Back to list of Stocks    See Also: Seasonal Analysis of ASAGenetic Algorithms Stock Portfolio Generator, and Fourier Calculator

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 (.9712*cosine), 107 weeks (.853*sine), and 170 weeks (.6039*cosine).

ASA (ASA Gold and Precious Metals L) has an average price of 9.8 (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 1/9/2017 for ASA (ASA Gold and Precious Metals L), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
09.80123   0 
11.96539 -6.05943 (1*2π)/20362,036 weeks
2-2.97494 -4.92568 (2*2π)/20361,018 weeks
3-2.2259 .49679 (3*2π)/2036679 weeks
4-1.05974 -.15492 (4*2π)/2036509 weeks
5-.44511 .81952 (5*2π)/2036407 weeks
6.60919 -.07785 (6*2π)/2036339 weeks
7.75735 .15331 (7*2π)/2036291 weeks
8.77783 -.69091 (8*2π)/2036255 weeks
9.00218 -1.14868 (9*2π)/2036226 weeks
10-.97121 -.49544 (10*2π)/2036204 weeks
11-.18324 -.02209 (11*2π)/2036185 weeks
12.60394 -.3029 (12*2π)/2036170 weeks
13.42935 -.11585 (13*2π)/2036157 weeks
14.28892 -.42656 (14*2π)/2036145 weeks
15.00312 -.28886 (15*2π)/2036136 weeks
16.1415 -.07325 (16*2π)/2036127 weeks
17.44278 .23652 (17*2π)/2036120 weeks
18.18829 -.29448 (18*2π)/2036113 weeks
19-.10099 -.853 (19*2π)/2036107 weeks
20-.18253 -.2411 (20*2π)/2036102 weeks
21.06336 -.09299 (21*2π)/203697 weeks
22.23277 -.57196 (22*2π)/203693 weeks
23-.16667 -.54548 (23*2π)/203689 weeks
24-.50345 -.20468 (24*2π)/203685 weeks
25-.08072 .11152 (25*2π)/203681 weeks
26.12325 .0923 (26*2π)/203678 weeks
27.07858 -.41855 (27*2π)/203675 weeks
28-.06812 -.43856 (28*2π)/203673 weeks
29-.11505 -.20228 (29*2π)/203670 weeks
30.0136 -.08596 (30*2π)/203668 weeks
31-.04148 -.02015 (31*2π)/203666 weeks
32.23694 -.33632 (32*2π)/203664 weeks
33-.24916 -.37441 (33*2π)/203662 weeks
34-.54621 -.05693 (34*2π)/203660 weeks
35-.25305 .08343 (35*2π)/203658 weeks
36-.00424 -.08188 (36*2π)/203657 weeks
37-.10122 -.18736 (37*2π)/203655 weeks
38-.04002 -.03072 (38*2π)/203654 weeks
39.04974 .01102 (39*2π)/203652 weeks
40-.00179 -.23119 (40*2π)/203651 weeks
41-.12361 -.14983 (41*2π)/203650 weeks
42-.08415 -.03758 (42*2π)/203648 weeks
43-.12374 .08824 (43*2π)/203647 weeks
44-.07183 .16206 (44*2π)/203646 weeks
45.11284 .00992 (45*2π)/203645 weeks
46.0023 -.06299 (46*2π)/203644 weeks
47-.07134 .02344 (47*2π)/203643 weeks
48-.02707 -.16151 (48*2π)/203642 weeks
49-.01745 -.04575 (49*2π)/203642 weeks
50-.0063 -.01397 (50*2π)/203641 weeks
51-.05698 -.23981 (51*2π)/203640 weeks
52-.1327 -.05024 (52*2π)/203639 weeks
53-.07147 -.04979 (53*2π)/203638 weeks
54.00402 .0386 (54*2π)/203638 weeks
55.0144 -.09733 (55*2π)/203637 weeks
56.09546 -.02784 (56*2π)/203636 weeks
57-.08837 .01186 (57*2π)/203636 weeks
58.10148 .0483 (58*2π)/203635 weeks
