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Fourier Analysis of FMSTX (Federated MDT Stock Trust IS Sh)


FMSTX (Federated MDT Stock Trust IS Sh) appears to have interesting cyclic behaviour every 37 weeks (.641*sine), 34 weeks (.498*sine), and 21 weeks (.3316*cosine).

FMSTX (Federated MDT Stock Trust IS Sh) has an average price of 19.01 (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 1/29/2010 to 3/20/2017 for FMSTX (Federated MDT Stock Trust IS Sh), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
019.00636   0 
1-.49011 -6.72476 (1*2π)/374374 weeks
2.24481 -1.22824 (2*2π)/374187 weeks
3.27528 -1.65133 (3*2π)/374125 weeks
4.2665 -1.60136 (4*2π)/37494 weeks
5.01326 -1.40421 (5*2π)/37475 weeks
6.07248 -1.10719 (6*2π)/37462 weeks
7.28502 -.3936 (7*2π)/37453 weeks
8-.00476 -.44871 (8*2π)/37447 weeks
9-.091 -.68545 (9*2π)/37442 weeks
10.05331 -.64096 (10*2π)/37437 weeks
11.1098 -.49797 (11*2π)/37434 weeks
12-.19428 -.40332 (12*2π)/37431 weeks
13-.15996 -.47239 (13*2π)/37429 weeks
14-.13856 -.30348 (14*2π)/37427 weeks
15-.09177 -.2381 (15*2π)/37425 weeks
16.05122 -.46788 (16*2π)/37423 weeks
17-.08658 -.31856 (17*2π)/37422 weeks
18-.33157 -.32404 (18*2π)/37421 weeks
19-.1325 -.23059 (19*2π)/37420 weeks
20-.03192 -.15863 (20*2π)/37419 weeks
21.0989 -.1265 (21*2π)/37418 weeks
22.01097 -.28686 (22*2π)/37417 weeks
23-.1176 -.31566 (23*2π)/37416 weeks
24-.04326 -.26428 (24*2π)/37416 weeks
25-.04536 -.16906 (25*2π)/37415 weeks
26-.05027 -.23687 (26*2π)/37414 weeks
27-.0787 -.21249 (27*2π)/37414 weeks
28.01193 -.27432 (28*2π)/37413 weeks
29-.03169 -.25368 (29*2π)/37413 weeks
30-.03958 -.13092 (30*2π)/37412 weeks
31-.05943 -.19708 (31*2π)/37412 weeks
32-.15956 -.25955 (32*2π)/37412 weeks
33-.02875 -.07508 (33*2π)/37411 weeks
34-.01884 -.18958 (34*2π)/37411 weeks
35-.03131 -.16211 (35*2π)/37411 weeks
36-.09227 -.15665 (36*2π)/37410 weeks
37-.10633 -.15013 (37*2π)/37410 weeks
38-.12699 -.13573 (38*2π)/37410 weeks
39-.01762 -.08405 (39*2π)/37410 weeks
40-.03213 -.12415 (40*2π)/3749 weeks
41-.01132 -.08147 (41*2π)/3749 weeks
42-.05668 -.07912 (42*2π)/3749 weeks
43-.08167 -.14481 (43*2π)/3749 weeks
44-.03936 -.07218 (44*2π)/3749 weeks
45.04356 -.12917 (45*2π)/3748 weeks
46-.11067 -.05999 (46*2π)/3748 weeks
47-.07706 -.11925 (47*2π)/3748 weeks
48-.03422 -.12821 (48*2π)/3748 weeks
49-.07544 -.15952 (49*2π)/3748 weeks
50-.08507 -.04102 (50*2π)/3747 weeks
51-.07212 -.08018 (51*2π)/3747 weeks
