AS NVARCHAR(3)) AS Pair_ID, a.Retdate , a.diffRetAvg*b.DiffRetAVG AS Multi FROM @DiffRetAvgTable a 
INNER JOIN @DiffRetAvgTable b on a.RetDate =b.RetDate) c 
GROUP BY ID1, ID2 

-- Step 4 Calculate the square of each DiffRetAvg for each occurence 
INSERT INTO @PairMultiTable 
SELECT ID1 , ID2, sum(Multi) AS Exp2 FROM (
SELECT a.ID AS ID1, b.ID AS ID2, a.Retdate , a.diffRetAvg*b.DiffRetAVG AS Multi FROM @DiffRetAvgTable a 
INNER JOIN @DiffRetAvgTable b ON a.RetDate =b.RetDate) c 
WHERE ID1=ID2 
GROUP BY ID1, ID2 

--Step 5 Calculate the correlation between each Item with this formula : SumPairMulti/sqrt(ID1_Exp2*ID2_EXP2) 
DELETE FROM CorrTable 
INSERT INTO CorrTable 
SELECT c.ID1, c.ID2, d.SumPairMulti/SQRTProd AS Correlation FROM (
SELECT a.ID1, b.ID2, sqrt(a.Exp2*b.Exp2) AS SQRTProd FROM @PairMultiTable a 
CROSS JOIN @PairMultiTable b) c 
INNER JOIN @PairMultiTable2 d ON d.ID1 = c.ID1 and d.id2 = c.id2 

--Step 6 Create Pivot Table using : 

SQL Server 2005 Pivot on Unknown Number of Columns

DECLARE @cols AS NVARCHAR(MAX), 
@query AS NVARCHAR(MAX) 
select @cols = STUFF((SELECT distinct ',' + QUOTENAME(ID2) 
      from CorrTable 
    FOR XML PATH(''), TYPE 
    ).value('.', 'NVARCHAR(MAX)') 
,1,1,'') 
set @query = 'SELECT ID1, ' + @cols + ' from 
     (
     select ID1, ID2, Correlation 
     from CorrTable 
    ) x 
    pivot 
    (
     min(Correlation) 
     for ID2 in (' + @cols + ') 
    ) p ' 
execute(@query)