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# Fourier Analysis of USERX (US Global Gold and Precious Met)

USERX (US Global Gold and Precious Met) appears to have interesting cyclic behaviour every 108 weeks (.4843*sine), 149 weeks (.3617*sine), and 162 weeks (.2984*sine).

USERX (US Global Gold and Precious Met) has an average price of 4.14 (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.

## Fourier Analysis

Using data from 1/2/1980 to 3/13/2017 for USERX (US Global Gold and Precious Met), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
04.13516   0
1.92527 -4.15137 (1*2π)/19411,941 weeks
2-1.22683 -3.02846 (2*2π)/1941971 weeks
3-1.00817 .38584 (3*2π)/1941647 weeks
4-.10955 -.19851 (4*2π)/1941485 weeks
5.22906 .33081 (5*2π)/1941388 weeks
6.27351 -.19411 (6*2π)/1941324 weeks
7.71717 -.2933 (7*2π)/1941277 weeks
8.2765 -.64682 (8*2π)/1941243 weeks
9-.19468 -.64778 (9*2π)/1941216 weeks
10-.16082 -.08829 (10*2π)/1941194 weeks
11.22497 -.04108 (11*2π)/1941176 weeks
12.13385 -.29839 (12*2π)/1941162 weeks
13.11075 -.36168 (13*2π)/1941149 weeks
14-.04557 -.25404 (14*2π)/1941139 weeks
15-.008 -.22383 (15*2π)/1941129 weeks
16.08713 -.06748 (16*2π)/1941121 weeks
17.17254 -.25716 (17*2π)/1941114 weeks
18-.03378 -.48433 (18*2π)/1941108 weeks
19-.13445 -.13531 (19*2π)/1941102 weeks
20.03069 -.14526 (20*2π)/194197 weeks
21-.02229 -.35751 (21*2π)/194192 weeks
22-.26784 -.24204 (22*2π)/194188 weeks
23-.21751 .05843 (23*2π)/194184 weeks
24.01059 .0852 (24*2π)/194181 weeks
25.20583 -.14245 (25*2π)/194178 weeks
26-.07569 -.24152 (26*2π)/194175 weeks
27-.12928 -.11801 (27*2π)/194172 weeks
28.00108 -.02282 (28*2π)/194169 weeks
29-.053 -.15562 (29*2π)/194167 weeks
30-.01121 -.12484 (30*2π)/194165 weeks
31-.17801 -.1217 (31*2π)/194163 weeks
32-.16962 .0056 (32*2π)/194161 weeks
33.01687 .09302 (33*2π)/194159 weeks
34.02765 -.03287 (34*2π)/194157 weeks
35-.04361 -.07803 (35*2π)/194155 weeks
36-.00511 .01262 (36*2π)/194154 weeks
37.04492 -.03631 (37*2π)/194152 weeks
38-.04395 -.10805 (38*2π)/194151 weeks
39-.09677 .00605 (39*2π)/194150 weeks
40-.02039 .04311 (40*2π)/194149 weeks
41.06965 .06837 (41*2π)/194147 weeks
42.11055 -.0252 (42*2π)/194146 weeks
43.06141 -.11634 (43*2π)/194145 weeks
44-.03108 -.06749 (44*2π)/194144 weeks
45.05697 -.06075 (45*2π)/194143 weeks
46-.03738 -.06195 (46*2π)/194142 weeks
47-.01874 -.04243 (47*2π)/194141 weeks
48.01646 -.06302 (48*2π)/194140 weeks
49-.05863 .00804 (49*2π)/194140 weeks
50.02699 .00345 (50*2π)/194139 weeks
51.0673 .01005 (51*2π)/194138 weeks
52.03624 -.10139 (52*2π)/194137 weeks
53.0309 -.04295 (53*2π)/194137 weeks
54-.03775 -.02636 (54*2π)/194136 weeks
55.06552 -.05789 (55*2π)/194135 weeks
56.00097 -.05125 (56*2π)/194135 weeks
57-.00817 -.02432 (57*2π)/194134 weeks
58.02236 -.03326 (58*2π)/194133 weeks
59.04168 -.02827 (59*2π)/194133 weeks
60.0495 -.05383 (60*2π)/194132 weeks
61.02843 -.109 (61*2π)/194132 weeks
62-.04408 -.06897 (62*2π)/194131 weeks
63-.00931 -.02872 (63*2π)/194131 weeks
