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Fourier Analysis of CN (Deutsche X-trackers MSCI All Ch)


CN (Deutsche X-trackers MSCI All Ch) appears to have interesting cyclic behaviour every 7 weeks (.3756*sine), 10 weeks (.3082*cosine), and 9 weeks (.3073*cosine).

CN (Deutsche X-trackers MSCI All Ch) has an average price of 26.33 (topmost row, frequency = 0).



Click on the checkboxes shown on the right to see how the various frequencies contribute to the graph. Look for large magnitude coefficients (sine or cosine), as these are associated with frequencies which contribute most to the associated stock plot. If you find a large magnitude coefficient which dramatically changes the graph, look at the associated "Period" in weeks, as you may have found a significant recurring cycle for the stock of interest.

Right click on the graph above to see the menu of operations (download, full screen, etc.)

Fourier Analysis

Using data from 4/30/2014 to 1/9/2017 for CN (Deutsche X-trackers MSCI All Ch), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
026.32591   0 
1-2.8433 .81603 (1*2π)/142142 weeks
2.12272 -3.6997 (2*2π)/14271 weeks
3.33684 -.22081 (3*2π)/14247 weeks
4-1.43443 -.59814 (4*2π)/14236 weeks
5.84609 -.77979 (5*2π)/14228 weeks
6-1.20125 .45263 (6*2π)/14224 weeks
7.51327 -.90298 (7*2π)/14220 weeks
8.0007 -.62469 (8*2π)/14218 weeks
9.03221 .19821 (9*2π)/14216 weeks
10-.05082 -.26908 (10*2π)/14214 weeks
11-.01342 -.22115 (11*2π)/14213 weeks
12-.25483 -.15187 (12*2π)/14212 weeks
13.17339 -.06241 (13*2π)/14211 weeks
14-.30822 -.27494 (14*2π)/14210 weeks
15.23768 -.01312 (15*2π)/1429 weeks
16-.30729 -.17663 (16*2π)/1429 weeks
17.1272 -.14418 (17*2π)/1428 weeks
18-.00418 .0408 (18*2π)/1428 weeks
19-.15164 -.37562 (19*2π)/1427 weeks
20.1422 .05664 (20*2π)/1427 weeks
21-.04834 -.1656 (21*2π)/1427 weeks
22.05092 -.18768 (22*2π)/1426 weeks
23.02783 -.14203 (23*2π)/1426 weeks
24-.14041 -.11893 (24*2π)/1426 weeks
25.03742 .02025 (25*2π)/1426 weeks
26-.08396 -.25861 (26*2π)/1425 weeks
27-.06328 -.21851 (27*2π)/1425 weeks
28-.04149 -.0056 (28*2π)/1425 weeks
29-.24484 -.26727 (29*2π)/1425 weeks
30.05197 .06023 (30*2π)/1425 weeks
31-.11042 -.24434 (31*2π)/1425 weeks
32-.06062 .05717 (32*2π)/1424 weeks
33-.10319 -.12864 (33*2π)/1424 weeks
34.01232 -.043 (34*2π)/1424 weeks
35-.22863 .0244 (35*2π)/1424 weeks
36.04278 -.13881 (36*2π)/1424 weeks
37-.11499 -.03621 (37*2π)/1424 weeks
38-.02393 .02121 (38*2π)/1424 weeks
39-.01614 -.0867 (39*2π)/1424 weeks
40-.18429 -.06941 (40*2π)/1424 weeks
41.00675 -.05769 (41*2π)/1423 weeks
42-.0771 .02661 (42*2π)/1423 weeks
43-.12915 -.03758 (43*2π)/1423 weeks
44.06485 -.13632 (44*2π)/1423 weeks
45-.10993 .00335 (45*2π)/1423 weeks
46.02287 -.16418 (46*2π)/1423 weeks
47-.00825 .07069 (47*2π)/1423 weeks
48-.13758 -.04712 (48*2π)/1423 weeks
49.06492 -.075 (49*2π)/1423 weeks
50-.07777 .07728 (50*2π)/1423 weeks
51-.10191 -.12205 (51*2π)/1423 weeks
52-.02763 .03046 (52*2π)/1423 weeks
53-.10261 -.03442 (53*2π)/1423 weeks
54-.07545 -.02597 (54*2π)/1423 weeks
55-.02696 -.0757 (55*2π)/1423 weeks
56.0018 .07224 (56*2π)/1423 weeks