59.03438 .0777 (59*2π)/203635 weeks
60-.06926 -.04713 (60*2π)/203634 weeks
61-.01872 -.085 (61*2π)/203633 weeks
62-.06434 .01373 (62*2π)/203633 weeks
63.03227 .08203 (63*2π)/203632 weeks
64.15504 .00646 (64*2π)/203632 weeks
65-.05033 -.16356 (65*2π)/203631 weeks
66-.11723 -.04279 (66*2π)/203631 weeks
67-.07925 -.07171 (67*2π)/203630 weeks
68.00984 .00225 (68*2π)/203630 weeks
69.09306 .02494 (69*2π)/203630 weeks
70.02322 -.11914 (70*2π)/203629 weeks
71.02305 -.04909 (71*2π)/203629 weeks
72-.00722 .0089 (72*2π)/203628 weeks
73.01043 -.0539 (73*2π)/203628 weeks
74-.08684 -.02762 (74*2π)/203628 weeks
75.02299 -.04296 (75*2π)/203627 weeks
76-.09814 .03005 (76*2π)/203627 weeks
77-.00734 .00328 (77*2π)/203626 weeks
78-.05837 .01472 (78*2π)/203626 weeks
79-.02398 .02573 (79*2π)/203626 weeks
80.0359 .02156 (80*2π)/203625 weeks
81.14906 .01938 (81*2π)/203625 weeks
82.04485 -.04352 (82*2π)/203625 weeks
83.02596 -.15811 (83*2π)/203625 weeks
84-.03922 -.11832 (84*2π)/203624 weeks
85-.10987 .00739 (85*2π)/203624 weeks
86-.04595 .03537 (86*2π)/203624 weeks
87-.03416 .08903 (87*2π)/203623 weeks
88.05742 -.0172 (88*2π)/203623 weeks
89.01566 -.08313 (89*2π)/203623 weeks
90-.08198 -.05327 (90*2π)/203623 weeks
91-.08241 .04309 (91*2π)/203622 weeks
92.08264 .04258 (92*2π)/203622 weeks
93.1529 -.05563 (93*2π)/203622 weeks
94.01182 -.04955 (94*2π)/203622 weeks
95.01138 -.04109 (95*2π)/203621 weeks
96.02618 -.02296 (96*2π)/203621 weeks
97.07768 -.06479 (97*2π)/203621 weeks
98.03446 -.05951 (98*2π)/203621 weeks
99-.06348 -.0481 (99*2π)/203621 weeks
100-.01278 .00604 (100*2π)/203620 weeks
101.06517 -.03297 (101*2π)/203620 weeks
102.03553 -.0537 (102*2π)/203620 weeks
103-.06045 -.10486 (103*2π)/203620 weeks
104-.09797 -.07544 (104*2π)/203620 weeks
105-.04342 .01634 (105*2π)/203619 weeks
106-.01797 .00099 (106*2π)/203619 weeks
107-.01529 -.06619 (107*2π)/203619 weeks
108.03136 -.0176 (108*2π)/203619 weeks
109.05697 -.05777 (109*2π)/203619 weeks
110-.00812 -.04561 (110*2π)/203619 weeks
111-.03314 .01494 (111*2π)/203618 weeks
112-.01454 -.03217 (112*2π)/203618 weeks
113-.0119 -.03057 (113*2π)/203618 weeks
114.01415 -.01931 (114*2π)/203618 weeks
115-.01082 -.01525 (115*2π)/203618 weeks
116-.01411 -.02838 (116*2π)/203618 weeks
117.04518 .03105 (117*2π)/203617 weeks
118-.00445 -.02633 (118*2π)/203617 weeks
119-.00964 .05549 (119*2π)/203617 weeks
120-.02445 -.03356 (120*2π)/203617 weeks
121-.01504 -.01463 (121*2π)/203617 weeks
122.04247 -.00781 (122*2π)/203617 weeks
123-.00626 -.11108 (123*2π)/203617 weeks
124-.05977 -.06129 (124*2π)/203616 weeks
125-.03227 -.01865 (125*2π)/203616 weeks
126-.00028 .02817 (126*2π)/203616 weeks
127.06245 .06121 (127*2π)/203616 weeks
128.05516 -.1148 (128*2π)/203616 weeks