64.00054 -.00539 (64*2π)/194130 weeks
65.04379 -.05569 (65*2π)/194130 weeks
66-.00709 -.07365 (66*2π)/194129 weeks
67.00489 -.04159 (67*2π)/194129 weeks
68-.02403 -.02369 (68*2π)/194129 weeks
69.01578 -.06009 (69*2π)/194128 weeks
70-.01214 -.00418 (70*2π)/194128 weeks
71.01959 -.06225 (71*2π)/194127 weeks
72.00049 .02562 (72*2π)/194127 weeks
73.02353 -.06426 (73*2π)/194127 weeks
74.07778 -.02289 (74*2π)/194126 weeks
75.00824 -.06537 (75*2π)/194126 weeks
76.01879 -.10054 (76*2π)/194126 weeks
77-.01499 -.08687 (77*2π)/194125 weeks
78-.01872 -.06852 (78*2π)/194125 weeks
79-.08387 -.02671 (79*2π)/194125 weeks
80-.03367 .01092 (80*2π)/194124 weeks
81.05238 .02431 (81*2π)/194124 weeks
82.04954 -.03938 (82*2π)/194124 weeks
83.03472 -.08792 (83*2π)/194123 weeks
84-.03173 -.06437 (84*2π)/194123 weeks
85-.02059 -.01837 (85*2π)/194123 weeks
86.04657 -.00827 (86*2π)/194123 weeks
87.04089 -.09309 (87*2π)/194122 weeks
88-.01502 -.12116 (88*2π)/194122 weeks
89-.07217 -.02738 (89*2π)/194122 weeks
90-.02162 -.04644 (90*2π)/194122 weeks
91-.01277 -.0254 (91*2π)/194121 weeks
92-.04348 -.04457 (92*2π)/194121 weeks
93-.01807 -.00835 (93*2π)/194121 weeks
94-.0095 .00046 (94*2π)/194121 weeks
95.01987 -.03815 (95*2π)/194120 weeks
96-.02436 -.0535 (96*2π)/194120 weeks
97-.03442 -.01591 (97*2π)/194120 weeks
98-.00401 .02178 (98*2π)/194120 weeks
99.02858 -.02108 (99*2π)/194120 weeks
100.02164 -.0443 (100*2π)/194119 weeks
101-.01227 -.04876 (101*2π)/194119 weeks
102.00596 -.02176 (102*2π)/194119 weeks
103-.01045 -.05163 (103*2π)/194119 weeks
104-.03124 -.034 (104*2π)/194119 weeks
105.00162 .01012 (105*2π)/194118 weeks
106.01244 -.0411 (106*2π)/194118 weeks
107.00196 -.03316 (107*2π)/194118 weeks
108-.00205 -.03055 (108*2π)/194118 weeks
109.00098 -.03837 (109*2π)/194118 weeks
110-.01179 -.03145 (110*2π)/194118 weeks
111.0124 -.05097 (111*2π)/194117 weeks
112-.03162 -.02726 (112*2π)/194117 weeks
113-.00629 -.0403 (113*2π)/194117 weeks
114-.01711 -.01633 (114*2π)/194117 weeks
115-.00315 -.04677 (115*2π)/194117 weeks
116-.03268 -.03559 (116*2π)/194117 weeks
117-.03442 .0048 (117*2π)/194117 weeks
118.02022 .00051 (118*2π)/194116 weeks
119.01482 -.04174 (119*2π)/194116 weeks
120-.00609 -.06296 (120*2π)/194116 weeks
121-.06378 -.03582 (121*2π)/194116 weeks
122-.03052 .03658 (122*2π)/194116 weeks
123.05034 -.00245 (123*2π)/194116 weeks
124.00098 -.05216 (124*2π)/194116 weeks
125-.02084 -.01752 (125*2π)/194116 weeks
126.0387 -.03277 (126*2π)/194115 weeks
127-.01623 -.07411 (127*2π)/194115 weeks
128-.05874 -.03864 (128*2π)/194115 weeks
129-.03917 -.00693 (129*2π)/194115 weeks
130-.00616 .01297 (130*2π)/194115 weeks
131-.01001 -.01589 (131*2π)/194115 weeks
132.00583 -.00986 (132*2π)/194115 weeks
133.00591 -.02113 (133*2π)/194115 weeks
134.00502 -.04593 (134*2π)/194114 weeks
135-.03756 -.02638 (135*2π)/194114 weeks
136-.01427 -.02157 (136*2π)/194114 weeks
137-.01339 .0015 (137*2π)/194114 weeks
138-.00849 -.0232 (138*2π)/194114 weeks
139.00548 -.00884 (139*2π)/194114 weeks
