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Fourier Analysis of ASA (ASA Gold and Precious Metals L)


ASA (ASA Gold and Precious Metals L) appears to have interesting cyclic behaviour every 204 weeks (.9748*cosine), 107 weeks (.843*sine), and 170 weeks (.6316*cosine).

ASA (ASA Gold and Precious Metals L) has an average price of 9.81 (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 1/3/1978 to 2/13/2017 for ASA (ASA Gold and Precious Metals L), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
09.80859   0 
11.9197 -6.08432 (1*2π)/20412,041 weeks
2-3.04701 -4.85497 (2*2π)/20411,021 weeks
3-2.18003 .57999 (3*2π)/2041680 weeks
4-1.00921 -.10832 (4*2π)/2041510 weeks
5-.34562 .83088 (5*2π)/2041408 weeks
6.66768 -.1298 (6*2π)/2041340 weeks
7.80444 .07616 (7*2π)/2041292 weeks
8.74395 -.77868 (8*2π)/2041255 weeks
9-.08369 -1.15577 (9*2π)/2041227 weeks
10-.97481 -.40673 (10*2π)/2041204 weeks
11-.11015 -.00988 (11*2π)/2041186 weeks
12.6316 -.36987 (12*2π)/2041170 weeks
13.44205 -.17284 (13*2π)/2041157 weeks
14.25358 -.46669 (14*2π)/2041146 weeks
15-.01193 -.28544 (15*2π)/2041136 weeks
16.16069 -.09111 (16*2π)/2041128 weeks
17.47566 .14397 (17*2π)/2041120 weeks
18.12197 -.37389 (18*2π)/2041113 weeks
19-.23799 -.84296 (19*2π)/2041107 weeks
20-.20319 -.19652 (20*2π)/2041102 weeks
21.0649 -.11921 (21*2π)/204197 weeks
22.12204 -.61235 (22*2π)/204193 weeks
23-.27866 -.4706 (23*2π)/204189 weeks
24-.50265 -.06145 (24*2π)/204185 weeks
25.00031 .13848 (25*2π)/204182 weeks
26.16802 .03376 (26*2π)/204179 weeks
27-.0056 -.45289 (27*2π)/204176 weeks
28-.15087 -.39474 (28*2π)/204173 weeks
29-.12988 -.13742 (29*2π)/204170 weeks
30.01953 -.06409 (30*2π)/204168 weeks
31-.02828 -.01334 (31*2π)/204166 weeks
32.13014 -.37663 (32*2π)/204164 weeks
33-.36367 -.2416 (33*2π)/204162 weeks
34-.50357 .14121 (34*2π)/204160 weeks
35-.13914 .15379 (35*2π)/204158 weeks
36.03836 -.08957 (36*2π)/204157 weeks
37-.09307 -.14272 (37*2π)/204155 weeks
38.0154 -.00397 (38*2π)/204154 weeks
39.09193 -.00958 (39*2π)/204152 weeks
40-.04602 -.21121 (40*2π)/204151 weeks
41-.12179 -.06603 (41*2π)/204150 weeks
42-.03473 .03168 (42*2π)/204149 weeks
43-.0256 .14521 (43*2π)/204147 weeks
44.05134 .15613 (44*2π)/204146 weeks
45.14903 -.0645 (45*2π)/204145 weeks
46-.00041 -.07623 (46*2π)/204144 weeks
47-.03256 .02257 (47*2π)/204143 weeks
48-.0471 -.16111 (48*2π)/204143 weeks
49.00651 -.03983 (49*2π)/204142 weeks
50.01467 -.02981 (50*2π)/204141 weeks
51-.11276 -.19778 (51*2π)/204140 weeks
52-.08194 .02398 (52*2π)/204139 weeks
53-.00916 -.01488 (53*2π)/204139 weeks
54.08676 .02135 (54*2π)/204138 weeks
55.0327 -.10488 (55*2π)/204137 weeks
56.12045 -.05194 (56*2π)/204136 weeks
