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Fourier Analysis of FKDNX (Franklin Dynatech Fund Class A)


FKDNX (Franklin Dynatech Fund Class A) appears to have interesting cyclic behaviour every 138 weeks (1.2969*sine), 193 weeks (1.256*sine), and 161 weeks (1.2147*sine).

FKDNX (Franklin Dynatech Fund Class A) has an average price of 14.51 (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 1/2/1980 to 1/17/2017 for FKDNX (Franklin Dynatech Fund Class A), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
014.50511   0 
14.34277 -11.61989 (1*2π)/19331,933 weeks
23.78976 -5.65731 (2*2π)/1933967 weeks
31.10808 -5.73877 (3*2π)/1933644 weeks
41.40642 -4.12107 (4*2π)/1933483 weeks
5-.62944 -4.39789 (5*2π)/1933387 weeks
6-.17297 -1.89003 (6*2π)/1933322 weeks
7.37221 -2.64573 (7*2π)/1933276 weeks
8-.40927 -2.0073 (8*2π)/1933242 weeks
9.0395 -2.01922 (9*2π)/1933215 weeks
10-.89504 -1.25603 (10*2π)/1933193 weeks
11.33779 -.49385 (11*2π)/1933176 weeks
12.34761 -1.2147 (12*2π)/1933161 weeks
13.19806 -1.16202 (13*2π)/1933149 weeks
14-.20734 -1.29687 (14*2π)/1933138 weeks
15-.11084 -.66239 (15*2π)/1933129 weeks
16.12998 -.84704 (16*2π)/1933121 weeks
17.14393 -.88733 (17*2π)/1933114 weeks
18-.17527 -1.15913 (18*2π)/1933107 weeks
19-.16139 -.45415 (19*2π)/1933102 weeks
20.35604 -.54899 (20*2π)/193397 weeks
21.10415 -.86962 (21*2π)/193392 weeks
22.14347 -.61352 (22*2π)/193388 weeks
23.03166 -.78908 (23*2π)/193384 weeks
24.10194 -.4294 (24*2π)/193381 weeks
25.31782 -.713 (25*2π)/193377 weeks
26.15212 -.79431 (26*2π)/193374 weeks
27-.00199 -.94161 (27*2π)/193372 weeks
28-.3123 -.773 (28*2π)/193369 weeks
29-.14106 -.47215 (29*2π)/193367 weeks
30.01755 -.45132 (30*2π)/193364 weeks
31.13545 -.56589 (31*2π)/193362 weeks
32-.11389 -.63205 (32*2π)/193360 weeks
33-.09078 -.50905 (33*2π)/193359 weeks
34-.07777 -.48436 (34*2π)/193357 weeks
35-.01234 -.48275 (35*2π)/193355 weeks
36-.07566 -.4131 (36*2π)/193354 weeks
37-.01943 -.37991 (37*2π)/193352 weeks
38-.06956 -.47652 (38*2π)/193351 weeks
39.03017 -.41841 (39*2π)/193350 weeks
40.01478 -.55627 (40*2π)/193348 weeks
41-.24489 -.46088 (41*2π)/193347 weeks
42-.21043 -.32825 (42*2π)/193346 weeks
43-.03945 -.17132 (43*2π)/193345 weeks
44.00754 -.37543 (44*2π)/193344 weeks
45-.11211 -.37604 (45*2π)/193343 weeks
46-.08587 -.27912 (46*2π)/193342 weeks
47-.01239 -.1832 (47*2π)/193341 weeks
48.10338 -.37438 (48*2π)/193340 weeks
49-.07136 -.37543 (49*2π)/193339 weeks
50-.07244 -.33883 (50*2π)/193339 weeks
51-.15428 -.17914 (51*2π)/193338 weeks