129-.09345 -.13439 (129*2π)/203616 weeks
130-.03173 .01066 (130*2π)/203616 weeks
131.01009 .01484 (131*2π)/203616 weeks
132-.0506 -.05362 (132*2π)/203615 weeks
133-.03912 .05583 (133*2π)/203615 weeks
134.00962 .05356 (134*2π)/203615 weeks
135.02921 -.00036 (135*2π)/203615 weeks
136.03493 -.0285 (136*2π)/203615 weeks
137-.04744 -.03262 (137*2π)/203615 weeks
138.03194 -.05944 (138*2π)/203615 weeks
139.02364 -.03983 (139*2π)/203615 weeks
140-.05946 -.03552 (140*2π)/203615 weeks
141-.03737 .06055 (141*2π)/203614 weeks
142.0385 .028 (142*2π)/203614 weeks
143.02062 .01358 (143*2π)/203614 weeks
144.03676 -.04493 (144*2π)/203614 weeks
145.04789 -.02479 (145*2π)/203614 weeks
146-.0099 -.05873 (146*2π)/203614 weeks
147-.04322 .00213 (147*2π)/203614 weeks
148-.00399 .03463 (148*2π)/203614 weeks
149.02208 .00582 (149*2π)/203614 weeks
150-.00864 -.0466 (150*2π)/203614 weeks
151-.02087 -.03659 (151*2π)/203613 weeks
152.02493 -.02461 (152*2π)/203613 weeks
153-.00918 -.0319 (153*2π)/203613 weeks
154-.00271 .01593 (154*2π)/203613 weeks
155.04013 -.01392 (155*2π)/203613 weeks
156.0179 -.00044 (156*2π)/203613 weeks
157.00541 -.01358 (157*2π)/203613 weeks
158.01216 .01723 (158*2π)/203613 weeks
159.03706 .00796 (159*2π)/203613 weeks
160.06366 -.02918 (160*2π)/203613 weeks
161.01453 -.06708 (161*2π)/203613 weeks
162-.05424 .00138 (162*2π)/203613 weeks
163-.00011 -.00468 (163*2π)/203612 weeks
164.05296 -.02413 (164*2π)/203612 weeks
165.03007 -.0907 (165*2π)/203612 weeks
166-.06472 -.00319 (166*2π)/203612 weeks
167-.01982 -.01723 (167*2π)/203612 weeks
168.02305 -.0226 (168*2π)/203612 weeks
169-.01716 -.03494 (169*2π)/203612 weeks
170-.01486 -.04149 (170*2π)/203612 weeks
171.01053 .01758 (171*2π)/203612 weeks
172.05214 .00273 (172*2π)/203612 weeks
173.04073 -.0152 (173*2π)/203612 weeks
174.00706 -.04108 (174*2π)/203612 weeks
175.0008 -.07303 (175*2π)/203612 weeks
176-.04487 -.03252 (176*2π)/203612 weeks
177.00653 .00604 (177*2π)/203612 weeks
178-.0038 .00669 (178*2π)/203611 weeks
179-.01688 -.02662 (179*2π)/203611 weeks
180-.00196 -.03708 (180*2π)/203611 weeks
181.00832 -.01414 (181*2π)/203611 weeks
182-.01568 -.02484 (182*2π)/203611 weeks
183.02933 -.03544 (183*2π)/203611 weeks
184.01918 -.03712 (184*2π)/203611 weeks
185.01972 -.05751 (185*2π)/203611 weeks
186-.04004 -.04478 (186*2π)/203611 weeks
187-.05421 -.02912 (187*2π)/203611 weeks
188.02413 .02323 (188*2π)/203611 weeks
189.02012 -.03169 (189*2π)/203611 weeks
190-.02258 -.06246 (190*2π)/203611 weeks
191-.06116 .00604 (191*2π)/203611 weeks
192.00607 .00642 (192*2π)/203611 weeks
193.01236 -.0229 (193*2π)/203611 weeks
194-.02691 -.02244 (194*2π)/203610 weeks
195-.02912 .02609 (195*2π)/203610 weeks