52-.11857 -.1434 (52*2π)/3747 weeks
53-.03308 -.10377 (53*2π)/3747 weeks
54.01081 -.10848 (54*2π)/3747 weeks
55-.05641 -.0915 (55*2π)/3747 weeks
56-.09012 -.10953 (56*2π)/3747 weeks
57-.01586 -.09761 (57*2π)/3747 weeks
58-.03708 -.06379 (58*2π)/3746 weeks
59-.07934 -.03974 (59*2π)/3746 weeks
60-.00382 -.02824 (60*2π)/3746 weeks
61-.00508 -.07334 (61*2π)/3746 weeks
62-.00969 -.08705 (62*2π)/3746 weeks
63-.0422 -.08397 (63*2π)/3746 weeks
64-.06796 -.08523 (64*2π)/3746 weeks
65-.08367 -.1163 (65*2π)/3746 weeks
66-.07086 -.0507 (66*2π)/3746 weeks
67-.05443 -.046 (67*2π)/3746 weeks
68-.03385 -.02476 (68*2π)/3746 weeks
69-.00249 -.06687 (69*2π)/3745 weeks
70-.04094 -.09976 (70*2π)/3745 weeks
71-.03279 -.06399 (71*2π)/3745 weeks
72-.09328 -.07413 (72*2π)/3745 weeks
73-.0342 -.04202 (73*2π)/3745 weeks
74.00155 -.03435 (74*2π)/3745 weeks
75-.03595 -.08168 (75*2π)/3745 weeks
76-.04524 -.06162 (76*2π)/3745 weeks
77-.03829 -.02856 (77*2π)/3745 weeks
78-.08173 -.04342 (78*2π)/3745 weeks
79-.03174 -.04 (79*2π)/3745 weeks
80-.02224 -.07315 (80*2π)/3745 weeks
81-.01871 -.08434 (81*2π)/3745 weeks
82-.07658 -.06328 (82*2π)/3745 weeks
83-.04438 -.04009 (83*2π)/3745 weeks
84-.08108 -.05003 (84*2π)/3744 weeks
85-.02295 -.02488 (85*2π)/3744 weeks
86-.02719 -.06419 (86*2π)/3744 weeks
87-.05601 -.0708 (87*2π)/3744 weeks
88-.05805 -.04266 (88*2π)/3744 weeks
89-.0734 -.07786 (89*2π)/3744 weeks
90-.08455 -.03325 (90*2π)/3744 weeks
91-.03311 -.01191 (91*2π)/3744 weeks
92.00866 -.05441 (92*2π)/3744 weeks
93-.03138 -.05581 (93*2π)/3744 weeks
94-.06241 -.03121 (94*2π)/3744 weeks
95-.05985 -.02977 (95*2π)/3744 weeks
96-.0119 -.03224 (96*2π)/3744 weeks
97-.01506 -.01147 (97*2π)/3744 weeks
98-.00404 -.03961 (98*2π)/3744 weeks
99-.05316 -.04946 (99*2π)/3744 weeks
100-.06183 -.03247 (100*2π)/3744 weeks
101-.01469 -.02689 (101*2π)/3744 weeks
102-.03849 -.03778 (102*2π)/3744 weeks
103-.07001 -.05986 (103*2π)/3744 weeks
104-.05457 -.06901 (104*2π)/3744 weeks
105-.05011 -.04397 (105*2π)/3744 weeks
106-.07598 -.03684 (106*2π)/3744 weeks
107-.06536 -.01864 (107*2π)/3743 weeks
108-.05626 -.06178 (108*2π)/3743 weeks
109-.03814 -.04521 (109*2π)/3743 weeks
110-.04369 -.03906 (110*2π)/3743 weeks
111-.06485 -.01825 (111*2π)/3743 weeks
112-.02132 -.0119 (112*2π)/3743 weeks
113-.04657 -.00525 (113*2π)/3743 weeks
114-.03878 -.03696 (114*2π)/3743 weeks
115-.03252 -.03563 (115*2π)/3743 weeks
116-.04331 -.013 (116*2π)/3743 weeks
117-.01702 -.03119 (117*2π)/3743 weeks
