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Fourier Analysis of SIL (Global X Silver Miners ETF)


SIL (Global X Silver Miners ETF) appears to have interesting cyclic behaviour every 25 weeks (2.1932*cosine), 15 weeks (1.5631*sine), and 24 weeks (1.3064*sine).

SIL (Global X Silver Miners ETF) has an average price of 45.17 (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 4/20/2010 to 1/17/2017 for SIL (Global X Silver Miners ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
045.17017   0 
11.34898 22.13293 (1*2π)/353353 weeks
2-1.66285 4.33441 (2*2π)/353177 weeks
3.24374 .15176 (3*2π)/353118 weeks
4-5.1667 -3.22589 (4*2π)/35388 weeks
5.01124 -3.05044 (5*2π)/35371 weeks
6-3.28797 -.39598 (6*2π)/35359 weeks
7-1.63615 -1.39199 (7*2π)/35350 weeks
81.57395 1.18061 (8*2π)/35344 weeks
9-1.71676 .85911 (9*2π)/35339 weeks
10.78055 .02353 (10*2π)/35335 weeks
111.29544 1.15666 (11*2π)/35332 weeks
12.0881 .82165 (12*2π)/35329 weeks
13-.64855 .11667 (13*2π)/35327 weeks
142.19323 -.32351 (14*2π)/35325 weeks
15-.18965 1.3064 (15*2π)/35324 weeks
161.02618 1.28455 (16*2π)/35322 weeks
17-.41276 -.09815 (17*2π)/35321 weeks
18-1.01197 -.2867 (18*2π)/35320 weeks
19-.26091 -.78409 (19*2π)/35319 weeks
20.20645 -.23257 (20*2π)/35318 weeks
21.4922 -.20606 (21*2π)/35317 weeks
22.80102 .25707 (22*2π)/35316 weeks
23-.24621 1.56308 (23*2π)/35315 weeks
24-.47029 .09071 (24*2π)/35315 weeks
25.09784 .0319 (25*2π)/35314 weeks
26.1564 .07583 (26*2π)/35314 weeks
27.01425 .15599 (27*2π)/35313 weeks
28.24288 -.38135 (28*2π)/35313 weeks
29-.08129 -.15832 (29*2π)/35312 weeks
30.61015 -.61052 (30*2π)/35312 weeks
31.33161 .24728 (31*2π)/35311 weeks
32-.12263 -.25402 (32*2π)/35311 weeks
33-.13372 .05626 (33*2π)/35311 weeks
34.44898 -.17943 (34*2π)/35310 weeks
35.25083 .66335 (35*2π)/35310 weeks
36-.2515 .28056 (36*2π)/35310 weeks
37.28517 .09623 (37*2π)/35310 weeks
38-.14731 -.53241 (38*2π)/3539 weeks
39.28625 -.29027 (39*2π)/3539 weeks
40.24561 -.12072 (40*2π)/3539 weeks
41.00216 .40918 (41*2π)/3539 weeks
42.01372 .2282 (42*2π)/3538 weeks
43-.09258 -.18964 (43*2π)/3538 weeks
44.4366 .09846 (44*2π)/3538 weeks
45-.0968 .25605 (45*2π)/3538 weeks
46-.28528 .17427 (46*2π)/3538 weeks
47.00721 -.36444 (47*2π)/3538 weeks
48.40867 -.57432 (48*2π)/3537 weeks
49.42957 -.01596 (49*2π)/3537 weeks
50.41656 .41444 (50*2π)/3537 weeks
51-.21468 .75523 (51*2π)/3537 weeks
52-.64455 .09069 (52*2π)/3537 weeks
53-.04417 -.50293 (53*2π)/3537 weeks
54.30938 -.06718 (54*2π)/3537 weeks
55.12651 .38864 (55*2π)/3536 weeks
56.13308 .12648 (56*2π)/3536 weeks
57-.07598 .03905 (57*2π)/3536 weeks
58-.00848 -.09625 (58*2π)/3536 weeks
59-.04901 .07578 (59*2π)/3536 weeks
60.14359 -.23169 (60*2π)/3536 weeks
61-.01559 .04552 (61*2π)/3536 weeks