196.03085 .00733 (196*2π)/203610 weeks
197.03119 -.05586 (197*2π)/203610 weeks
198.00366 -.05446 (198*2π)/203610 weeks
199-.02909 -.04807 (199*2π)/203610 weeks
200-.04219 -.01067 (200*2π)/203610 weeks
201-.00566 .02989 (201*2π)/203610 weeks
202-.01345 .01604 (202*2π)/203610 weeks
203.01879 -.00276 (203*2π)/203610 weeks
204.03732 -.00979 (204*2π)/203610 weeks
205.00455 -.02745 (205*2π)/203610 weeks
206-.00449 -.01281 (206*2π)/203610 weeks
207.01497 -.03868 (207*2π)/203610 weeks
208-.03409 -.01153 (208*2π)/203610 weeks
209-.03217 .01444 (209*2π)/203610 weeks
210.01421 .00905 (210*2π)/203610 weeks
211.02668 -.01711 (211*2π)/203610 weeks
212.00025 -.0199 (212*2π)/203610 weeks
213-.01104 -.02418 (213*2π)/203610 weeks
214-.003 .01945 (214*2π)/203610 weeks
215.01985 -.00204 (215*2π)/20369 weeks
216.04381 -.0219 (216*2π)/20369 weeks
217.04424 -.02054 (217*2π)/20369 weeks
218-.0108 -.03576 (218*2π)/20369 weeks
219.018 -.03768 (219*2π)/20369 weeks
220.02296 -.03291 (220*2π)/20369 weeks
221-.02387 -.04417 (221*2π)/20369 weeks
222-.03978 -.0423 (222*2π)/20369 weeks
223-.04356 .01715 (223*2π)/20369 weeks
224.02478 .01543 (224*2π)/20369 weeks
225.03182 -.01885 (225*2π)/20369 weeks
226-.00793 -.07959 (226*2π)/20369 weeks
227-.03148 -.04362 (227*2π)/20369 weeks
228-.01734 -.0049 (228*2π)/20369 weeks
229.01362 -.00991 (229*2π)/20369 weeks
230-.01332 -.01396 (230*2π)/20369 weeks
231-.00344 -.02846 (231*2π)/20369 weeks
232-.02039 -.01418 (232*2π)/20369 weeks
233.01059 -.01067 (233*2π)/20369 weeks
234-.01855 -.00422 (234*2π)/20369 weeks
235-.03866 -.06168 (235*2π)/20369 weeks
236-.01374 -.02009 (236*2π)/20369 weeks
237-.02014 .01877 (237*2π)/20369 weeks
238-.00761 -.00211 (238*2π)/20369 weeks
239-.00208 -.02711 (239*2π)/20369 weeks
240-.04511 -.0289 (240*2π)/20368 weeks
241-.02376 -.00661 (241*2π)/20368 weeks
242-.01259 .00946 (242*2π)/20368 weeks
243.01027 .00875 (243*2π)/20368 weeks
244.03318 .01057 (244*2π)/20368 weeks
245-.00385 -.03178 (245*2π)/20368 weeks
246-.01512 -.02354 (246*2π)/20368 weeks
247-.00441 .00352 (247*2π)/20368 weeks
248-.00554 -.03588 (248*2π)/20368 weeks
249-.00095 .00861 (249*2π)/20368 weeks
250-.00801 -.01196 (250*2π)/20368 weeks
251-.00261 -.01702 (251*2π)/20368 weeks
252-.01782 -.05221 (252*2π)/20368 weeks
253-.0296 .024 (253*2π)/20368 weeks
254-.02384 .03258 (254*2π)/20368 weeks
255.07501 .02072 (255*2π)/20368 weeks
256.04929 -.06582 (256*2π)/20368 weeks
257-.04085 -.05459 (257*2π)/20368 weeks
258-.01915 -.00872 (258*2π)/20368 weeks
259-.0064 .00474 (259*2π)/20368 weeks
260-.0057 -.00594 (260*2π)/20368 weeks
261.00202 -.00343 (261*2π)/20368 weeks
262.00369 .00209 (262*2π)/20368 weeks
263-.0107 -.03951 (263*2π)/20368 weeks
264-.03357 -.0458 (264*2π)/20368 weeks
