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# Fourier Analysis of DATA (Tableau Software)

DATA (Tableau Software) appears to have interesting cyclic behaviour every 24 weeks (4.5944*sine), 24 weeks (3.2463*cosine), and 19 weeks (2.4322*cosine).

DATA (Tableau Software) has an average price of 71.42 (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 5/17/2013 to 5/21/2018 for DATA (Tableau Software), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
071.42205   0
1-4.43475 13.15596 (1*2π)/263263 weeks
28.62906 -14.86067 (2*2π)/263132 weeks
3-2.27076 5.2378 (3*2π)/26388 weeks
4-4.07312 -5.90022 (4*2π)/26366 weeks
5-.38277 -.31384 (5*2π)/26353 weeks
62.83283 -3.91726 (6*2π)/26344 weeks
7.64893 -1.77141 (7*2π)/26338 weeks
81.21651 2.29896 (8*2π)/26333 weeks
9-3.06261 -3.94272 (9*2π)/26329 weeks
10-.65525 .32876 (10*2π)/26326 weeks
11-3.24628 -4.59444 (11*2π)/26324 weeks
122.2501 -1.17649 (12*2π)/26322 weeks
13-.38767 -2.4999 (13*2π)/26320 weeks
142.43215 1.76203 (14*2π)/26319 weeks
15.2452 .14373 (15*2π)/26318 weeks
16-.59829 -.63038 (16*2π)/26316 weeks
17.32391 -2.24284 (17*2π)/26315 weeks
18.17101 -.8766 (18*2π)/26315 weeks
191.57712 -.62592 (19*2π)/26314 weeks
20.59159 -.06359 (20*2π)/26313 weeks
21-.4722 -.20785 (21*2π)/26313 weeks
22-1.49424 -1.02547 (22*2π)/26312 weeks
23.65225 -.05604 (23*2π)/26311 weeks
24-.60488 -1.18544 (24*2π)/26311 weeks
25-.43651 -.87333 (25*2π)/26311 weeks
26.11216 -1.38989 (26*2π)/26310 weeks
27-.11109 -.13215 (27*2π)/26310 weeks
28.03748 -1.04395 (28*2π)/2639 weeks
29-1.26041 .25025 (29*2π)/2639 weeks
30-.22417 -1.36236 (30*2π)/2639 weeks
31-.19603 -.2712 (31*2π)/2638 weeks
32-.02457 -.77986 (32*2π)/2638 weeks
33-.64609 -.50839 (33*2π)/2638 weeks
34.26239 -1.20674 (34*2π)/2638 weeks
35-.29036 .13287 (35*2π)/2638 weeks
36-.76774 -.74417 (36*2π)/2637 weeks
37-.4344 -1.11293 (37*2π)/2637 weeks
38.384 .26674 (38*2π)/2637 weeks
39-.67642 -.78 (39*2π)/2637 weeks
40.00676 -.16376 (40*2π)/2637 weeks
41.31887 -.46057 (41*2π)/2636 weeks
42-.19233 .41542 (42*2π)/2636 weeks
43.12351 -.2481 (43*2π)/2636 weeks
44-.25185 -.63804 (44*2π)/2636 weeks
45-.36731 -.32748 (45*2π)/2636 weeks
46.16905 -.64469 (46*2π)/2636 weeks
47-.13807 .4089 (47*2π)/2636 weeks
48-.4491 -.60723 (48*2π)/2635 weeks
49.401 .14775 (49*2π)/2635 weeks
50-.52841 -.31635 (50*2π)/2635 weeks
51-.19635 .14611 (51*2π)/2635 weeks
52-.51421 -.56994 (52*2π)/2635 weeks
53-.35044 -.12105 (53*2π)/2635 weeks
54-.04119 -.26496 (54*2π)/2635 weeks
55-.33518 -.23836 (55*2π)/2635 weeks
56-.30637 .12719 (56*2π)/2635 weeks