57-.02667 .05366 (57*2π)/204136 weeks
58.15698 -.00832 (58*2π)/204135 weeks
59.07202 .03601 (59*2π)/204135 weeks
60-.06824 -.04042 (60*2π)/204134 weeks
61-.01566 -.07899 (61*2π)/204133 weeks
62.00288 .03133 (62*2π)/204133 weeks
63.11273 .01734 (63*2π)/204132 weeks
64.13358 -.11096 (64*2π)/204132 weeks
65-.13338 -.12787 (65*2π)/204131 weeks
66-.08731 .01554 (66*2π)/204131 weeks
67-.03922 -.04269 (67*2π)/204130 weeks
68.07743 -.02666 (68*2π)/204130 weeks
69.12262 -.05763 (69*2π)/204130 weeks
70-.02422 -.12727 (70*2π)/204129 weeks
71.02307 -.04456 (71*2π)/204129 weeks
72.02065 .00917 (72*2π)/204128 weeks
73-.00308 -.05493 (73*2π)/204128 weeks
74-.05434 .01827 (74*2π)/204128 weeks
75.03569 -.05077 (75*2π)/204127 weeks
76-.02404 .06847 (76*2π)/204127 weeks
77.04136 -.02319 (77*2π)/204127 weeks
78.0059 .01076 (78*2π)/204126 weeks
79.04852 -.01729 (79*2π)/204126 weeks
80.08643 -.06377 (80*2π)/204126 weeks
81.13335 -.11888 (81*2π)/204125 weeks
82-.01963 -.0931 (82*2π)/204125 weeks
83-.08208 -.14274 (83*2π)/204125 weeks
84-.07594 -.03451 (84*2π)/204124 weeks
85-.02761 .08644 (85*2π)/204124 weeks
86.04402 .03041 (86*2π)/204124 weeks
87.06646 .03063 (87*2π)/204123 weeks
88.04499 -.11345 (88*2π)/204123 weeks
89-.03256 -.09723 (89*2π)/204123 weeks
90-.05424 -.00241 (90*2π)/204123 weeks
91.03627 .02911 (91*2π)/204122 weeks
92.13327 -.10535 (92*2π)/204122 weeks
93.07056 -.18157 (93*2π)/204122 weeks
94-.03416 -.05322 (94*2π)/204122 weeks
95-.00795 -.05727 (95*2π)/204121 weeks
96.01502 -.06118 (96*2π)/204121 weeks
97.01178 -.1108 (97*2π)/204121 weeks
98-.02365 -.05099 (98*2π)/204121 weeks
99-.06356 .01277 (99*2π)/204121 weeks
100.02239 -.01459 (100*2π)/204120 weeks
101.02325 -.0918 (101*2π)/204120 weeks
102-.03366 -.05747 (102*2π)/204120 weeks
103-.11258 -.01537 (103*2π)/204120 weeks
104-.06542 .02037 (104*2π)/204120 weeks
105.04349 .01629 (105*2π)/204119 weeks
106.02312 -.03267 (106*2π)/204119 weeks
107-.01823 -.0735 (107*2π)/204119 weeks
108.04775 -.06207 (108*2π)/204119 weeks
109.01431 -.08384 (109*2π)/204119 weeks
110-.01463 -.0092 (110*2π)/204119 weeks
111.01732 .02403 (111*2π)/204118 weeks
112-.00731 -.03742 (112*2π)/204118 weeks
113.00462 -.03294 (113*2π)/204118 weeks
114.02603 -.03962 (114*2π)/204118 weeks
115.00831 -.01719 (115*2π)/204118 weeks
116.00746 -.02821 (116*2π)/204118 weeks
117.071 -.03405 (117*2π)/204117 weeks
118-.0181 -.02316 (118*2π)/204117 weeks
119.03694 .0137 (119*2π)/204117 weeks
120-.04648 -.04406 (120*2π)/204117 weeks
121-.0072 -.0397 (121*2π)/204117 weeks
122.01042 -.07361 (122*2π)/204117 weeks
123-.09002 -.06326 (123*2π)/204117 weeks
124-.03169 .01089 (124*2π)/204116 weeks
125.03045 -.01168 (125*2π)/204116 weeks