52.08468 -.28977 (52*2π)/193337 weeks
53-.06758 -.33696 (53*2π)/193336 weeks
54-.11465 -.22954 (54*2π)/193336 weeks
55-.04046 -.21635 (55*2π)/193335 weeks
56-.11462 -.23329 (56*2π)/193335 weeks
57.01657 -.16482 (57*2π)/193334 weeks
58-.0825 -.2122 (58*2π)/193333 weeks
59.00633 -.11065 (59*2π)/193333 weeks
60.03504 -.15869 (60*2π)/193332 weeks
61.14727 -.2343 (61*2π)/193332 weeks
62-.02664 -.3687 (62*2π)/193331 weeks
63-.05158 -.21122 (63*2π)/193331 weeks
64.00702 -.17805 (64*2π)/193330 weeks
65.03557 -.20847 (65*2π)/193330 weeks
66.01024 -.28646 (66*2π)/193329 weeks
67-.054 -.22638 (67*2π)/193329 weeks
68.03988 -.20935 (68*2π)/193328 weeks
69-.06735 -.24341 (69*2π)/193328 weeks
70-.00433 -.226 (70*2π)/193328 weeks
71-.06702 -.24639 (71*2π)/193327 weeks
72-.03056 -.19714 (72*2π)/193327 weeks
73-.01779 -.21182 (73*2π)/193326 weeks
74-.00083 -.20851 (74*2π)/193326 weeks
75-.08324 -.18053 (75*2π)/193326 weeks
76.06036 -.15462 (76*2π)/193325 weeks
77.02324 -.29753 (77*2π)/193325 weeks
78-.05631 -.22077 (78*2π)/193325 weeks
79-.06051 -.246 (79*2π)/193324 weeks
80-.12538 -.18064 (80*2π)/193324 weeks
81-.08083 -.17337 (81*2π)/193324 weeks
82-.11423 -.11913 (82*2π)/193324 weeks
83-.0301 -.06073 (83*2π)/193323 weeks
84-.02025 -.11916 (84*2π)/193323 weeks
85-.01817 -.1159 (85*2π)/193323 weeks
86.03163 -.15727 (86*2π)/193322 weeks
87-.03763 -.11018 (87*2π)/193322 weeks
88.04244 -.128 (88*2π)/193322 weeks
89-.02583 -.14045 (89*2π)/193322 weeks
90-.00786 -.11475 (90*2π)/193321 weeks
91-.00425 -.12573 (91*2π)/193321 weeks
92.08008 -.08991 (92*2π)/193321 weeks
93.08568 -.20232 (93*2π)/193321 weeks
94.00682 -.21507 (94*2π)/193321 weeks
95-.05045 -.19404 (95*2π)/193320 weeks
96-.03005 -.07801 (96*2π)/193320 weeks
97.04105 -.12168 (97*2π)/193320 weeks
98.01953 -.14306 (98*2π)/193320 weeks
99.02519 -.11926 (99*2π)/193320 weeks
100.08854 -.1502 (100*2π)/193319 weeks
101.04885 -.20534 (101*2π)/193319 weeks
102.06324 -.21612 (102*2π)/193319 weeks
103-.00456 -.23648 (103*2π)/193319 weeks
104-.0359 -.21869 (104*2π)/193319 weeks
105-.02902 -.18754 (105*2π)/193318 weeks
106.00161 -.20351 (106*2π)/193318 weeks
107-.06582 -.22529 (107*2π)/193318 weeks
108-.08652 -.18774 (108*2π)/193318 weeks
109-.09407 -.13416 (109*2π)/193318 weeks
110-.02804 -.13798 (110*2π)/193318 weeks
111-.05599 -.15653 (111*2π)/193317 weeks
112-.09075 -.13456 (112*2π)/193317 weeks
113-.05981 -.08838 (113*2π)/193317 weeks
114.00345 -.08228 (114*2π)/193317 weeks
115.00741 -.16425 (115*2π)/193317 weeks