140-.00409 -.03949 (140*2π)/194114 weeks
141-.01998 -.03403 (141*2π)/194114 weeks
142-.02978 .00175 (142*2π)/194114 weeks
143.00032 -.01656 (143*2π)/194114 weeks
144.00043 -.03389 (144*2π)/194113 weeks
145-.03242 -.01347 (145*2π)/194113 weeks
146-.00047 -.01299 (146*2π)/194113 weeks
147-.0325 -.00756 (147*2π)/194113 weeks
148.01171 -.03042 (148*2π)/194113 weeks
149-.01028 -.00418 (149*2π)/194113 weeks
150-.03287 -.03766 (150*2π)/194113 weeks
151-.01772 -.00713 (151*2π)/194113 weeks
152-.02958 .00148 (152*2π)/194113 weeks
153.00145 .02103 (153*2π)/194113 weeks
154.02095 -.02758 (154*2π)/194113 weeks
155-.01824 -.02453 (155*2π)/194113 weeks
156-.02864 -.01147 (156*2π)/194112 weeks
157.00332 .02061 (157*2π)/194112 weeks
158.01192 -.02893 (158*2π)/194112 weeks
159-.00736 -.02458 (159*2π)/194112 weeks
160-.02394 -.00439 (160*2π)/194112 weeks
161.00627 -.00935 (161*2π)/194112 weeks
162-.00023 -.02865 (162*2π)/194112 weeks
163-.03085 -.02022 (163*2π)/194112 weeks
164-.02811 .00218 (164*2π)/194112 weeks
165-.00032 .0234 (165*2π)/194112 weeks
166.01612 -.00038 (166*2π)/194112 weeks
167.0207 -.03006 (167*2π)/194112 weeks
168-.01606 -.02695 (168*2π)/194112 weeks
169-.00894 -.01179 (169*2π)/194111 weeks
170-.00883 -.00585 (170*2π)/194111 weeks
171-.00389 -.01224 (171*2π)/194111 weeks
172-.00967 -.01325 (172*2π)/194111 weeks
173.00149 -.00666 (173*2π)/194111 weeks
174-.00668 -.00042 (174*2π)/194111 weeks
175.00528 -.01468 (175*2π)/194111 weeks
176.01292 -.0095 (176*2π)/194111 weeks
177.00032 -.03269 (177*2π)/194111 weeks
178-.00755 -.02852 (178*2π)/194111 weeks
179-.02191 -.00495 (179*2π)/194111 weeks
180.00127 -.00905 (180*2π)/194111 weeks
181.00753 -.02291 (181*2π)/194111 weeks
182-.01809 -.02841 (182*2π)/194111 weeks
183-.01335 -.00701 (183*2π)/194111 weeks
184-.00275 -.01929 (184*2π)/194111 weeks
185-.0256 -.02016 (185*2π)/194110 weeks
186-.01608 .0024 (186*2π)/194110 weeks
187-.00473 .01201 (187*2π)/194110 weeks
188.01287 -.02022 (188*2π)/194110 weeks
189.00748 -.0199 (189*2π)/194110 weeks
190-.01455 -.03439 (190*2π)/194110 weeks
191-.02952 -.01581 (191*2π)/194110 weeks
192-.02307 -.00887 (192*2π)/194110 weeks
193-.02229 .01317 (193*2π)/194110 weeks
194.00383 .0086 (194*2π)/194110 weeks
195.01367 -.005 (195*2π)/194110 weeks
196-.00424 -.02412 (196*2π)/194110 weeks
197-.00308 -.01051 (197*2π)/194110 weeks
198-.01764 -.02142 (198*2π)/194110 weeks
199-.01888 -.00869 (199*2π)/194110 weeks
200-.01802 .0091 (200*2π)/194110 weeks
201.00283 .00747 (201*2π)/194110 weeks
202-.00054 -.00394 (202*2π)/194110 weeks
203-.00061 -.01131 (203*2π)/194110 weeks
204-.00636 .00455 (204*2π)/194110 weeks
205.00042 .00223 (205*2π)/19419 weeks
206.01327 -.00079 (206*2π)/19419 weeks
207.01642 -.01354 (207*2π)/19419 weeks
208-.00106 -.01425 (208*2π)/19419 weeks
209.00884 -.01477 (209*2π)/19419 weeks
210.00586 -.02668 (210*2π)/19419 weeks
211-.00942 -.02482 (211*2π)/19419 weeks
212-.02273 -.01411 (212*2π)/19419 weeks
213-.00912 .00878 (213*2π)/19419 weeks