57-.12172 .00463 (57*2π)/1422 weeks
58-.06346 -.0277 (58*2π)/1422 weeks
59-.05551 -.11332 (59*2π)/1422 weeks
60-.0104 .05045 (60*2π)/1422 weeks
61-.1014 -.04709 (61*2π)/1422 weeks
62-.05106 .05819 (62*2π)/1422 weeks
63-.12165 -.07743 (63*2π)/1422 weeks
64.03668 .05979 (64*2π)/1422 weeks
65-.0018 .01986 (65*2π)/1422 weeks
66-.11187 -.10915 (66*2π)/1422 weeks
67-.06284 .11997 (67*2π)/1422 weeks
68.02842 -.04941 (68*2π)/1422 weeks
69-.13347 -.08263 (69*2π)/1422 weeks
70.02974 .02853 (70*2π)/1422 weeks
71-.13074   (71*2π)/1422 weeks
72.02974 -.02853 (72*2π)/1422 weeks
73-.13347 .08263 (73*2π)/1422 weeks
74.02842 .04941 (74*2π)/1422 weeks
75-.06284 -.11997 (75*2π)/1422 weeks
76-.11187 .10915 (76*2π)/1422 weeks
77-.0018 -.01986 (77*2π)/1422 weeks
78.03668 -.05979 (78*2π)/1422 weeks
79-.12165 .07743 (79*2π)/1422 weeks
80-.05106 -.05819 (80*2π)/1422 weeks
81-.1014 .04709 (81*2π)/1422 weeks
82-.0104 -.05045 (82*2π)/1422 weeks
83-.05551 .11332 (83*2π)/1422 weeks
84-.06346 .0277 (84*2π)/1422 weeks
85-.12172 -.00463 (85*2π)/1422 weeks
86.0018 -.07224 (86*2π)/1422 weeks
87-.02696 .0757 (87*2π)/1422 weeks
88-.07545 .02597 (88*2π)/1422 weeks
89-.10261 .03442 (89*2π)/1422 weeks
90-.02763 -.03046 (90*2π)/1422 weeks
91-.10191 .12205 (91*2π)/1422 weeks
92-.07777 -.07728 (92*2π)/1422 weeks
93.06492 .075 (93*2π)/1422 weeks
94-.13758 .04712 (94*2π)/1422 weeks
95-.00825 -.07069 (95*2π)/1421 weeks
96.02287 .16418 (96*2π)/1421 weeks
97-.10993 -.00335 (97*2π)/1421 weeks
98.06485 .13632 (98*2π)/1421 weeks
99-.12915 .03758 (99*2π)/1421 weeks
100-.0771 -.02661 (100*2π)/1421 weeks
101.00675 .05769 (101*2π)/1421 weeks
102-.18429 .06941 (102*2π)/1421 weeks
103-.01614 .0867 (103*2π)/1421 weeks
104-.02393 -.02121 (104*2π)/1421 weeks
105-.11499 .03621 (105*2π)/1421 weeks
106.04278 .13881 (106*2π)/1421 weeks
107-.22863 -.0244 (107*2π)/1421 weeks
108.01232 .043 (108*2π)/1421 weeks
109-.10319 .12864 (109*2π)/1421 weeks
110-.06062 -.05717 (110*2π)/1421 weeks
111-.11042 .24434 (111*2π)/1421 weeks
112.05197 -.06023 (112*2π)/1421 weeks
113-.24484 .26727 (113*2π)/1421 weeks
114-.04149 .0056 (114*2π)/1421 weeks
115-.06328 .21851 (115*2π)/1421 weeks
116-.08396 .25861 (116*2π)/1421 weeks
117.03742 -.02025 (117*2π)/1421 weeks
118-.14041 .11893 (118*2π)/1421 weeks
119.02783 .14203 (119*2π)/1421 weeks
120.05092 .18768 (120*2π)/1421 weeks
121-.04834 .1656 (121*2π)/1421 weeks
122.1422 -.05664 (122*2π)/1421 weeks
123-.15164 .37562 (123*2π)/1421 weeks
124-.00418 -.0408 (124*2π)/1421 weeks
125.1272 .14418 (125*2π)/1421 weeks
126-.30729 .17663 (126*2π)/1421 weeks
127.23768 .01312 (127*2π)/1421 weeks
128-.30822 .27494 (128*2π)/1421 weeks
129.17339 .06241 (129*2π)/1421 weeks
130-.25483 .15187 (130*2π)/1421 weeks
131-.01342 .22115 (131*2π)/1421 weeks
132-.05082 .26908 (132*2π)/1421 weeks
133.03221 -.19821 (133*2π)/1421 weeks
134.0007 .62469 (134*2π)/1421 weeks
135.51327 .90298 (135*2π)/1421 weeks
136-1.20125 -.45263 (136*2π)/1421 weeks
137.84609 .77979 (137*2π)/1421 weeks
138-1.43443 .59814 (138*2π)/1421 weeks
139.33684 .22081 (139*2π)/1421 weeks
140.12272 3.6997 (140*2π)/1421 weeks

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