118-.05299 -.03886 (118*2π)/3743 weeks
119-.04935 -.03926 (119*2π)/3743 weeks
120-.04193 -.02143 (120*2π)/3743 weeks
121-.03221 -.02303 (121*2π)/3743 weeks
122-.04576 -.02209 (122*2π)/3743 weeks
123-.04326 -.02755 (123*2π)/3743 weeks
124-.03271 -.0387 (124*2π)/3743 weeks
125-.05261 -.01268 (125*2π)/3743 weeks
126-.05411 -.01726 (126*2π)/3743 weeks
127-.01973 -.02322 (127*2π)/3743 weeks
128-.03937 -.02857 (128*2π)/3743 weeks
129-.04976 .00017 (129*2π)/3743 weeks
130-.0438 -.01416 (130*2π)/3743 weeks
131-.02706 -.03047 (131*2π)/3743 weeks
132-.0327 -.01092 (132*2π)/3743 weeks
133-.05421 .02307 (133*2π)/3743 weeks
134-.04663 -.02425 (134*2π)/3743 weeks
135-.03762 -.01473 (135*2π)/3743 weeks
136-.01227 -.02407 (136*2π)/3743 weeks
137-.04231 .0023 (137*2π)/3743 weeks
138-.06834 -.02753 (138*2π)/3743 weeks
139-.05033 -.05501 (139*2π)/3743 weeks
140-.06303 -.01934 (140*2π)/3743 weeks
141-.03641 -.01068 (141*2π)/3743 weeks
142-.04327 -.01995 (142*2π)/3743 weeks
143-.05905 -.0223 (143*2π)/3743 weeks
144-.03382 -.01755 (144*2π)/3743 weeks
145-.01878 -.02881 (145*2π)/3743 weeks
146-.07077 -.00766 (146*2π)/3743 weeks
147-.03746 -.01125 (147*2π)/3743 weeks
148-.03171 -.01486 (148*2π)/3743 weeks
149-.03597 -.02208 (149*2π)/3743 weeks
150-.03683 -.01335 (150*2π)/3742 weeks
151-.02769 .00996 (151*2π)/3742 weeks
152-.03274 -.00163 (152*2π)/3742 weeks
153-.05379 .00437 (153*2π)/3742 weeks
154-.02452 -.02501 (154*2π)/3742 weeks
155-.02632 -.02715 (155*2π)/3742 weeks
156-.06567 -.01279 (156*2π)/3742 weeks
157-.06639 .01161 (157*2π)/3742 weeks
158-.03824 .00127 (158*2π)/3742 weeks
159-.04153 -.00571 (159*2π)/3742 weeks
160-.04642 .00637 (160*2π)/3742 weeks
161-.03103 .00102 (161*2π)/3742 weeks
162-.06705 .01057 (162*2π)/3742 weeks
163-.00984 -.01359 (163*2π)/3742 weeks
164-.02713 .01277 (164*2π)/3742 weeks
165-.05675 -.01567 (165*2π)/3742 weeks
166-.03468 -.01306 (166*2π)/3742 weeks
167-.01718 -.00387 (167*2π)/3742 weeks
168-.01964 -.02703 (168*2π)/3742 weeks
169-.0713 .00244 (169*2π)/3742 weeks
170-.02997 .00788 (170*2π)/3742 weeks
171-.04717 -.02385 (171*2π)/3742 weeks
172-.05177 .01095 (172*2π)/3742 weeks
173-.01917 -.01023 (173*2π)/3742 weeks
174-.06289 -.01839 (174*2π)/3742 weeks
175-.05233 -.02088 (175*2π)/3742 weeks
176-.03275 -.02427 (176*2π)/3742 weeks
177-.04898   (177*2π)/3742 weeks
178-.06302 .00269 (178*2π)/3742 weeks
179-.02938 .04338 (179*2π)/3742 weeks
180-.02891 .00449 (180*2π)/3742 weeks