57-.96885 -.36446 (57*2π)/2635 weeks
58.25427 -.57021 (58*2π)/2635 weeks
59-.66372 -.1682 (59*2π)/2634 weeks
60.2741 -.373 (60*2π)/2634 weeks
61-.19886 -.22038 (61*2π)/2634 weeks
62-.28138 -.18185 (62*2π)/2634 weeks
63.09688 -.59863 (63*2π)/2634 weeks
64-.43447 .36719 (64*2π)/2634 weeks
65.05606 -.75527 (65*2π)/2634 weeks
66-.28009 .05236 (66*2π)/2634 weeks
67.13376 -.80666 (67*2π)/2634 weeks
68-.45586 .37338 (68*2π)/2634 weeks
69.29082 -.725 (69*2π)/2634 weeks
70-.3966 .20487 (70*2π)/2634 weeks
71-.1658 -.59706 (71*2π)/2634 weeks
72.02316 .07399 (72*2π)/2634 weeks
73.18607 -.10065 (73*2π)/2634 weeks
74-.36466 .12847 (74*2π)/2634 weeks
75.13939 .00648 (75*2π)/2634 weeks
76-.04826 -.21859 (76*2π)/2633 weeks
77-.18071 .10932 (77*2π)/2633 weeks
78-.53619 -.35816 (78*2π)/2633 weeks
79.23241 .10067 (79*2π)/2633 weeks
80-.15875 -.43188 (80*2π)/2633 weeks
81.04807 -.19074 (81*2π)/2633 weeks
82-.23743 -.1665 (82*2π)/2633 weeks
83-.46389 -.1738 (83*2π)/2633 weeks
84.08355 .0895 (84*2π)/2633 weeks
85-.01565 -.11798 (85*2π)/2633 weeks
86-.03761 .33053 (86*2π)/2633 weeks
87-.37679 -.53298 (87*2π)/2633 weeks
88.02478 .24981 (88*2π)/2633 weeks
89-.36028 -.29737 (89*2π)/2633 weeks
90.03943 .35618 (90*2π)/2633 weeks
91-.0308 -.32731 (91*2π)/2633 weeks
92.09712 .0093 (92*2π)/2633 weeks
93-.19441 -.27595 (93*2π)/2633 weeks
94-.01139 -.00994 (94*2π)/2633 weeks
95-.187 -.09889 (95*2π)/2633 weeks
96-.49166 -.02696 (96*2π)/2633 weeks
97-.44279 -.37152 (97*2π)/2633 weeks
98-.53206 -.19548 (98*2π)/2633 weeks
99-.09526 -.1783 (99*2π)/2633 weeks
100-.58618 .14541 (100*2π)/2633 weeks
101-.45246 -.39513 (101*2π)/2633 weeks
102-.25889 -.08659 (102*2π)/2633 weeks
103-.36715 -.08773 (103*2π)/2633 weeks
104.19218 -.34172 (104*2π)/2633 weeks
105-.32111 .21134 (105*2π)/2633 weeks
106.10532 -.14903 (106*2π)/2632 weeks
107-.37475 .1256 (107*2π)/2632 weeks
108.06769 -.1804 (108*2π)/2632 weeks
109-.20485 .00713 (109*2π)/2632 weeks
110.10492 -.28941 (110*2π)/2632 weeks
111-.25444 .17042 (111*2π)/2632 weeks
112-.23997 -.09819 (112*2π)/2632 weeks
113-.52812 -.0805 (113*2π)/2632 weeks
114.12665 -.2984 (114*2π)/2632 weeks
115-.33394 .0483 (115*2π)/2632 weeks
116-.20562 .25655 (116*2π)/2632 weeks
117-.16619 -.08865 (117*2π)/2632 weeks
118-.11222 .2659 (118*2π)/2632 weeks
119-.33458 -.39874 (119*2π)/2632 weeks
120-.01405 .35286 (120*2π)/2632 weeks
121-.38728 .17435 (121*2π)/2632 weeks
122-.15848 .08515 (122*2π)/2632 weeks
123.01194 .29206 (123*2π)/2632 weeks
124-.5788 -.21475 (124*2π)/2632 weeks
125-.03371 .03708 (125*2π)/2632 weeks
126-.28021 .15717 (126*2π)/2632 weeks
