A MULTIPLE CORRELATION INDEX: CORRUPTION AND EXTENSION OF THE ORIGINAL PEARSON PRODUCT (PART 2)

As a follow-up. Here we have got 3 time series featuring 3 different kind of shares. The first share belongs to a fabric corporation, the second share belongs to a petroleum corporation and the third share belongs to a grocery corporation. The skewed Pearson Correlation indexes for each couple are: 0.6651, 0.6727 and 0.6427. Now the raw average price for each trading day:

FABRICS	OIL & GAS	GROCERIES
65,10	3.869,42	24.077,00
68,27	3.860,90	23.843,18
71,08	3.791,27	23.674,54
70,86	3.746,08	23.665,48
69,61	3.698,01	23.084,56
70,91	3.617,88	22.495,30
71,63	3.579,54	22.094,81
71,07	3.621,66	21.910,14
68,17	3.595,94	21.711,46
68,35	3.575,26	21.307,96
69,02	3.597,24	21.226,38
70,87	3.690,66	21.880,14
72,31	3.706,20	22.729,31
71,49	3.699,86	22.932,26
70,44	3.790,14	22.910,22
71,32	3.743,88	23.499,11
72,44	3.740,50	23.422,12
73,95	3.749,48	23.600,99
73,46	3.742,19	23.406,75
73,37	3.738,92	23.806,03
71,75	3.733,71	24.173,57
71,22	3.710,75	24.086,27
70,72	3.694,24	23.794,90
70,97	3.654,79	23.952,48
68,35	3.600,30	23.804,88
71,02	3.643,38	23.920,07
69,56	3.669,10	23.981,40
71,69	3.678,68	24.109,30
73,16	3.702,06	23.275,96
75,38	3.706,62	23.455,27
75,64	3.706,42	23.844,62
72,86	3610,87	23581,93
73,59	3605,19	23347,24
73,2	3623,37	23691,06
74,9	3651,15	23945,73
74,81	3660,14	24018,57
74,02	3619,38	23866,32
74,42	3641,45	23687,05
75,26	3759,57	24152,72
73,89	3856,61	24147,52
74,06	3870,49	22968,05
72,59	3892,56	23028,89
71,37	3873,3	23080,17
71,43	3803,2	22524,51
71,86	3834,58	23072,63
72,88	3884,78	23563,11
74,02	3867,9	23573,5
72,97	3842,18	23059,16
72,42	3818,36	23000,79
73,41	3866,75	22993,5
73,6	3894,27	22867,91
73,41	3976	23010,92
73,82	4069,19	23521,07
72,9	4090,19	23850,26
73,26	4144,15	24071,89
72,75	4081,99	23994,51
71,69	3878,94	23556,18
73,28	3848,36	23504,43
73,27	3836,8	23132,36
74,45	3919,65	23013,05
73,42	3888,22	23005,2
72,2	3926,04	22917,16
71,37	3887,87	22790,82
71,64	3834,56	22889,26
71,49	3774,58	22940,21
71,79	3927,68	22868,54
73,05	3930	22894,61
73,47	3902,05	23020,61
73,45	3915,34	23126,91
72,46	3901,71	23002,63
71,94	3911,94	23014,98
71,91	3900,49	22954,69
70,88	3942,77	22907,7
70,06	3932,33	22786
70,34	3947,59	22737,64
69,22	3951,29	22939,9
71,04	3994,35	23320,87
71,25	4014,27	24242,4
70,51	4027,99	24132,24
71,06	3999,16	23899,82
71,5	4060,33	23954,47
70,97	4044,01	23729,92
70,43	4016,05	23837,89
70,31	3974,01	23793,8
70,09	4010,84	23962,9
71,16	4037,01	24234,67
72,13	4023,77	24221,85
72,95	4066,31	24413
72,3	4046,55	24169,03
72,61	4021,81	24219,63
73,88	4024,89	24229,18
75,24	4012,94	24247,06
75,29	4004,14	24537,92
76,19	3986,96	24893,58
75,41	3981,21	24682,99
74,02	3932,97	24455,89
74,56	3934,09	24438,97
74,22	3874,82	23722,63
74,85	3862,77	23756,54
74,53	3893,18	23765,09
75,59	3994,93	23944,58
76,67	4039,33	23810,71
77,06	4080,31	23797,53
77,48	4110,17	23891,81
77,62	4171,82	24361,05
78,58	4184,78	24687,21
78,94	4103,64	24094,74
79,11	4123,51	24384,35
79,41	4154,09	24422,02
78,26	4142,23	24427,63
79,06	4177,08	24639,66
78,55	4125,09	24376,14
79,34	4144,72	24284,61
80,05	4152,71	24275,73
80,93	4160,73	24352,85
82,21	4190,32	24447,54
82,99	4237,14	24788,28
83,92	4285,22	25196,38
84,17	4286,16	25833,83
83,5	4224,51	25615,49
82,94	4255,18	25325,63
83,34	4280,31	25497,93
83,75	4249,61	25478,48

 

As we explained previously, Both covariance and correlation are measures of SECOND DEGREE. Every isolated line with a product MUST BE turned into its SECOND DEGREE twin. How? Read the following example:

If we know the averages of each set we have to proceed to calculate the differentials as seen on the regular covariance formula. The first line of our "threesome" turns out to be: -8.6254, -34.3924, 409.5620

In order to apply a transformation/conversion we need to use the absolute values. The product of our "threesome" is equal to 121496.645. This is a third-degree value and we need a second-degree one.

121496.645^(2/3) = -2453.0676 Why the negative condition if 2 of the arguments are negative?

RULE OF THUMB: The algebraic law of products is not respected here. We have to apply Boolean Logics. If all of the differentials display the same symbol, the final value is positive. If at least one of the differentials displays a symbol not equal to the remaining arguments, so therefore, the final value is negative.

The skewed covariance is: 3630.2961

The standard deviations of each series are: 3.7080, 185.9578 and 814.4545

Again, the product after the 3 standard deviations has to be rewritten in second-degree

The skewed and consolidated correlation is:

0,5333257994

Why the final value is lesser than the regular coupled-pearson index? We have enhanced the probability space and the number of coincidences are fewer than those watched while our sets are studied as couples.

Sources: RiskCenter, Investopedia, Wikipedia, EdX.org, Coursera.org