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Fourier Analysis of ASHR (Deutsche X-Trackers Harvest CSI)


ASHR (Deutsche X-Trackers Harvest CSI) appears to have interesting cyclic behaviour every 16 weeks (.7124*sine), 11 weeks (.4319*cosine), and 6 weeks (.2622*cosine).

ASHR (Deutsche X-Trackers Harvest CSI) has an average price of 24.23 (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 11/6/2013 to 11/21/2016 for ASHR (Deutsche X-Trackers Harvest CSI), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
024.22838   0 
1-5.4195 -3.02409 (1*2π)/160160 weeks
23.63493 -1.54586 (2*2π)/16080 weeks
3-1.05402 -.33421 (3*2π)/16053 weeks
4.99657 -.78761 (4*2π)/16040 weeks
5-1.02921 -.28892 (5*2π)/16032 weeks
61.15559 .18155 (6*2π)/16027 weeks
7-1.06755 -1.01579 (7*2π)/16023 weeks
8.47312 .3567 (8*2π)/16020 weeks
9.07587 .2194 (9*2π)/16018 weeks
10-.04524 -.71237 (10*2π)/16016 weeks
11.05135 -.02604 (11*2π)/16015 weeks
12-.12263 -.03337 (12*2π)/16013 weeks
13.03096 -.11674 (13*2π)/16012 weeks
14.19431 -.13779 (14*2π)/16011 weeks
15-.43187 -.1942 (15*2π)/16011 weeks
16.14441 .17267 (16*2π)/16010 weeks
17-.11362 -.36154 (17*2π)/1609 weeks
18-.22683 .1513 (18*2π)/1609 weeks
19.01803 -.28298 (19*2π)/1608 weeks
20-.0482 -.00207 (20*2π)/1608 weeks
21.01905 -.35562 (21*2π)/1608 weeks
22-.15566 .18641 (22*2π)/1607 weeks
23.16398 -.16406 (23*2π)/1607 weeks
24-.1217 -.02188 (24*2π)/1607 weeks
25.0231 -.10278 (25*2π)/1606 weeks
26-.07086 -.0493 (26*2π)/1606 weeks
27-.07816 -.16949 (27*2π)/1606 weeks
28-.26216 -.04866 (28*2π)/1606 weeks
29.12184 -.02249 (29*2π)/1606 weeks
30-.16007 -.01527 (30*2π)/1605 weeks
31.08019 -.15376 (31*2π)/1605 weeks
32-.18868 .05146 (32*2π)/1605 weeks
33.18121 -.23239 (33*2π)/1605 weeks
34-.20523 -.1033 (34*2π)/1605 weeks
35-.02088 .08809 (35*2π)/1605 weeks
36.02147 -.18069 (36*2π)/1604 weeks
37-.10748 .04474 (37*2π)/1604 weeks
38.03428 -.09382 (38*2π)/1604 weeks
39-.16272 .09072 (39*2π)/1604 weeks
40.11609 -.19791 (40*2π)/1604 weeks
41-.17897 -.00463 (41*2π)/1604 weeks
42.02369 -.02185 (42*2π)/1604 weeks
43.04774 -.06597 (43*2π)/1604 weeks
44-.02355 -.04605 (44*2π)/1604 weeks
45-.12097 -.03998 (45*2π)/1604 weeks
46.05095 .03684 (46*2π)/1603 weeks
47-.10821 -.03264 (47*2π)/1603 weeks
48.00917 -.06156 (48*2π)/1603 weeks
49-.13187 .10913 (49*2π)/1603 weeks
50.04876 -.12821 (50*2π)/1603 weeks
51-.16918 -.01719 (51*2π)/1603 weeks
52.10432 -.00358 (52*2π)/1603 weeks
53-.1982 -.01365 (53*2π)/1603 weeks
54.06987 -.08187 (54*2π)/1603 weeks
55-.16823 -.04249 (55*2π)/1603 weeks
56.05502 -.07565 (56*2π)/1603 weeks
57-.10581 .0231 (57*2π)/1603 weeks
58.02837 -.06519 (58*2π)/1603 weeks
59-.13558 .00659 (59*2π)/1603 weeks
60.00675 .002 (60*2π)/1603 weeks
61-.04861 -.00079 (61*2π)/1603 weeks
62-.1074 -.01359 (62*2π)/1603 weeks
63.07321 -.09973 (63*2π)/1603 weeks
64-.14946 .0235 (64*2π)/1603 weeks
65-.03111 -.05182 (65*2π)/1602 weeks
66.02425 -.07731 (66*2π)/1602 weeks
67-.14937 .07637 (67*2π)/1602 weeks
68.04062 -.04785 (68*2π)/1602 weeks
69-.1089 -.04751 (69*2π)/1602 weeks
70-.05545 .0798 (70*2π)/1602 weeks
71-.05326 -.12452 (71*2π)/1602 weeks
72-.07043 .08106 (72*2π)/1602 weeks
73-.07965 .048 (73*2π)/1602 weeks