214.01571 .00155 (214*2π)/19419 weeks
215.01574 -.03 (215*2π)/19419 weeks
216-.00891 -.03157 (216*2π)/19419 weeks
217-.02602 -.00598 (217*2π)/19419 weeks
218.00534 -.0079 (218*2π)/19419 weeks
219.00303 -.01198 (219*2π)/19419 weeks
220-.00748 -.02868 (220*2π)/19419 weeks
221-.01728 -.00402 (221*2π)/19419 weeks
222-.00547 -.01762 (222*2π)/19419 weeks
223.0133 -.01219 (223*2π)/19419 weeks
224-.03277 -.02576 (224*2π)/19419 weeks
225-.01926 -.0154 (225*2π)/19419 weeks
226-.01058 .01159 (226*2π)/19419 weeks
227-.00228 -.01003 (227*2π)/19419 weeks
228-.00958 -.01139 (228*2π)/19419 weeks
229-.01496 -.00778 (229*2π)/19418 weeks
230-.01749 .00473 (230*2π)/19418 weeks
231.00366 .00582 (231*2π)/19418 weeks
232.00733 -.00051 (232*2π)/19418 weeks
233.00285 -.02249 (233*2π)/19418 weeks
234-.00822 -.0087 (234*2π)/19418 weeks
235-.00868 -.00415 (235*2π)/19418 weeks
236.0051 -.01934 (236*2π)/19418 weeks
237-.01803 -.00488 (237*2π)/19418 weeks
238-.00935 -.00907 (238*2π)/19418 weeks
239-.00299 .00211 (239*2π)/19418 weeks
240-.01702 -.01266 (240*2π)/19418 weeks
241-.00088 .01648 (241*2π)/19418 weeks
242.00782 .00956 (242*2π)/19418 weeks
243.03554 -.01838 (243*2π)/19418 weeks
244-.00517 -.04514 (244*2π)/19418 weeks
245-.03301 -.01318 (245*2π)/19418 weeks
246-.0121 .00388 (246*2π)/19418 weeks
247.00095 .00042 (247*2π)/19418 weeks
248.00078 -.00736 (248*2π)/19418 weeks
249-.00098 -.0059 (249*2π)/19418 weeks
250.00136 -.0216 (250*2π)/19418 weeks
251-.01468 -.01122 (251*2π)/19418 weeks
252-.01757 -.00353 (252*2π)/19418 weeks
253.00277 .00799 (253*2π)/19418 weeks
254-.00149 -.01164 (254*2π)/19418 weeks
255-.01138 -.00125 (255*2π)/19418 weeks
256.01289 .00436 (256*2π)/19418 weeks
257.00743 -.01021 (257*2π)/19418 weeks
258.00616 -.02077 (258*2π)/19418 weeks
259-.00793 -.02442 (259*2π)/19417 weeks
260-.01748 -.00676 (260*2π)/19417 weeks
261-.00742 .00475 (261*2π)/19417 weeks
262.00957 -.00425 (262*2π)/19417 weeks
263.01001 -.01955 (263*2π)/19417 weeks
264-.00515 -.02466 (264*2π)/19417 weeks
265-.02086 -.01901 (265*2π)/19417 weeks
266-.01362 -.00778 (266*2π)/19417 weeks
267-.0186 -.00383 (267*2π)/19417 weeks
268-.00658 .011 (268*2π)/19417 weeks
269.00679 -.00409 (269*2π)/19417 weeks
270.00439 -.016 (270*2π)/19417 weeks
271-.01397 -.01307 (271*2π)/19417 weeks
272-.01629 -.00969 (272*2π)/19417 weeks
273-.00752 .00705 (273*2π)/19417 weeks
274-.00031 .00943 (274*2π)/19417 weeks
275.01598 -.01123 (275*2π)/19417 weeks
276.00293 -.02333 (276*2π)/19417 weeks
277-.02125 -.02212 (277*2π)/19417 weeks
278-.01875 .00142 (278*2π)/19417 weeks
279-.01213 .01008 (279*2π)/19417 weeks
280.00802 .0058 (280*2π)/19417 weeks
281.01631 -.0052 (281*2π)/19417 weeks
282-.00296 -.02584 (282*2π)/19417 weeks
283-.0133 -.01335 (283*2π)/19417 weeks
284-.00631 -.00718 (284*2π)/19417 weeks
285-.01615 .00013 (285*2π)/19417 weeks
286-.00972 .00027 (286*2π)/19417 weeks
287.00569 .0114 (287*2π)/19417 weeks
288.0135 -.0081 (288*2π)/19417 weeks
289.00415 -.0095 (289*2π)/19417 weeks
290-.00039 -.02919 (290*2π)/19417 weeks