126.06378 -.02719 (126*2π)/204116 weeks
127.06309 -.06518 (127*2π)/204116 weeks
128-.10066 -.10835 (128*2π)/204116 weeks
129-.10897 .0295 (129*2π)/204116 weeks
130.07511 .01864 (130*2π)/204116 weeks
131.05001 -.02488 (131*2π)/204116 weeks
132-.02787 -.00535 (132*2π)/204115 weeks
133.08004 .01469 (133*2π)/204115 weeks
134.05671 -.05187 (134*2π)/204115 weeks
135-.00143 -.08046 (135*2π)/204115 weeks
136-.02061 -.06845 (136*2π)/204115 weeks
137-.04367 -.00711 (137*2π)/204115 weeks
138-.00661 -.08685 (138*2π)/204115 weeks
139.00682 -.03319 (139*2π)/204115 weeks
140-.00894 .02712 (140*2π)/204115 weeks
141.07937 .0017 (141*2π)/204114 weeks
142.04007 -.0867 (142*2π)/204114 weeks
143-.00093 -.05817 (143*2π)/204114 weeks
144-.03495 -.08143 (144*2π)/204114 weeks
145-.00499 -.05108 (145*2π)/204114 weeks
146-.04375 -.00509 (146*2π)/204114 weeks
147.01758 .02048 (147*2π)/204114 weeks
148.03676 -.03176 (148*2π)/204114 weeks
149-.00809 -.05951 (149*2π)/204114 weeks
150-.05324 -.03961 (150*2π)/204114 weeks
151-.01833 -.03141 (151*2π)/204114 weeks
152.01089 -.06174 (152*2π)/204113 weeks
153-.00631 -.02498 (153*2π)/204113 weeks
154.0339 -.03098 (154*2π)/204113 weeks
155.004 -.07242 (155*2π)/204113 weeks
156.00332 -.03053 (156*2π)/204113 weeks
157-.01091 -.03118 (157*2π)/204113 weeks
158.0134 -.03626 (158*2π)/204113 weeks
159-.00975 -.06018 (159*2π)/204113 weeks
160-.04168 -.06409 (160*2π)/204113 weeks
161-.06307 -.00403 (161*2π)/204113 weeks
162-.00215 .04111 (162*2π)/204113 weeks
163-.00864 -.0491 (163*2π)/204113 weeks
164-.02604 -.07116 (164*2π)/204112 weeks
165-.06823 -.02255 (165*2π)/204112 weeks
166.0094 .0608 (166*2π)/204112 weeks
167-.0066 -.03437 (167*2π)/204112 weeks
168-.00688 -.05428 (168*2π)/204112 weeks
169-.02434 -.01028 (169*2π)/204112 weeks
170-.00854 -.02928 (170*2π)/204112 weeks
171.03879 -.04279 (171*2π)/204112 weeks
172-.00312 -.06463 (172*2π)/204112 weeks
173-.03292 -.02686 (173*2π)/204112 weeks
174-.05193 .00185 (174*2π)/204112 weeks
175-.04679 -.00184 (175*2π)/204112 weeks
176.00636 .02694 (176*2π)/204112 weeks
177.03055 -.03161 (177*2π)/204112 weeks
178-.00406 -.01255 (178*2π)/204111 weeks
179-.03682 -.01517 (179*2π)/204111 weeks
180-.0238 -.03211 (180*2π)/204111 weeks
181-.00187 -.02756 (181*2π)/204111 weeks
182-.0231 -.01313 (182*2π)/204111 weeks
183-.02041 -.05009 (183*2π)/204111 weeks
184-.0202 -.01496 (184*2π)/204111 weeks
185-.02561 -.00462 (185*2π)/204111 weeks
186-.00247 .03877 (186*2π)/204111 weeks
187.01714 .00457 (187*2π)/204111 weeks
188.04265 -.06025 (188*2π)/204111 weeks
189-.03237 -.02082 (189*2π)/204111 weeks
190-.02377 .01779 (190*2π)/204111 weeks
191.04335 .01634 (191*2π)/204111 weeks