181-.02917 -.01716 (181*2π)/3742 weeks
182-.0553 .01448 (182*2π)/3742 weeks
183-.06206 .02917 (183*2π)/3742 weeks
184-.03952 .02608 (184*2π)/3742 weeks
185-.01155 -.00498 (185*2π)/3742 weeks
186-.04135 .00658 (186*2π)/3742 weeks
187-.07148   (187*2π)/3742 weeks
188-.04135 -.00658 (188*2π)/3742 weeks
189-.01155 .00498 (189*2π)/3742 weeks
190-.03952 -.02608 (190*2π)/3742 weeks
191-.06206 -.02917 (191*2π)/3742 weeks
192-.0553 -.01448 (192*2π)/3742 weeks
193-.02917 .01716 (193*2π)/3742 weeks
194-.02891 -.00449 (194*2π)/3742 weeks
195-.02938 -.04338 (195*2π)/3742 weeks
196-.06302 -.00269 (196*2π)/3742 weeks
197-.04898   (197*2π)/3742 weeks
198-.03275 .02427 (198*2π)/3742 weeks
199-.05233 .02088 (199*2π)/3742 weeks
200-.06289 .01839 (200*2π)/3742 weeks
201-.01917 .01023 (201*2π)/3742 weeks
202-.05177 -.01095 (202*2π)/3742 weeks
203-.04717 .02385 (203*2π)/3742 weeks
204-.02997 -.00788 (204*2π)/3742 weeks
205-.0713 -.00244 (205*2π)/3742 weeks
206-.01964 .02703 (206*2π)/3742 weeks
207-.01718 .00387 (207*2π)/3742 weeks
208-.03468 .01306 (208*2π)/3742 weeks
209-.05675 .01567 (209*2π)/3742 weeks
210-.02713 -.01277 (210*2π)/3742 weeks
211-.00984 .01359 (211*2π)/3742 weeks
212-.06705 -.01057 (212*2π)/3742 weeks
213-.03103 -.00102 (213*2π)/3742 weeks
214-.04642 -.00637 (214*2π)/3742 weeks
215-.04153 .00571 (215*2π)/3742 weeks
216-.03824 -.00127 (216*2π)/3742 weeks
217-.06639 -.01161 (217*2π)/3742 weeks
218-.06567 .01279 (218*2π)/3742 weeks
219-.02632 .02715 (219*2π)/3742 weeks
220-.02452 .02501 (220*2π)/3742 weeks
221-.05379 -.00437 (221*2π)/3742 weeks
222-.03274 .00163 (222*2π)/3742 weeks
223-.02769 -.00996 (223*2π)/3742 weeks
224-.03683 .01335 (224*2π)/3742 weeks
225-.03597 .02208 (225*2π)/3742 weeks
226-.03171 .01486 (226*2π)/3742 weeks
227-.03746 .01125 (227*2π)/3742 weeks
228-.07077 .00766 (228*2π)/3742 weeks
229-.01878 .02881 (229*2π)/3742 weeks
230-.03382 .01755 (230*2π)/3742 weeks
231-.05905 .0223 (231*2π)/3742 weeks
232-.04327 .01995 (232*2π)/3742 weeks
233-.03641 .01068 (233*2π)/3742 weeks
234-.06303 .01934 (234*2π)/3742 weeks
235-.05033 .05501 (235*2π)/3742 weeks
236-.06834 .02753 (236*2π)/3742 weeks
237-.04231 -.0023 (237*2π)/3742 weeks
238-.01227 .02407 (238*2π)/3742 weeks
239-.03762 .01473 (239*2π)/3742 weeks
240-.04663 .02425 (240*2π)/3742 weeks
241-.05421 -.02307 (241*2π)/3742 weeks
242-.0327 .01092 (242*2π)/3742 weeks
243-.02706 .03047 (243*2π)/3742 weeks
244-.0438 .01416 (244*2π)/3742 weeks