62.14391 .04598 (62*2π)/3536 weeks
63.03985 .0324 (63*2π)/3536 weeks
64-.1719 -.22113 (64*2π)/3536 weeks
65-.02031 -.13205 (65*2π)/3535 weeks
66-.41109 -.18223 (66*2π)/3535 weeks
67-.05292 -.08387 (67*2π)/3535 weeks
68-.41169 .21268 (68*2π)/3535 weeks
69-.05027 -.13796 (69*2π)/3535 weeks
70-.05895 .23325 (70*2π)/3535 weeks
71.00306 .03822 (71*2π)/3535 weeks
72-.25192 .01729 (72*2π)/3535 weeks
73.02177 -.0638 (73*2π)/3535 weeks
74.05741 .11951 (74*2π)/3535 weeks
75.06846 -.02439 (75*2π)/3535 weeks
76-.00289 .05562 (76*2π)/3535 weeks
77.05601 -.10758 (77*2π)/3535 weeks
78.0614 .00257 (78*2π)/3535 weeks
79.01938 .03259 (79*2π)/3534 weeks
80.1954 .28646 (80*2π)/3534 weeks
81-.17871 .15799 (81*2π)/3534 weeks
82-.30532 .04148 (82*2π)/3534 weeks
83.18333 .00664 (83*2π)/3534 weeks
84.04334 -.06101 (84*2π)/3534 weeks
85.12358 -.03713 (85*2π)/3534 weeks
86-.06156 -.34183 (86*2π)/3534 weeks
87.57149 -.17967 (87*2π)/3534 weeks
88.25106 .25912 (88*2π)/3534 weeks
89.03276 .33404 (89*2π)/3534 weeks
90-.3071 .02907 (90*2π)/3534 weeks
91-.17362 -.24106 (91*2π)/3534 weeks
92.14791 .02462 (92*2π)/3534 weeks
93-.00161 .05178 (93*2π)/3534 weeks
94-.00685 .15667 (94*2π)/3534 weeks
95-.05091 -.02508 (95*2π)/3534 weeks
96.17343 -.0906 (96*2π)/3534 weeks
97-.02291 -.02507 (97*2π)/3534 weeks
98.12012 .07044 (98*2π)/3534 weeks
99.22741 -.00902 (99*2π)/3534 weeks
100-.00263 .08534 (100*2π)/3534 weeks
101.10889 .07705 (101*2π)/3533 weeks
102.04005 .07673 (102*2π)/3533 weeks
103-.1248 .24255 (103*2π)/3533 weeks
104.01379 -.07827 (104*2π)/3533 weeks
105-.13893 .13709 (105*2π)/3533 weeks
106.0384 -.16305 (106*2π)/3533 weeks
107.03807 -.0752 (107*2π)/3533 weeks
108.06355 -.01508 (108*2π)/3533 weeks
109-.07976 -.12425 (109*2π)/3533 weeks
110.13172 -.08887 (110*2π)/3533 weeks
111-.108 -.10462 (111*2π)/3533 weeks
112.01394 .00918 (112*2π)/3533 weeks
113-.04312 .03478 (113*2π)/3533 weeks
114.01434 .03643 (114*2π)/3533 weeks
115-.10698 .07609 (115*2π)/3533 weeks
116.12362 .01563 (116*2π)/3533 weeks
117.05642 .09691 (117*2π)/3533 weeks
118.11825 -.00104 (118*2π)/3533 weeks
119.04464 -.00201 (119*2π)/3533 weeks
120.19608 -.03922 (120*2π)/3533 weeks
121.09158 .10167 (121*2π)/3533 weeks
122-.02308 .02997 (122*2π)/3533 weeks
123-.01692 .04122 (123*2π)/3533 weeks
124.03295 -.14335 (124*2π)/3533 weeks
125.1301 -.15794 (125*2π)/3533 weeks
126.13751 -.00652 (126*2π)/3533 weeks
127.05063 .01836 (127*2π)/3533 weeks
128.02641 -.06329 (128*2π)/3533 weeks
129.06251 -.08625 (129*2π)/3533 weeks
130.13631 .0946 (130*2π)/3533 weeks
131-.0801 .16526 (131*2π)/3533 weeks
132-.13845 -.05031 (132*2π)/3533 weeks
133.0778 .06022 (133*2π)/3533 weeks
134.06297 .22312 (134*2π)/3533 weeks
135.14773 .11044 (135*2π)/3533 weeks
136-.04617 .10266 (136*2π)/3533 weeks