127-.26963 .0641 (127*2π)/2632 weeks
128-.26891 -.11729 (128*2π)/2632 weeks
129-.3043 .20919 (129*2π)/2632 weeks
130-.20083 -.39484 (130*2π)/2632 weeks
131-.37721 .16884 (131*2π)/2632 weeks
132-.37721 -.16884 (132*2π)/2632 weeks
133-.20083 .39484 (133*2π)/2632 weeks
134-.3043 -.20919 (134*2π)/2632 weeks
135-.26891 .11729 (135*2π)/2632 weeks
136-.26963 -.0641 (136*2π)/2632 weeks
137-.28021 -.15717 (137*2π)/2632 weeks
138-.03371 -.03708 (138*2π)/2632 weeks
139-.5788 .21475 (139*2π)/2632 weeks
140.01194 -.29206 (140*2π)/2632 weeks
141-.15848 -.08515 (141*2π)/2632 weeks
142-.38728 -.17435 (142*2π)/2632 weeks
143-.01405 -.35286 (143*2π)/2632 weeks
144-.33458 .39874 (144*2π)/2632 weeks
145-.11222 -.2659 (145*2π)/2632 weeks
146-.16619 .08865 (146*2π)/2632 weeks
147-.20562 -.25655 (147*2π)/2632 weeks
148-.33394 -.0483 (148*2π)/2632 weeks
149.12665 .2984 (149*2π)/2632 weeks
150-.52812 .0805 (150*2π)/2632 weeks
151-.23997 .09819 (151*2π)/2632 weeks
152-.25444 -.17042 (152*2π)/2632 weeks
153.10492 .28941 (153*2π)/2632 weeks
154-.20485 -.00713 (154*2π)/2632 weeks
155.06769 .1804 (155*2π)/2632 weeks
156-.37475 -.1256 (156*2π)/2632 weeks
157.10532 .14903 (157*2π)/2632 weeks
158-.32111 -.21134 (158*2π)/2632 weeks
159.19218 .34172 (159*2π)/2632 weeks
160-.36715 .08773 (160*2π)/2632 weeks
161-.25889 .08659 (161*2π)/2632 weeks
162-.45246 .39513 (162*2π)/2632 weeks
163-.58618 -.14541 (163*2π)/2632 weeks
164-.09526 .1783 (164*2π)/2632 weeks
165-.53206 .19548 (165*2π)/2632 weeks
166-.44279 .37152 (166*2π)/2632 weeks
167-.49166 .02696 (167*2π)/2632 weeks
168-.187 .09889 (168*2π)/2632 weeks
169-.01139 .00994 (169*2π)/2632 weeks
170-.19441 .27595 (170*2π)/2632 weeks
171.09712 -.0093 (171*2π)/2632 weeks
172-.0308 .32731 (172*2π)/2632 weeks
173.03943 -.35618 (173*2π)/2632 weeks
174-.36028 .29737 (174*2π)/2632 weeks
175.02478 -.24981 (175*2π)/2632 weeks
176-.37679 .53298 (176*2π)/2631 weeks
177-.03761 -.33053 (177*2π)/2631 weeks
178-.01565 .11798 (178*2π)/2631 weeks
179.08355 -.0895 (179*2π)/2631 weeks
180-.46389 .1738 (180*2π)/2631 weeks
181-.23743 .1665 (181*2π)/2631 weeks
182.04807 .19074 (182*2π)/2631 weeks
183-.15875 .43188 (183*2π)/2631 weeks
184.23241 -.10067 (184*2π)/2631 weeks
185-.53619 .35816 (185*2π)/2631 weeks
186-.18071 -.10932 (186*2π)/2631 weeks
187-.04826 .21859 (187*2π)/2631 weeks
188.13939 -.00648 (188*2π)/2631 weeks
189-.36466 -.12847 (189*2π)/2631 weeks
190.18607 .10065 (190*2π)/2631 weeks
191.02316 -.07399 (191*2π)/2631 weeks
192-.1658 .59706 (192*2π)/2631 weeks
193-.3966 -.20487 (193*2π)/2631 weeks
194.29082 .725 (194*2π)/2631 weeks