245-.04976 -.00017 (245*2π)/3742 weeks
246-.03937 .02857 (246*2π)/3742 weeks
247-.01973 .02322 (247*2π)/3742 weeks
248-.05411 .01726 (248*2π)/3742 weeks
249-.05261 .01268 (249*2π)/3742 weeks
250-.03271 .0387 (250*2π)/3741 weeks
251-.04326 .02755 (251*2π)/3741 weeks
252-.04576 .02209 (252*2π)/3741 weeks
253-.03221 .02303 (253*2π)/3741 weeks
254-.04193 .02143 (254*2π)/3741 weeks
255-.04935 .03926 (255*2π)/3741 weeks
256-.05299 .03886 (256*2π)/3741 weeks
257-.01702 .03119 (257*2π)/3741 weeks
258-.04331 .013 (258*2π)/3741 weeks
259-.03252 .03563 (259*2π)/3741 weeks
260-.03878 .03696 (260*2π)/3741 weeks
261-.04657 .00525 (261*2π)/3741 weeks
262-.02132 .0119 (262*2π)/3741 weeks
263-.06485 .01825 (263*2π)/3741 weeks
264-.04369 .03906 (264*2π)/3741 weeks
265-.03814 .04521 (265*2π)/3741 weeks
266-.05626 .06178 (266*2π)/3741 weeks
267-.06536 .01864 (267*2π)/3741 weeks
268-.07598 .03684 (268*2π)/3741 weeks
269-.05011 .04397 (269*2π)/3741 weeks
270-.05457 .06901 (270*2π)/3741 weeks
271-.07001 .05986 (271*2π)/3741 weeks
272-.03849 .03778 (272*2π)/3741 weeks
273-.01469 .02689 (273*2π)/3741 weeks
274-.06183 .03247 (274*2π)/3741 weeks
275-.05316 .04946 (275*2π)/3741 weeks
276-.00404 .03961 (276*2π)/3741 weeks
277-.01506 .01147 (277*2π)/3741 weeks
278-.0119 .03224 (278*2π)/3741 weeks
279-.05985 .02977 (279*2π)/3741 weeks
280-.06241 .03121 (280*2π)/3741 weeks
281-.03138 .05581 (281*2π)/3741 weeks
282.00866 .05441 (282*2π)/3741 weeks
283-.03311 .01191 (283*2π)/3741 weeks
284-.08455 .03325 (284*2π)/3741 weeks
285-.0734 .07786 (285*2π)/3741 weeks
286-.05805 .04266 (286*2π)/3741 weeks
287-.05601 .0708 (287*2π)/3741 weeks
288-.02719 .06419 (288*2π)/3741 weeks
289-.02295 .02488 (289*2π)/3741 weeks
290-.08108 .05003 (290*2π)/3741 weeks
291-.04438 .04009 (291*2π)/3741 weeks
292-.07658 .06328 (292*2π)/3741 weeks
293-.01871 .08434 (293*2π)/3741 weeks
294-.02224 .07315 (294*2π)/3741 weeks
295-.03174 .04 (295*2π)/3741 weeks
296-.08173 .04342 (296*2π)/3741 weeks
297-.03829 .02856 (297*2π)/3741 weeks
298-.04524 .06162 (298*2π)/3741 weeks
299-.03595 .08168 (299*2π)/3741 weeks
300.00155 .03435 (300*2π)/3741 weeks
301-.0342 .04202 (301*2π)/3741 weeks
302-.09328 .07413 (302*2π)/3741 weeks
303-.03279 .06399 (303*2π)/3741 weeks
304-.04094 .09976 (304*2π)/3741 weeks
305-.00249 .06687 (305*2π)/3741 weeks
306-.03385 .02476 (306*2π)/3741 weeks
307-.05443 .046 (307*2π)/3741 weeks
308-.07086 .0507 (308*2π)/3741 weeks
309-.08367 .1163 (309*2π)/3741 weeks