137-.08964 -.07598 (137*2π)/3533 weeks
138.11957 -.13331 (138*2π)/3533 weeks
139.12916 .07618 (139*2π)/3533 weeks
140.03366 -.0033 (140*2π)/3533 weeks
141.15471 .10154 (141*2π)/3533 weeks
142-.0146 .15366 (142*2π)/3532 weeks
143.04282 .12383 (143*2π)/3532 weeks
144-.10539 .09891 (144*2π)/3532 weeks
145-.09427 .02752 (145*2π)/3532 weeks
146.12002 -.15268 (146*2π)/3532 weeks
147.0631 .09788 (147*2π)/3532 weeks
148.14772 .04202 (148*2π)/3532 weeks
149.08748 .15356 (149*2π)/3532 weeks
150-.03889 -.01405 (150*2π)/3532 weeks
151-.00353 .12167 (151*2π)/3532 weeks
152-.11294 -.02548 (152*2π)/3532 weeks
153-.07292 -.09697 (153*2π)/3532 weeks
154.06465 -.16424 (154*2π)/3532 weeks
155.2076 -.08102 (155*2π)/3532 weeks
156.11336 .04399 (156*2π)/3532 weeks
157-.04731 .08097 (157*2π)/3532 weeks
158-.11785 .13697 (158*2π)/3532 weeks
159-.10395 -.03612 (159*2π)/3532 weeks
160-.11781 .03458 (160*2π)/3532 weeks
161-.11279 -.05393 (161*2π)/3532 weeks
162.04883 .12006 (162*2π)/3532 weeks
163-.10426 .00669 (163*2π)/3532 weeks
164.08599 -.06467 (164*2π)/3532 weeks
165.13883 .05623 (165*2π)/3532 weeks
166.00894 .16946 (166*2π)/3532 weeks
167-.04954 .07595 (167*2π)/3532 weeks
168.00755 -.05666 (168*2π)/3532 weeks
169-.06767 .11673 (169*2π)/3532 weeks
170-.00947 .13172 (170*2π)/3532 weeks
171-.0924 .21981 (171*2π)/3532 weeks
172-.22998 .0479 (172*2π)/3532 weeks
173-.03208 -.01058 (173*2π)/3532 weeks
174.08673 -.09147 (174*2π)/3532 weeks
175-.00917 .07535 (175*2π)/3532 weeks
176-.02022 .09473 (176*2π)/3532 weeks
177-.02022 -.09473 (177*2π)/3532 weeks
178-.00917 -.07535 (178*2π)/3532 weeks
179.08673 .09147 (179*2π)/3532 weeks
180-.03208 .01058 (180*2π)/3532 weeks
181-.22998 -.0479 (181*2π)/3532 weeks
182-.0924 -.21981 (182*2π)/3532 weeks
183-.00947 -.13172 (183*2π)/3532 weeks
184-.06767 -.11673 (184*2π)/3532 weeks
185.00755 .05666 (185*2π)/3532 weeks
186-.04954 -.07595 (186*2π)/3532 weeks
187.00894 -.16946 (187*2π)/3532 weeks
188.13883 -.05623 (188*2π)/3532 weeks
189.08599 .06467 (189*2π)/3532 weeks
190-.10426 -.00669 (190*2π)/3532 weeks
191.04883 -.12006 (191*2π)/3532 weeks
192-.11279 .05393 (192*2π)/3532 weeks
193-.11781 -.03458 (193*2π)/3532 weeks
194-.10395 .03612 (194*2π)/3532 weeks
195-.11785 -.13697 (195*2π)/3532 weeks
196-.04731 -.08097 (196*2π)/3532 weeks
197.11336 -.04399 (197*2π)/3532 weeks
198.2076 .08102 (198*2π)/3532 weeks
199.06465 .16424 (199*2π)/3532 weeks
200-.07292 .09697 (200*2π)/3532 weeks
201-.11294 .02548 (201*2π)/3532 weeks
202-.00353 -.12167 (202*2π)/3532 weeks
203-.03889 .01405 (203*2π)/3532 weeks
204.08748 -.15356 (204*2π)/3532 weeks
205.14772 -.04202 (205*2π)/3532 weeks
206.0631 -.09788 (206*2π)/3532 weeks
207.12002 .15268 (207*2π)/3532 weeks
208-.09427 -.02752 (208*2π)/3532 weeks