291-.01195 -.0102 (291*2π)/19417 weeks
292-.02077 -.00222 (292*2π)/19417 weeks
293.00152 .00118 (293*2π)/19417 weeks
294-.00341 .00122 (294*2π)/19417 weeks
295.0131 -.00585 (295*2π)/19417 weeks
296-.00239 -.0174 (296*2π)/19417 weeks
297-.0115 -.02616 (297*2π)/19417 weeks
298-.00849 .01149 (298*2π)/19417 weeks
299-.01125 -.01045 (299*2π)/19416 weeks
300  -.00129 (300*2π)/19416 weeks
301-.0012 -.0043 (301*2π)/19416 weeks
302-.00088 -.00176 (302*2π)/19416 weeks
303.00099 -.00835 (303*2π)/19416 weeks
304.00415 -.00655 (304*2π)/19416 weeks
305-.00604 -.02256 (305*2π)/19416 weeks
306-.00733 -.00003 (306*2π)/19416 weeks
307.00221 -.0038 (307*2π)/19416 weeks
308.00385 -.018 (308*2π)/19416 weeks
309-.01431 -.01958 (309*2π)/19416 weeks
310-.00834 -.00464 (310*2π)/19416 weeks
311-.00886 -.00779 (311*2π)/19416 weeks
312-.00647 -.00681 (312*2π)/19416 weeks
313-.00962 -.00888 (313*2π)/19416 weeks
314-.01502 -.00665 (314*2π)/19416 weeks
315-.0045 .01393 (315*2π)/19416 weeks
316.01386 -.01495 (316*2π)/19416 weeks
317-.01098 -.02159 (317*2π)/19416 weeks
318-.02858 -.00445 (318*2π)/19416 weeks
319-.00848 .01184 (319*2π)/19416 weeks
320.00861 .00844 (320*2π)/19416 weeks
321.00598 -.01669 (321*2π)/19416 weeks
322-.00866 -.01852 (322*2π)/19416 weeks
323-.02694 .00411 (323*2π)/19416 weeks
324.00137 .01499 (324*2π)/19416 weeks
325.01968 -.00432 (325*2π)/19416 weeks
326.0003 -.02249 (326*2π)/19416 weeks
327-.01711 -.01689 (327*2π)/19416 weeks
328-.01663 .00208 (328*2π)/19416 weeks
329-.00341 .00024 (329*2π)/19416 weeks
330-.00516 -.0018 (330*2π)/19416 weeks
331-.00438 -.0013 (331*2π)/19416 weeks
332-.00611 -.0008 (332*2π)/19416 weeks
333-.00041 -.00024 (333*2π)/19416 weeks
334-.00483 -.00373 (334*2π)/19416 weeks
335.00431 -.00133 (335*2π)/19416 weeks
336-.00352 -.00183 (336*2π)/19416 weeks
337.00266 -.0129 (337*2π)/19416 weeks
338-.00828 -.00429 (338*2π)/19416 weeks
339-.00835 -.00387 (339*2π)/19416 weeks
340.00338 .00024 (340*2π)/19416 weeks
341.00334 -.00403 (341*2π)/19416 weeks
342-.01102 -.01674 (342*2π)/19416 weeks
343-.00638 -.00302 (343*2π)/19416 weeks
344-.0081 .002 (344*2π)/19416 weeks
345.00049 .00267 (345*2π)/19416 weeks
346.00759 -.00549 (346*2π)/19416 weeks
347-.00459 -.02469 (347*2π)/19416 weeks
348-.02051 -.00072 (348*2π)/19416 weeks
349-.00983 .00256 (349*2π)/19416 weeks
350-.00332 .00225 (350*2π)/19416 weeks
351-.00703 .00504 (351*2π)/19416 weeks
352.00498 .0014 (352*2π)/19416 weeks
353-.00329 -.00652 (353*2π)/19415 weeks
354-.00069 .00239 (354*2π)/19415 weeks
355-.00082 -.00297 (355*2π)/19415 weeks
356-.00322 -.00461 (356*2π)/19415 weeks
357-.00251 .00054 (357*2π)/19415 weeks
358-.00317 -.00849 (358*2π)/19415 weeks
359-.00926 .00621 (359*2π)/19415 weeks
360-.00335 .00566 (360*2π)/19415 weeks
361.00415 .00717 (361*2π)/19415 weeks
362.00647 .00169 (362*2π)/19415 weeks
363.00733 .00108 (363*2π)/19415 weeks
364.00609 -.0041 (364*2π)/19415 weeks
365.01212 -.00458 (365*2π)/19415 weeks
366.00175 -.00928 (366*2π)/19415 weeks
367-.0024 -.01171