310-.06796 .08523 (310*2π)/3741 weeks
311-.0422 .08397 (311*2π)/3741 weeks
312-.00969 .08705 (312*2π)/3741 weeks
313-.00508 .07334 (313*2π)/3741 weeks
314-.00382 .02824 (314*2π)/3741 weeks
315-.07934 .03974 (315*2π)/3741 weeks
316-.03708 .06379 (316*2π)/3741 weeks
317-.01586 .09761 (317*2π)/3741 weeks
318-.09012 .10953 (318*2π)/3741 weeks
319-.05641 .0915 (319*2π)/3741 weeks
320.01081 .10848 (320*2π)/3741 weeks
321-.03308 .10377 (321*2π)/3741 weeks
322-.11857 .1434 (322*2π)/3741 weeks
323-.07212 .08018 (323*2π)/3741 weeks
324-.08507 .04102 (324*2π)/3741 weeks
325-.07544 .15952 (325*2π)/3741 weeks
326-.03422 .12821 (326*2π)/3741 weeks
327-.07706 .11925 (327*2π)/3741 weeks
328-.11067 .05999 (328*2π)/3741 weeks
329.04356 .12917 (329*2π)/3741 weeks
330-.03936 .07218 (330*2π)/3741 weeks
331-.08167 .14481 (331*2π)/3741 weeks
332-.05668 .07912 (332*2π)/3741 weeks
333-.01132 .08147 (333*2π)/3741 weeks
334-.03213 .12415 (334*2π)/3741 weeks
335-.01762 .08405 (335*2π)/3741 weeks
336-.12699 .13573 (336*2π)/3741 weeks
337-.10633 .15013 (337*2π)/3741 weeks
338-.09227 .15665 (338*2π)/3741 weeks
339-.03131 .16211 (339*2π)/3741 weeks
340-.01884 .18958 (340*2π)/3741 weeks
341-.02875 .07508 (341*2π)/3741 weeks
342-.15956 .25955 (342*2π)/3741 weeks
343-.05943 .19708 (343*2π)/3741 weeks
344-.03958 .13092 (344*2π)/3741 weeks
345-.03169 .25368 (345*2π)/3741 weeks
346.01193 .27432 (346*2π)/3741 weeks
347-.0787 .21249 (347*2π)/3741 weeks
348-.05027 .23687 (348*2π)/3741 weeks
349-.04536 .16906 (349*2π)/3741 weeks
350-.04326 .26428 (350*2π)/3741 weeks
351-.1176 .31566 (351*2π)/3741 weeks
352.01097 .28686 (352*2π)/3741 weeks
353.0989 .1265 (353*2π)/3741 weeks
354-.03192 .15863 (354*2π)/3741 weeks
355-.1325 .23059 (355*2π)/3741 weeks
356-.33157 .32404 (356*2π)/3741 weeks
357-.08658 .31856 (357*2π)/3741 weeks
358.05122 .46788 (358*2π)/3741 weeks
359-.09177 .2381 (359*2π)/3741 weeks
360-.13856 .30348 (360*2π)/3741 weeks
361-.15996 .47239 (361*2π)/3741 weeks
362-.19428 .40332 (362*2π)/3741 weeks
363.1098 .49797 (363*2π)/3741 weeks
364.05331 .64096 (364*2π)/3741 weeks
365-.091 .68545 (365*2π)/3741 weeks
366-.00476 .44871 (366*2π)/3741 weeks
367.28502 .3936 (367*2π)/3741 weeks
368.07248 1.10719 (368*2π)/3741 weeks
369.01326 1.40421 (369*2π)/3741 weeks
370.2665 1.60136 (370*2π)/3741 weeks
371.27528 1.65133 (371*2π)/3741 weeks
372.24481 1.22824 (372*2π)/3741 weeks

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