116-.06138 -.15748 (116*2π)/193317 weeks
117-.07716 -.12493 (117*2π)/193317 weeks
118-.05101 -.05198 (118*2π)/193316 weeks
119.01833 -.09802 (119*2π)/193316 weeks
120.01554 -.1121 (120*2π)/193316 weeks
121-.0333 -.16501 (121*2π)/193316 weeks
122-.06585 -.08118 (122*2π)/193316 weeks
123.00392 -.09988 (123*2π)/193316 weeks
124-.03114 -.10779 (124*2π)/193316 weeks
125-.00845 -.09021 (125*2π)/193315 weeks
126-.00916 -.12703 (126*2π)/193315 weeks
127.01266 -.07217 (127*2π)/193315 weeks
128.01344 -.15499 (128*2π)/193315 weeks
129-.01826 -.12381 (129*2π)/193315 weeks
130.00588 -.14302 (130*2π)/193315 weeks
131-.02942 -.12147 (131*2π)/193315 weeks
132-.02538 -.12445 (132*2π)/193315 weeks
133-.06593 -.11667 (133*2π)/193315 weeks
134-.02041 -.0788 (134*2π)/193314 weeks
135-.02605 -.09967 (135*2π)/193314 weeks
136.00917 -.0702 (136*2π)/193314 weeks
137-.0014 -.14551 (137*2π)/193314 weeks
138-.02633 -.10837 (138*2π)/193314 weeks
139.00277 -.10262 (139*2π)/193314 weeks
140.00625 -.09929 (140*2π)/193314 weeks
141.02709 -.11726 (141*2π)/193314 weeks
142-.01007 -.16221 (142*2π)/193314 weeks
143-.02597 -.14539 (143*2π)/193314 weeks
144-.04215 -.1458 (144*2π)/193313 weeks
145-.06512 -.1072 (145*2π)/193313 weeks
146-.04048 -.07116 (146*2π)/193313 weeks
147-.00741 -.11139 (147*2π)/193313 weeks
148-.04478 -.10769 (148*2π)/193313 weeks
149-.02463 -.11099 (149*2π)/193313 weeks
150-.03965 -.10065 (150*2π)/193313 weeks
151-.04643 -.08326 (151*2π)/193313 weeks
152-.01252 -.07281 (152*2π)/193313 weeks
153-.01118 -.07773 (153*2π)/193313 weeks
154.02178 -.09113 (154*2π)/193313 weeks
155-.01584 -.10647 (155*2π)/193312 weeks
156.02632 -.13608 (156*2π)/193312 weeks
157-.05981 -.14684 (157*2π)/193312 weeks
158-.02141 -.07951 (158*2π)/193312 weeks
159-.02755 -.13175 (159*2π)/193312 weeks
160-.03858 -.10318 (160*2π)/193312 weeks
161-.06333 -.09516 (161*2π)/193312 weeks
162-.01407 -.0624 (162*2π)/193312 weeks
163-.02031 -.12293 (163*2π)/193312 weeks
164-.07369 -.07962 (164*2π)/193312 weeks
165-.0451 -.08011 (165*2π)/193312 weeks
166-.05949 -.04201 (166*2π)/193312 weeks
167.03201 -.02585 (167*2π)/193312 weeks
168.02007 -.09106 (168*2π)/193312 weeks
169.00503 -.08724 (169*2π)/193311 weeks
170.00559 -.08788 (170*2π)/193311 weeks
171.00628 -.09557 (171*2π)/193311 weeks
172.00961 -.14004 (172*2π)/193311 weeks
173-.04841 -.10972 (173*2π)/193311 weeks
174-.00982 -.08811 (174*2π)/193311 weeks
175-.02075 -.11931 (175*2π)/193311 weeks
176-.03978 -.10376 (176*2π)/193311 weeks
177-.03084 -.09677 (177*2π)/193311 weeks