209-.10539 -.09891 (209*2π)/3532 weeks
210.04282 -.12383 (210*2π)/3532 weeks
211-.0146 -.15366 (211*2π)/3532 weeks
212.15471 -.10154 (212*2π)/3532 weeks
213.03366 .0033 (213*2π)/3532 weeks
214.12916 -.07618 (214*2π)/3532 weeks
215.11957 .13331 (215*2π)/3532 weeks
216-.08964 .07598 (216*2π)/3532 weeks
217-.04617 -.10266 (217*2π)/3532 weeks
218.14773 -.11044 (218*2π)/3532 weeks
219.06297 -.22312 (219*2π)/3532 weeks
220.0778 -.06022 (220*2π)/3532 weeks
221-.13845 .05031 (221*2π)/3532 weeks
222-.0801 -.16526 (222*2π)/3532 weeks
223.13631 -.0946 (223*2π)/3532 weeks
224.06251 .08625 (224*2π)/3532 weeks
225.02641 .06329 (225*2π)/3532 weeks
226.05063 -.01836 (226*2π)/3532 weeks
227.13751 .00652 (227*2π)/3532 weeks
228.1301 .15794 (228*2π)/3532 weeks
229.03295 .14335 (229*2π)/3532 weeks
230-.01692 -.04122 (230*2π)/3532 weeks
231-.02308 -.02997 (231*2π)/3532 weeks
232.09158 -.10167 (232*2π)/3532 weeks
233.19608 .03922 (233*2π)/3532 weeks
234.04464 .00201 (234*2π)/3532 weeks
235.11825 .00104 (235*2π)/3532 weeks
236.05642 -.09691 (236*2π)/3531 weeks
237.12362 -.01563 (237*2π)/3531 weeks
238-.10698 -.07609 (238*2π)/3531 weeks
239.01434 -.03643 (239*2π)/3531 weeks
240-.04312 -.03478 (240*2π)/3531 weeks
241.01394 -.00918 (241*2π)/3531 weeks
242-.108 .10462 (242*2π)/3531 weeks
243.13172 .08887 (243*2π)/3531 weeks
244-.07976 .12425 (244*2π)/3531 weeks
245.06355 .01508 (245*2π)/3531 weeks
246.03807 .0752 (246*2π)/3531 weeks
247.0384 .16305 (247*2π)/3531 weeks
248-.13893 -.13709 (248*2π)/3531 weeks
249.01379 .07827 (249*2π)/3531 weeks
250-.1248 -.24255 (250*2π)/3531 weeks
251.04005 -.07673 (251*2π)/3531 weeks
252.10889 -.07705 (252*2π)/3531 weeks
253-.00263 -.08534 (253*2π)/3531 weeks
254.22741 .00902 (254*2π)/3531 weeks
255.12012 -.07044 (255*2π)/3531 weeks
256-.02291 .02507 (256*2π)/3531 weeks
257.17343 .0906 (257*2π)/3531 weeks
258-.05091 .02508 (258*2π)/3531 weeks
259-.00685 -.15667 (259*2π)/3531 weeks
260-.00161 -.05178 (260*2π)/3531 weeks
261.14791 -.02462 (261*2π)/3531 weeks
262-.17362 .24106 (262*2π)/3531 weeks
263-.3071 -.02907 (263*2π)/3531 weeks
264.03276 -.33404 (264*2π)/3531 weeks
265.25106 -.25912 (265*2π)/3531 weeks
266.57149 .17967 (266*2π)/3531 weeks
267-.06156 .34183 (267*2π)/3531 weeks
268.12358 .03713 (268*2π)/3531 weeks
269.04334 .06101 (269*2π)/3531 weeks
270.18333 -.00664 (270*2π)/3531 weeks
271-.30532 -.04148 (271*2π)/3531 weeks
272-.17871 -.15799 (272*2π)/3531 weeks
273.1954 -.28646 (273*2π)/3531 weeks
274.01938 -.03259 (274*2π)/3531 weeks
275.0614 -.00257 (275*2π)/3531 weeks
276.05601 .10758 (276*2π)/3531 weeks
277-.00289 -.05562 (277*2π)/3531 weeks
278.06846 .02439 (278*2π)/3531 weeks
279.05741 -.11951 (279*2π)/3531 weeks
280.02177 .0638 (280*2π)/3531 weeks
281-.25192 -.01729 (281*2π)/3531 weeks