265-.03822 .00363 (265*2π)/20368 weeks
266.02382 .00966 (266*2π)/20368 weeks
267.01061 -.04075 (267*2π)/20368 weeks
268-.02863 -.00103 (268*2π)/20368 weeks
269-.00299 .01765 (269*2π)/20368 weeks
270-.00716 .02475 (270*2π)/20368 weeks
271.02118 -.00605 (271*2π)/20368 weeks
272.02848 -.03997 (272*2π)/20367 weeks
273-.02596 -.02015 (273*2π)/20367 weeks
274-.02481 -.00429 (274*2π)/20367 weeks
275.01229 .01204 (275*2π)/20367 weeks
276.02096 -.00678 (276*2π)/20367 weeks
277.02864 -.02629 (277*2π)/20367 weeks
278.00166 -.0313 (278*2π)/20367 weeks
279-.01269 -.01242 (279*2π)/20367 weeks
280-.00797 -.02041 (280*2π)/20367 weeks
281-.02812 -.03234 (281*2π)/20367 weeks
282-.01665 -.00264 (282*2π)/20367 weeks
283.00108 -.00411 (283*2π)/20367 weeks
284.02528 -.03246 (284*2π)/20367 weeks
285.00835 -.03149 (285*2π)/20367 weeks
286-.0369 -.04677 (286*2π)/20367 weeks
287-.03277 -.01301 (287*2π)/20367 weeks
288-.02633 .03772 (288*2π)/20367 weeks
289.01995 .00901 (289*2π)/20367 weeks
290.02151 -.02207 (290*2π)/20367 weeks
291.01091 -.04418 (291*2π)/20367 weeks
292-.00986 -.01922 (292*2π)/20367 weeks
293-.03293 -.01766 (293*2π)/20367 weeks
294-.03622 -.0129 (294*2π)/20367 weeks
295-.01152 .03144 (295*2π)/20367 weeks
296.01489 .00616 (296*2π)/20367 weeks
297.02174 -.01358 (297*2π)/20367 weeks
298-.00945 -.00939 (298*2π)/20367 weeks
299-.01704 -.04889 (299*2π)/20367 weeks
300-.02473 -.03824 (300*2π)/20367 weeks
301-.04072 .00778 (301*2π)/20367 weeks
302-.01809 .01153 (302*2π)/20367 weeks
303.00848 -.01149 (303*2π)/20367 weeks
304.00868 .02789 (304*2π)/20367 weeks
305.00655 -.00959 (305*2π)/20367 weeks
306.00435 -.03261 (306*2π)/20367 weeks
307-.00225 -.01796 (307*2π)/20367 weeks
308-.0205 -.02254 (308*2π)/20367 weeks
309-.04581 -.00542 (309*2π)/20367 weeks
310-.00047 .03025 (310*2π)/20367 weeks
311.0291 .00033 (311*2π)/20367 weeks
312.00787 -.04898 (312*2π)/20367 weeks
313-.03316 -.00282 (313*2π)/20367 weeks
314-.0209 -.00643 (314*2π)/20366 weeks
315.00122 -.00997 (315*2π)/20366 weeks
316-.00796 -.01477 (316*2π)/20366 weeks
317-.02911 -.01803 (317*2π)/20366 weeks
318-.00999 .00454 (318*2π)/20366 weeks
319-.00462 .00072 (319*2π)/20366 weeks
320.00838 .01478 (320*2π)/20366 weeks
321-.01007 -.01795 (321*2π)/20366 weeks
322-.03372 -.03029 (322*2π)/20366 weeks
323-.01538 .03011 (323*2π)/20366 weeks
324.02124 .01458 (324*2π)/20366 weeks
325.01619 -.01493 (325*2π)/20366 weeks
326-.00304 -.01325 (326*2π)/20366 weeks
327-.00718 -.00709 (327*2π)/20366 weeks
328-.00025 .00779 (328*2π)/20366 weeks
329.02089 .00229 (329*2π)/20366 weeks
330.00916 -.04416 (330*2π)/20366 weeks
331-.04961 -.0159 (331*2π)/20366 weeks
332-.0104 .0284 (332*2π)/20366 weeks
333.01507 .00883 (333*2π)/20366 weeks
334.02571