178-.03788 -.06489 (178*2π)/193311 weeks
179.01218 -.07823 (179*2π)/193311 weeks
180.0039 -.11468 (180*2π)/193311 weeks
181-.04059 -.1157 (181*2π)/193311 weeks
182-.01337 -.0984 (182*2π)/193311 weeks
183-.0383 -.11875 (183*2π)/193311 weeks
184-.06927 -.09594 (184*2π)/193311 weeks
185-.04248 -.06285 (185*2π)/193310 weeks
186-.02952 -.08605 (186*2π)/193310 weeks
187-.03309 -.06942 (187*2π)/193310 weeks
188-.00729 -.10101 (188*2π)/193310 weeks
189-.04962 -.08291 (189*2π)/193310 weeks
190-.01794 -.09993 (190*2π)/193310 weeks
191-.06297 -.07768 (191*2π)/193310 weeks
192-.03119 -.06892 (192*2π)/193310 weeks
193-.04029 -.07296 (193*2π)/193310 weeks
194-.01522 -.07407 (194*2π)/193310 weeks
195-.03868 -.09619 (195*2π)/193310 weeks
196-.05582 -.08797 (196*2π)/193310 weeks
197-.07699 -.05585 (197*2π)/193310 weeks
198-.04542 -.03198 (198*2π)/193310 weeks
199-.0124 -.02488 (199*2π)/193310 weeks
200.01465 -.07785 (200*2π)/193310 weeks
201-.02429 -.06943 (201*2π)/193310 weeks
202-.01617 -.06268 (202*2π)/193310 weeks
203-.01256 -.07675 (203*2π)/193310 weeks
204-.01636 -.08969 (204*2π)/19339 weeks
205-.03427 -.07588 (205*2π)/19339 weeks
206-.02546 -.07481 (206*2π)/19339 weeks
207-.03045 -.07003 (207*2π)/19339 weeks
208-.02787 -.05568 (208*2π)/19339 weeks
209-.02544 -.07873 (209*2π)/19339 weeks
210-.04507 -.05838 (210*2π)/19339 weeks
211-.02095 -.03283 (211*2π)/19339 weeks
212-.0151 -.05307 (212*2π)/19339 weeks
213-.00114 -.05513 (213*2π)/19339 weeks
214-.02106 -.06634 (214*2π)/19339 weeks
215-.0137 -.05453 (215*2π)/19339 weeks
216-.01697 -.07183 (216*2π)/19339 weeks
217-.02488 -.05923 (217*2π)/19339 weeks
218-.01563 -.04401 (218*2π)/19339 weeks
219.01399 -.0581 (219*2π)/19339 weeks
220.00355 -.08427 (220*2π)/19339 weeks
221-.01761 -.08218 (221*2π)/19339 weeks
222-.01039 -.08691 (222*2π)/19339 weeks
223-.04105 -.07431 (223*2π)/19339 weeks
224-.00515 -.07242 (224*2π)/19339 weeks
225-.04791 -.08129 (225*2π)/19339 weeks
226-.03666 -.0391 (226*2π)/19339 weeks
227-.02811 -.06017 (227*2π)/19339 weeks
228-.00096 -.0413 (228*2π)/19338 weeks
229-.0146 -.07887 (229*2π)/19338 weeks
230-.01688 -.04876 (230*2π)/19338 weeks
231-.01203 -.06006 (231*2π)/19338 weeks
232.01649 -.05724 (232*2π)/19338 weeks
233-.00103 -.09044 (233*2π)/19338 weeks
234-.01755 -.0842 (234*2π)/19338 weeks
235-.0118 -.0916 (235*2π)/19338 weeks
236-.04598 -.0937 (236*2π)/19338 weeks
237-.04325 -.05559 (237*2π)/19338 weeks
238-.05013 -.06354 (238*2π)/19338 weeks
239-.02337 -.03648 (239*2π)/19338 weeks
240-.00764 -.04104 (240*2π)/19338 weeks