282.00306 -.03822 (282*2π)/3531 weeks
283-.05895 -.23325 (283*2π)/3531 weeks
284-.05027 .13796 (284*2π)/3531 weeks
285-.41169 -.21268 (285*2π)/3531 weeks
286-.05292 .08387 (286*2π)/3531 weeks
287-.41109 .18223 (287*2π)/3531 weeks
288-.02031 .13205 (288*2π)/3531 weeks
289-.1719 .22113 (289*2π)/3531 weeks
290.03985 -.0324 (290*2π)/3531 weeks
291.14391 -.04598 (291*2π)/3531 weeks
292-.01559 -.04552 (292*2π)/3531 weeks
293.14359 .23169 (293*2π)/3531 weeks
294-.04901 -.07578 (294*2π)/3531 weeks
295-.00848 .09625 (295*2π)/3531 weeks
296-.07598 -.03905 (296*2π)/3531 weeks
297.13308 -.12648 (297*2π)/3531 weeks
298.12651 -.38864 (298*2π)/3531 weeks
299.30938 .06718 (299*2π)/3531 weeks
300-.04417 .50293 (300*2π)/3531 weeks
301-.64455 -.09069 (301*2π)/3531 weeks
302-.21468 -.75523 (302*2π)/3531 weeks
303.41656 -.41444 (303*2π)/3531 weeks
304.42957 .01596 (304*2π)/3531 weeks
305.40867 .57432 (305*2π)/3531 weeks
306.00721 .36444 (306*2π)/3531 weeks
307-.28528 -.17427 (307*2π)/3531 weeks
308-.0968 -.25605 (308*2π)/3531 weeks
309.4366 -.09846 (309*2π)/3531 weeks
310-.09258 .18964 (310*2π)/3531 weeks
311.01372 -.2282 (311*2π)/3531 weeks
312.00216 -.40918 (312*2π)/3531 weeks
313.24561 .12072 (313*2π)/3531 weeks
314.28625 .29027 (314*2π)/3531 weeks
315-.14731 .53241 (315*2π)/3531 weeks
316.28517 -.09623 (316*2π)/3531 weeks
317-.2515 -.28056 (317*2π)/3531 weeks
318.25083 -.66335 (318*2π)/3531 weeks
319.44898 .17943 (319*2π)/3531 weeks
320-.13372 -.05626 (320*2π)/3531 weeks
321-.12263 .25402 (321*2π)/3531 weeks
322.33161 -.24728 (322*2π)/3531 weeks
323.61015 .61052 (323*2π)/3531 weeks
324-.08129 .15832 (324*2π)/3531 weeks
325.24288 .38135 (325*2π)/3531 weeks
326.01425 -.15599 (326*2π)/3531 weeks
327.1564 -.07583 (327*2π)/3531 weeks
328.09784 -.0319 (328*2π)/3531 weeks
329-.47029 -.09071 (329*2π)/3531 weeks
330-.24621 -1.56308 (330*2π)/3531 weeks
331.80102 -.25707 (331*2π)/3531 weeks
332.4922 .20606 (332*2π)/3531 weeks
333.20645 .23257 (333*2π)/3531 weeks
334-.26091 .78409 (334*2π)/3531 weeks
335-1.01197 .2867 (335*2π)/3531 weeks
336-.41276 .09815 (336*2π)/3531 weeks
3371.02618 -1.28455 (337*2π)/3531 weeks
338-.18965 -1.3064 (338*2π)/3531 weeks
3392.19323 .32351 (339*2π)/3531 weeks
340-.64855 -.11667 (340*2π)/3531 weeks
341.0881 -.82165 (341*2π)/3531 weeks
3421.29544 -1.15666 (342*2π)/3531 weeks
343.78055 -.02353 (343*2π)/3531 weeks
344-1.71676 -.85911 (344*2π)/3531 weeks
3451.57395 -1.18061 (345*2π)/3531 weeks
346-1.63615 1.39199 (346*2π)/3531 weeks
347-3.28797 .39598 (347*2π)/3531 weeks
348.01124 3.05044 (348*2π)/3531 weeks
349-5.1667 3.22589 (349*2π)/3531 weeks
350.24374 -.15176 (350*2π)/3531 weeks
351-1.66285 -4.33441 (351*2π)/3531 weeks

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