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Fourier Analysis of WAGE (WageWorks, Inc. Common Stock)


WAGE (WageWorks, Inc. Common Stock) appears to have interesting cyclic behaviour every 25 weeks (2.5263*sine), 20 weeks (2.1857*sine), and 23 weeks (2.122*sine).

WAGE (WageWorks, Inc. Common Stock) has an average price of 45.33 (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 5/11/2012 to 3/13/2017 for WAGE (WageWorks, Inc. Common Stock), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
045.3348   0 
1-6.10099 -8.80988 (1*2π)/254254 weeks
22.07319 -13.67884 (2*2π)/254127 weeks
32.92123 -10.16545 (3*2π)/25485 weeks
4-.64023 -.55154 (4*2π)/25464 weeks
5-1.42764 -6.63901 (5*2π)/25451 weeks
61.40772 -1.66253 (6*2π)/25442 weeks
7-.06177 -3.97796 (7*2π)/25436 weeks
8-1.28171 -3.35156 (8*2π)/25432 weeks
9-.41814 -1.93798 (9*2π)/25428 weeks
10-.71734 -2.52633 (10*2π)/25425 weeks
11.03378 -2.12197 (11*2π)/25423 weeks
12-.62895 -.53863 (12*2π)/25421 weeks
13-.20769 -2.18572 (13*2π)/25420 weeks
14.05249 -.36914 (14*2π)/25418 weeks
15-.10975 -1.62348 (15*2π)/25417 weeks
16.2489 -1.04053 (16*2π)/25416 weeks
17-.31787 -1.51164 (17*2π)/25415 weeks
18.51595 -1.74014 (18*2π)/25414 weeks
19-.13939 -1.01036 (19*2π)/25413 weeks
20-.64848 -1.51062 (20*2π)/25413 weeks
21.07845 -1.28758 (21*2π)/25412 weeks
22-1.31089 -1.1704 (22*2π)/25412 weeks
23-.1507 -1.20936 (23*2π)/25411 weeks
24-.50345 -.56849 (24*2π)/25411 weeks
25-.68414 -1.01375 (25*2π)/25410 weeks
26-.22508 -.20056 (26*2π)/25410 weeks
27-.18534 -.6119 (27*2π)/2549 weeks
28.05814 -.94157 (28*2π)/2549 weeks
29-.06483 -.9399 (29*2π)/2549 weeks
30-.02705 -.58739 (30*2π)/2548 weeks
31-.12139 -1.25679 (31*2π)/2548 weeks
32-.3695 -.77459 (32*2π)/2548 weeks
33-.25367 -.98234 (33*2π)/2548 weeks
34-.61503 -.84729 (34*2π)/2547 weeks
35.213 -.13524 (35*2π)/2547 weeks
36-.88272 -.60165 (36*2π)/2547 weeks
37-.10742 -.62098 (37*2π)/2547 weeks
38-.56463 -.37776 (38*2π)/2547 weeks
39.3399 -.64644 (39*2π)/2547 weeks
40-.70774 -.17705 (40*2π)/2546 weeks
41-.12359 -.32025 (41*2π)/2546 weeks
42.01555 -.80543 (42*2π)/2546 weeks
43-.01603 -.30749 (43*2π)/2546 weeks
44-.19948 -.29548 (44*2π)/2546 weeks
45-.504 -.74453 (45*2π)/2546 weeks
46-.20716 -.5354 (46*2π)/2546 weeks
47-.48927 -.42197 (47*2π)/2545 weeks
48-.4502 -.2725 (48*2π)/2545 weeks
49-.53167 -.52913 (49*2π)/2545 weeks
50-.26568 -.20266 (50*2π)/2545 weeks
51-.07999 -.16412 (51*2π)/2545 weeks
52-.25017 -.51126 (52*2π)/2545 weeks
53-.35219 -.22742 (53*2π)/2545 weeks
54-.08009 -.22173 (54*2π)/2545 weeks
55-.0937 -.29147 (55*2π)/2545 weeks
56-.31917 -.51786 (56*2π)/2545 weeks
57-.15282 -.41134 (57*2π)/2544 weeks
58-.223 -.19595 (58*2π)/2544 weeks
59-.19451 -.17838 (59*2π)/2544 weeks
60-.31701 -.41386 (60*2π)/2544 weeks
61-.19523 -.40475 (61*2π)/2544 weeks
62-.33658 -.05988 (62*2π)/2544 weeks
63-.11301 -.23444 (63*2π)/2544 weeks
64-.34249 -.17928 (64*2π)/2544 weeks
65-.16755 -.31167 (65*2π)/2544 weeks
66-.45985 -.1131 (66*2π)/2544 weeks
67.03247 -.16345 (67*2π)/2544 weeks
68-.3159 -.44885 (68*2π)/2544 weeks
69-.17917 -.20056 (69*2π)/2544 weeks
70-.22249 -.37227 (70*2π)/2544 weeks
71-.42533 -.28273 (71*2π)/2544 weeks
72-.19677 -.36216 (72*2π)/2544 weeks
73-.37851 -.13321 (73*2π)/2543 weeks
74-.137 -.07417 (74*2π)/2543 weeks
75-.28635 -.28441 (75*2π)/2543 weeks
76-.30654 -.07455 (76*2π)/2543 weeks
77-.1112 -.0819 (77*2π)/2543 weeks
78-.18791 -.21272 (78*2π)/2543 weeks
79-.25525 -.12639 (79*2π)/2543 weeks
80-.16082 -.25469 (80*2π)/2543 weeks
81-.16463 -.50235 (81*2π)/2543 weeks
82-.2796 -.02716 (82*2π)/2543 weeks