241.01285 -.04932 (241*2π)/19338 weeks
242-.00138 -.08731 (242*2π)/19338 weeks
243-.02732 -.08696 (243*2π)/19338 weeks
244-.02628 -.06517 (244*2π)/19338 weeks
245-.03075 -.07259 (245*2π)/19338 weeks
246-.02017 -.05485 (246*2π)/19338 weeks
247-.01249 -.05655 (247*2π)/19338 weeks
248.01113 -.06146 (248*2π)/19338 weeks
249-.01132 -.1004 (249*2π)/19338 weeks
250-.04259 -.07587 (250*2π)/19338 weeks
251-.02273 -.03926 (251*2π)/19338 weeks
252-.00152 -.07644 (252*2π)/19338 weeks
253-.01619 -.08984 (253*2π)/19338 weeks
254-.03382 -.08061 (254*2π)/19338 weeks
255-.02599 -.07076 (255*2π)/19338 weeks
256-.03399 -.07886 (256*2π)/19338 weeks
257-.01894 -.07506 (257*2π)/19338 weeks
258-.05112 -.10118 (258*2π)/19337 weeks
259-.07561 -.05622 (259*2π)/19337 weeks
260-.04803 -.03739 (260*2π)/19337 weeks
261-.03235 -.03015 (261*2π)/19337 weeks
262-.01173 -.06756 (262*2π)/19337 weeks
263-.04664 -.06418 (263*2π)/19337 weeks
264-.03935 -.04019 (264*2π)/19337 weeks
265-.04964 -.04102 (265*2π)/19337 weeks
266-.02232 -.01008 (266*2π)/19337 weeks
267.00962 -.04788 (267*2π)/19337 weeks
268-.00303 -.04431 (268*2π)/19337 weeks
269.0035 -.06926 (269*2π)/19337 weeks
270-.02971 -.07797 (270*2π)/19337 weeks
271-.04801 -.06912 (271*2π)/19337 weeks
272-.04025 -.04457 (272*2π)/19337 weeks
273-.02039 -.03928 (273*2π)/19337 weeks
274-.00989 -.05099 (274*2π)/19337 weeks
275-.01225 -.0616 (275*2π)/19337 weeks
276-.02409 -.07895 (276*2π)/19337 weeks
277-.04363 -.06935 (277*2π)/19337 weeks
278-.04649 -.03807 (278*2π)/19337 weeks
279-.02384 -.02501 (279*2π)/19337 weeks
280-.0076 -.04449 (280*2π)/19337 weeks
281-.01062 -.06155 (281*2π)/19337 weeks
282-.02339 -.05273 (282*2π)/19337 weeks
283-.00929 -.05678 (283*2π)/19337 weeks
284-.02625 -.06046 (284*2π)/19337 weeks
285-.02282 -.06761 (285*2π)/19337 weeks
286-.04602 -.05841 (286*2π)/19337 weeks
287-.02953 -.03083 (287*2π)/19337 weeks
288-.00378 -.05105 (288*2π)/19337 weeks
289-.01878 -.05172 (289*2π)/19337 weeks
290-.01074 -.06442 (290*2π)/19337 weeks
291-.03736 -.05933 (291*2π)/19337 weeks
292-.01833 -.05294 (292*2π)/19337 weeks
293-.02837 -.04779 (293*2π)/19337 weeks
294-.02858 -.04966 (294*2π)/19337 weeks
295-.01404 -.04192 (295*2π)/19337 weeks
296-.01182 -.05869 (296*2π)/19337 weeks
297-.01532 -.05904 (297*2π)/19337 weeks
298-.01809 -.06823 (298*2π)/19336 weeks
299-.03117 -.07663 (299*2π)/19336 weeks
300-.05716 -.04422 (300*2π)/19336 weeks
301-.0094 -.04181 (301*2π)/19336 weeks
302-.02208 -.06592 (302*2π)/19336 weeks
303-.02577 -.05939 (303*2π)/19336 weeks