192.01337 -.06008 (192*2π)/204111 weeks
193-.01629 -.03242 (193*2π)/204111 weeks
194-.00135 .00137 (194*2π)/204111 weeks
195.02617 -.02391 (195*2π)/204110 weeks
196-.02194 -.06875 (196*2π)/204110 weeks
197-.05918 -.02917 (197*2π)/204110 weeks
198-.01569 .00679 (198*2π)/204110 weeks
199.00902 .01555 (199*2π)/204110 weeks
200.04088 -.00601 (200*2π)/204110 weeks
201.04116 -.047 (201*2π)/204110 weeks
202-.00497 -.03292 (202*2π)/204110 weeks
203-.02237 -.05451 (203*2π)/204110 weeks
204-.0215 -.03809 (204*2π)/204110 weeks
205-.02477 .00292 (205*2π)/204110 weeks
206-.00438 -.00541 (206*2π)/204110 weeks
207-.01921 -.01849 (207*2π)/204110 weeks
208.01731 .01575 (208*2π)/204110 weeks
209.01549 -.02358 (209*2π)/204110 weeks
210-.01453 -.05804 (210*2π)/204110 weeks
211-.03289 -.03339 (211*2π)/204110 weeks
212-.01737 -.00277 (212*2π)/204110 weeks
213-.01071 -.01136 (213*2π)/204110 weeks
214.01209 -.03156 (214*2π)/204110 weeks
215-.03335 -.03987 (215*2π)/20419 weeks
216-.03911 -.03191 (216*2π)/20419 weeks
217-.02412 -.00204 (217*2π)/20419 weeks
218-.02483 .0365 (218*2π)/20419 weeks
219-.0166 -.00956 (219*2π)/20419 weeks
220-.00487 .00684 (220*2π)/20419 weeks
221-.0021 .03934 (221*2π)/20419 weeks
222.01301 .01089 (222*2π)/20419 weeks
223.03971 -.02197 (223*2π)/20419 weeks
224-.01617 -.06043 (224*2π)/20419 weeks
225-.04333 -.00888 (225*2π)/20419 weeks
226-.04148 .03166 (226*2π)/20419 weeks
227.02896 .00701 (227*2π)/20419 weeks
228.03241 -.02654 (228*2π)/20419 weeks
229.00034 -.03019 (229*2π)/20419 weeks
230.00045 .00541 (230*2π)/20419 weeks
231-.00756 -.01048 (231*2π)/20419 weeks
232.0119 -.00375 (232*2π)/20419 weeks
233.00023 -.02444 (233*2π)/20419 weeks
234.00261 .01138 (234*2π)/20419 weeks
235-.02594 .00716 (235*2π)/20419 weeks
236.0303 -.03969 (236*2π)/20419 weeks
237.02894 -.02617 (237*2π)/20419 weeks
238-.01759 -.02356 (238*2π)/20419 weeks
239-.01979 -.01345 (239*2π)/20419 weeks
240.00681 .00152 (240*2π)/20419 weeks
241.01208 -.04722 (241*2π)/20418 weeks
242.00355 -.04671 (242*2π)/20418 weeks
243-.01556 -.04418 (243*2π)/20418 weeks
244-.02056 -.02686 (244*2π)/20418 weeks
245-.02888 .0209 (245*2π)/20418 weeks
246.00096 -.00574 (246*2π)/20418 weeks
247.0055 -.02496 (247*2π)/20418 weeks
248-.02336 -.00954 (248*2π)/20418 weeks
249.01711 -.02561 (249*2π)/20418 weeks
250-.01705 -.00624 (250*2π)/20418 weeks
251-.01247 -.01392 (251*2π)/20418 weeks
252-.00998 -.00533 (252*2π)/20418 weeks
253.04301 -.0387 (253*2π)/20418 weeks
254-.0175 -.0413 (254*2π)/20418 weeks
255-.06262 -.05944 (255*2π)/20418 weeks
256-.05288 .04657 (256*2π)/20418 weeks
257.03496 .04886 (257*2π)/20418 weeks
258.03105 -.03461 (258*2π)/20418 weeks
259.00553 -.02748 (259*2π)/20418 weeks