74.0774 -.00754 (74*2π)/1602 weeks
75-.07852 -.14106 (75*2π)/1602 weeks
76-.18344 .04564 (76*2π)/1602 weeks
77-.01267 .05811 (77*2π)/1602 weeks
78.01036 -.05129 (78*2π)/1602 weeks
79-.16029 .03727 (79*2π)/1602 weeks
80.0099   (80*2π)/1602 weeks
81-.16029 -.03727 (81*2π)/1602 weeks
82.01036 .05129 (82*2π)/1602 weeks
83-.01267 -.05811 (83*2π)/1602 weeks
84-.18344 -.04564 (84*2π)/1602 weeks
85-.07852 .14106 (85*2π)/1602 weeks
86.0774 .00754 (86*2π)/1602 weeks
87-.07965 -.048 (87*2π)/1602 weeks
88-.07043 -.08106 (88*2π)/1602 weeks
89-.05326 .12452 (89*2π)/1602 weeks
90-.05545 -.0798 (90*2π)/1602 weeks
91-.1089 .04751 (91*2π)/1602 weeks
92.04062 .04785 (92*2π)/1602 weeks
93-.14937 -.07637 (93*2π)/1602 weeks
94.02425 .07731 (94*2π)/1602 weeks
95-.03111 .05182 (95*2π)/1602 weeks
96-.14946 -.0235 (96*2π)/1602 weeks
97.07321 .09973 (97*2π)/1602 weeks
98-.1074 .01359 (98*2π)/1602 weeks
99-.04861 .00079 (99*2π)/1602 weeks
100.00675 -.002 (100*2π)/1602 weeks
101-.13558 -.00659 (101*2π)/1602 weeks
102.02837 .06519 (102*2π)/1602 weeks
103-.10581 -.0231 (103*2π)/1602 weeks
104.05502 .07565 (104*2π)/1602 weeks
105-.16823 .04249 (105*2π)/1602 weeks
106.06987 .08187 (106*2π)/1602 weeks
107-.1982 .01365 (107*2π)/1601 weeks
108.10432 .00358 (108*2π)/1601 weeks
109-.16918 .01719 (109*2π)/1601 weeks
110.04876 .12821 (110*2π)/1601 weeks
111-.13187 -.10913 (111*2π)/1601 weeks
112.00917 .06156 (112*2π)/1601 weeks
113-.10821 .03264 (113*2π)/1601 weeks
114.05095 -.03684 (114*2π)/1601 weeks
115-.12097 .03998 (115*2π)/1601 weeks
116-.02355 .04605 (116*2π)/1601 weeks
117.04774 .06597 (117*2π)/1601 weeks
118.02369 .02185 (118*2π)/1601 weeks
119-.17897 .00463 (119*2π)/1601 weeks
120.11609 .19791 (120*2π)/1601 weeks
121-.16272 -.09072 (121*2π)/1601 weeks
122.03428 .09382 (122*2π)/1601 weeks
123-.10748 -.04474 (123*2π)/1601 weeks
124.02147 .18069 (124*2π)/1601 weeks
125-.02088 -.08809 (125*2π)/1601 weeks
126-.20523 .1033 (126*2π)/1601 weeks
127.18121 .23239 (127*2π)/1601 weeks
128-.18868 -.05146 (128*2π)/1601 weeks
129.08019 .15376 (129*2π)/1601 weeks
130-.16007 .01527 (130*2π)/1601 weeks
131.12184 .02249 (131*2π)/1601 weeks
132-.26216 .04866 (132*2π)/1601 weeks
133-.07816 .16949 (133*2π)/1601 weeks
134-.07086 .0493 (134*2π)/1601 weeks
135.0231 .10278 (135*2π)/1601 weeks
136-.1217 .02188 (136*2π)/1601 weeks
137.16398 .16406 (137*2π)/1601 weeks
138-.15566 -.18641 (138*2π)/1601 weeks
139.01905 .35562 (139*2π)/1601 weeks
140-.0482 .00207 (140*2π)/1601 weeks
141.01803 .28298 (141*2π)/1601 weeks
142-.22683 -.1513 (142*2π)/1601 weeks
143-.11362 .36154 (143*2π)/1601 weeks
144.14441 -.17267 (144*2π)/1601 weeks
145-.43187 .1942 (145*2π)/1601 weeks
146.19431 .13779 (146*2π)/1601 weeks
147.03096 .11674 (147*2π)/1601 weeks
148-.12263 .03337 (148*2π)/1601 weeks
149.05135 .02604 (149*2π)/1601 weeks
150-.04524 .71237 (150*2π)/1601 weeks
151.07587 -.2194 (151*2π)/1601 weeks
152.47312 -.3567 (152*2π)/1601 weeks
153-1.06755 1.01579 (153*2π)/1601 weeks
1541.15559 -.18155 (154*2π)/1601 weeks
155-1.02921 .28892 (155*2π)/1601 weeks
156.99657 .78761 (156*2π)/1601 weeks
157-1.05402 .33421 (157*2π)/1601 weeks
1583.63493 1.54586 (158*2π)/1601 weeks

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