304-.04443 -.06778 (304*2π)/19336 weeks
305-.04029 -.03957 (305*2π)/19336 weeks
306-.01156 -.06123 (306*2π)/19336 weeks
307-.03372 -.06591 (307*2π)/19336 weeks
308-.04552 -.06581 (308*2π)/19336 weeks
309-.06453 -.0456 (309*2π)/19336 weeks
310-.03692 -.03959 (310*2π)/19336 weeks
311-.04147 -.05569 (311*2π)/19336 weeks
312-.04514 -.03253 (312*2π)/19336 weeks
313-.0416 -.04347 (313*2π)/19336 weeks
314-.05611 -.02927 (314*2π)/19336 weeks
315-.01684 -.02067 (315*2π)/19336 weeks
316-.02759 -.04272 (316*2π)/19336 weeks
317-.03431 -.03411 (317*2π)/19336 weeks
318-.03301 -.0297 (318*2π)/19336 weeks
319-.01475 -.02273 (319*2π)/19336 weeks
320-.02326 -.0466 (320*2π)/19336 weeks
321-.01211 -.03871 (321*2π)/19336 weeks
322-.03276 -.05034 (322*2π)/19336 weeks
323-.02841 -.03341 (323*2π)/19336 weeks
324-.02399 -.03367 (324*2π)/19336 weeks
325-.01466 -.03935 (325*2π)/19336 weeks
326-.03022 -.04473 (326*2π)/19336 weeks
327-.02953 -.03461 (327*2π)/19336 weeks
328-.03277 -.03692 (328*2π)/19336 weeks
329-.01847 -.02308 (329*2π)/19336 weeks
330-.00581 -.03111 (330*2π)/19336 weeks
331-.00243 -.0416 (331*2π)/19336 weeks
332-.00441 -.0557 (332*2π)/19336 weeks
333-.03126 -.06091 (333*2π)/19336 weeks
334-.02532 -.04537 (334*2π)/19336 weeks
335-.02921 -.0422 (335*2π)/19336 weeks
336-.02172 -.03116 (336*2π)/19336 weeks
337-.01973 -.0472 (337*2π)/19336 weeks
338-.02577 -.03789 (338*2π)/19336 weeks
339-.01926 -.04979 (339*2π)/19336 weeks
340-.02844 -.03892 (340*2π)/19336 weeks
341-.02036 -.04301 (341*2π)/19336 weeks
342-.02654 -.04333 (342*2π)/19336 weeks
343-.02429 -.04007 (343*2π)/19336 weeks
344-.02952 -.04091 (344*2π)/19336 weeks
345-.01549 -.02001 (345*2π)/19336 weeks
346-.005 -.05145 (346*2π)/19336 weeks
347-.03108 -.04325 (347*2π)/19336 weeks
348-.01337 -.04639 (348*2π)/19336 weeks
349-.03114 -.03457 (349*2π)/19336 weeks
350-.00374 -.03648 (350*2π)/19336 weeks
351-.01947 -.06349 (351*2π)/19336 weeks
352-.02776 -.05304 (352*2π)/19335 weeks
353-.02713 -.04836 (353*2π)/19335 weeks
354-.02142 -.05309 (354*2π)/19335 weeks
355-.04024 -.04898 (355*2π)/19335 weeks
356-.03146 -.04384 (356*2π)/19335 weeks
357-.04414 -.05953 (357*2π)/19335 weeks
358-.04517 -.02893 (358*2π)/19335 weeks
359-.02363 -.0343 (359*2π)/19335 weeks
360-.0419 -.03024 (360*2π)/19335 weeks
361-.01235 -.03176 (361*2π)/19335 weeks
362-.03821 -.05969 (362*2π)/19335 weeks
363-.03597 -.02012 (363*2π)/19335 weeks
364-.01164 -.03733 (364*2π)/19335 weeks
365-.02947 -.03494 (365*2π)/19335 weeks
366-.02225 -.04566 (366*2π)/19335 weeks
367-.04111