195-.45586 -.37338 (195*2π)/2631 weeks
196.13376 .80666 (196*2π)/2631 weeks
197-.28009 -.05236 (197*2π)/2631 weeks
198.05606 .75527 (198*2π)/2631 weeks
199-.43447 -.36719 (199*2π)/2631 weeks
200.09688 .59863 (200*2π)/2631 weeks
201-.28138 .18185 (201*2π)/2631 weeks
202-.19886 .22038 (202*2π)/2631 weeks
203.2741 .373 (203*2π)/2631 weeks
204-.66372 .1682 (204*2π)/2631 weeks
205.25427 .57021 (205*2π)/2631 weeks
206-.96885 .36446 (206*2π)/2631 weeks
207-.30637 -.12719 (207*2π)/2631 weeks
208-.33518 .23836 (208*2π)/2631 weeks
209-.04119 .26496 (209*2π)/2631 weeks
210-.35044 .12105 (210*2π)/2631 weeks
211-.51421 .56994 (211*2π)/2631 weeks
212-.19635 -.14611 (212*2π)/2631 weeks
213-.52841 .31635 (213*2π)/2631 weeks
214.401 -.14775 (214*2π)/2631 weeks
215-.4491 .60723 (215*2π)/2631 weeks
216-.13807 -.4089 (216*2π)/2631 weeks
217.16905 .64469 (217*2π)/2631 weeks
218-.36731 .32748 (218*2π)/2631 weeks
219-.25185 .63804 (219*2π)/2631 weeks
220.12351 .2481 (220*2π)/2631 weeks
221-.19233 -.41542 (221*2π)/2631 weeks
222.31887 .46057 (222*2π)/2631 weeks
223.00676 .16376 (223*2π)/2631 weeks
224-.67642 .78 (224*2π)/2631 weeks
225.384 -.26674 (225*2π)/2631 weeks
226-.4344 1.11293 (226*2π)/2631 weeks
227-.76774 .74417 (227*2π)/2631 weeks
228-.29036 -.13287 (228*2π)/2631 weeks
229.26239 1.20674 (229*2π)/2631 weeks
230-.64609 .50839 (230*2π)/2631 weeks
231-.02457 .77986 (231*2π)/2631 weeks
232-.19603 .2712 (232*2π)/2631 weeks
233-.22417 1.36236 (233*2π)/2631 weeks
234-1.26041 -.25025 (234*2π)/2631 weeks
235.03748 1.04395 (235*2π)/2631 weeks
236-.11109 .13215 (236*2π)/2631 weeks
237.11216 1.38989 (237*2π)/2631 weeks
238-.43651 .87333 (238*2π)/2631 weeks
239-.60488 1.18544 (239*2π)/2631 weeks
240.65225 .05604 (240*2π)/2631 weeks
241-1.49424 1.02547 (241*2π)/2631 weeks
242-.4722 .20785 (242*2π)/2631 weeks
243.59159 .06359 (243*2π)/2631 weeks
2441.57712 .62592 (244*2π)/2631 weeks
245.17101 .8766 (245*2π)/2631 weeks
246.32391 2.24284 (246*2π)/2631 weeks
247-.59829 .63038 (247*2π)/2631 weeks
248.2452 -.14373 (248*2π)/2631 weeks
2492.43215 -1.76203 (249*2π)/2631 weeks
250-.38767 2.4999 (250*2π)/2631 weeks
2512.2501 1.17649 (251*2π)/2631 weeks
252-3.24628 4.59444 (252*2π)/2631 weeks
253-.65525 -.32876 (253*2π)/2631 weeks
254-3.06261 3.94272 (254*2π)/2631 weeks
2551.21651 -2.29896 (255*2π)/2631 weeks
256.64893 1.77141 (256*2π)/2631 weeks
2572.83283 3.91726 (257*2π)/2631 weeks
258-.38277 .31384 (258*2π)/2631 weeks
259-4.07312 5.90022 (259*2π)/2631 weeks
260-2.27076 -5.2378 (260*2π)/2631 weeks
2618.62906 14.86067 (261*2π)/2631 weeks