260-.01138 -.01262 (260*2π)/20418 weeks
261-.00913 -.01466 (261*2π)/20418 weeks
262-.00993 -.00484 (262*2π)/20418 weeks
263-.0238 .01376 (263*2π)/20418 weeks
264.00706 -.00597 (264*2π)/20418 weeks
265.02432 -.04468 (265*2π)/20418 weeks
266-.02331 -.05699 (266*2π)/20418 weeks
267-.02149 .00454 (267*2π)/20418 weeks
268.0318 -.01105 (268*2π)/20418 weeks
269-.00541 -.03804 (269*2π)/20418 weeks
270-.01939 -.01479 (270*2π)/20418 weeks
271-.04853 -.01024 (271*2π)/20418 weeks
272-.02558 .00823 (272*2π)/20418 weeks
273.02603 .01414 (273*2π)/20417 weeks
274.00083 -.02475 (274*2π)/20417 weeks
275-.01961 -.03774 (275*2π)/20417 weeks
276-.02839 -.00162 (276*2π)/20417 weeks
277-.01671 .00904 (277*2π)/20417 weeks
278.01144 .01917 (278*2π)/20417 weeks
279.01707 -.00021 (279*2π)/20417 weeks
280-.00433 -.00493 (280*2π)/20417 weeks
281.00152 -.00348 (281*2π)/20417 weeks
282.00431 -.03609 (282*2π)/20417 weeks
283-.01834 -.02328 (283*2π)/20417 weeks
284-.02191 -.00771 (284*2π)/20417 weeks
285.01826 .0059 (285*2π)/20417 weeks
286.02521 .00693 (286*2π)/20417 weeks
287.02374 -.04716 (287*2π)/20417 weeks
288.0055 -.0493 (288*2π)/20417 weeks
289-.05177 -.02124 (289*2π)/20417 weeks
290-.02434 .01111 (290*2π)/20417 weeks
291.00425 .01005 (291*2π)/20417 weeks
292.03346 -.00845 (292*2π)/20417 weeks
293.01607 -.01002 (293*2π)/20417 weeks
294.00035 -.03213 (294*2π)/20417 weeks
295-.00853 -.05011 (295*2π)/20417 weeks
296-.04078 -.00832 (296*2π)/20417 weeks
297-.01765 .00882 (297*2π)/20417 weeks
298.00994 .01516 (298*2π)/20417 weeks
299-.01016 .00542 (299*2π)/20417 weeks
300.01724 -.03069 (300*2π)/20417 weeks
301.01951 -.04572 (301*2π)/20417 weeks
302-.02839 -.03845 (302*2π)/20417 weeks
303-.03422 -.0217 (303*2π)/20417 weeks
304.00067 -.01872 (304*2π)/20417 weeks
305-.02716 .01885 (305*2π)/20417 weeks
306-.0085 .00516 (306*2π)/20417 weeks
307.01433 -.01349 (307*2π)/20417 weeks
308.00936 -.00921 (308*2π)/20417 weeks
309.00533 -.02778 (309*2π)/20417 weeks
310-.03031 -.04874 (310*2π)/20417 weeks
311-.03907 .00611 (311*2π)/20417 weeks
312-.00143 .02524 (312*2π)/20417 weeks
313.03522 -.02064 (313*2π)/20417 weeks
314-.01978 -.02312 (314*2π)/20417 weeks
315-.02049 -.02222 (315*2π)/20416 weeks
316-.00233 -.00923 (316*2π)/20416 weeks
317-.00067 -.01551 (317*2π)/20416 weeks
318-.0145 -.03883 (318*2π)/20416 weeks
319-.01846 -.01469 (319*2π)/20416 weeks
320-.01402 -.01236 (320*2π)/20416 weeks
321-.0129 .0156 (321*2π)/20416 weeks
322-.00459 -.01423 (322*2π)/20416 weeks
323-.01277 -.05379 (323*2π)/20416 weeks
324-.04427 -.00315 (324*2π)/20416 weeks
325-.01351 .0195 (325*2π)/20416 weeks
326.00744 .0008 (326*2π)/20416 weeks
327-.00294 -.01145 (327*2π)/20416 weeks
328-.01054 -.01342