83-.29862 -.3513 (83*2π)/2543 weeks
84-.18963 -.22803 (84*2π)/2543 weeks
85-.32091 -.37249 (85*2π)/2543 weeks
86-.30419 -.19127 (86*2π)/2543 weeks
87-.27036 -.15174 (87*2π)/2543 weeks
88-.27112 -.20266 (88*2π)/2543 weeks
89-.26981 -.2609 (89*2π)/2543 weeks
90-.41817 -.17693 (90*2π)/2543 weeks
91-.21628 -.06553 (91*2π)/2543 weeks
92-.19149 -.26877 (92*2π)/2543 weeks
93-.38907 -.17859 (93*2π)/2543 weeks
94-.31615 .00396 (94*2π)/2543 weeks
95-.24699 -.16368 (95*2π)/2543 weeks
96-.3329 -.12679 (96*2π)/2543 weeks
97-.33865 -.01065 (97*2π)/2543 weeks
98-.29699 -.2252 (98*2π)/2543 weeks
99-.38584 -.07391 (99*2π)/2543 weeks
100-.38574 -.09837 (100*2π)/2543 weeks
101-.30764 -.05862 (101*2π)/2543 weeks
102-.34801 -.15251 (102*2π)/2542 weeks
103-.38468 .04983 (103*2π)/2542 weeks
104-.26549 -.18901 (104*2π)/2542 weeks
105-.18697 -.0173 (105*2π)/2542 weeks
106-.22953 -.14026 (106*2π)/2542 weeks
107-.3157 -.35299 (107*2π)/2542 weeks
108-.34664 -.03999 (108*2π)/2542 weeks
109-.35541 -.11833 (109*2π)/2542 weeks
110-.25653 -.11999 (110*2π)/2542 weeks
111-.34705 -.07882 (111*2π)/2542 weeks
112-.39359 -.07881 (112*2π)/2542 weeks
113-.24563 .00459 (113*2π)/2542 weeks
114-.38287 .24063 (114*2π)/2542 weeks
115-.21478 -.15307 (115*2π)/2542 weeks
116-.27554 .13291 (116*2π)/2542 weeks
117-.35324 .01441 (117*2π)/2542 weeks
118-.06094 .02066 (118*2π)/2542 weeks
119-.27032 .13311 (119*2π)/2542 weeks
120-.38192 -.17253 (120*2π)/2542 weeks
121-.17627 .11053 (121*2π)/2542 weeks
122-.24932 -.03924 (122*2π)/2542 weeks
123-.12259 .12196 (123*2π)/2542 weeks
124-.20826 .00017 (124*2π)/2542 weeks
125-.21792 -.22452 (125*2π)/2542 weeks
126-.32604 .08735 (126*2π)/2542 weeks
127-.34882   (127*2π)/2542 weeks
128-.32604 -.08735 (128*2π)/2542 weeks
129-.21792 .22452 (129*2π)/2542 weeks
130-.20826 -.00017 (130*2π)/2542 weeks
131-.12259 -.12196 (131*2π)/2542 weeks
132-.24932 .03924 (132*2π)/2542 weeks
133-.17627 -.11053 (133*2π)/2542 weeks
134-.38192 .17253 (134*2π)/2542 weeks
135-.27032 -.13311 (135*2π)/2542 weeks
136-.06094 -.02066 (136*2π)/2542 weeks
137-.35324 -.01441 (137*2π)/2542 weeks
138-.27554 -.13291 (138*2π)/2542 weeks
139-.21478 .15307 (139*2π)/2542 weeks
140-.38287 -.24063 (140*2π)/2542 weeks
141-.24563 -.00459 (141*2π)/2542 weeks
142-.39359 .07881 (142*2π)/2542 weeks
143-.34705 .07882 (143*2π)/2542 weeks
144-.25653 .11999 (144*2π)/2542 weeks
145-.35541 .11833 (145*2π)/2542 weeks
146-.34664 .03999 (146*2π)/2542 weeks
147-.3157 .35299 (147*2π)/2542 weeks
148-.22953 .14026 (148*2π)/2542 weeks
149-.18697 .0173 (149*2π)/2542 weeks
150-.26549 .18901 (150*2π)/2542 weeks
151-.38468 -.04983 (151*2π)/2542 weeks
152-.34801 .15251 (152*2π)/2542 weeks
153-.30764 .05862 (153*2π)/2542 weeks
154-.38574 .09837 (154*2π)/2542 weeks
155-.38584 .07391 (155*2π)/2542 weeks
156-.29699 .2252 (156*2π)/2542 weeks
157-.33865 .01065 (157*2π)/2542 weeks
158-.3329 .12679 (158*2π)/2542 weeks
159-.24699 .16368 (159*2π)/2542 weeks
160-.31615 -.00396 (160*2π)/2542 weeks
161-.38907 .17859 (161*2π)/2542 weeks
162-.19149 .26877 (162*2π)/2542 weeks
163-.21628 .06553 (163*2π)/2542 weeks
164-.41817 .17693 (164*2π)/2542 weeks
165-.26981 .2609 (165*2π)/2542 weeks
166-.27112 .20266 (166*2π)/2542 weeks
167-.27036 .15174 (167*2π)/2542 weeks
168-.30419 .19127 (168*2π)/2542 weeks
169-.32091 .37249 (169*2π)/2542 weeks
170-.18963 .22803 (170*2π)/2541 weeks
171-.29862 .3513 (171*2π)/2541 weeks
172-.2796 .02716 (172*2π)/2541 weeks
173-.16463 .50235 (173*2π)/2541 weeks
174-.16082 .25469 (174*2π)/2541 weeks
175-.25525 .12639 (175*2π)/2541 weeks
176-.18791 .21272 (176*2π)/2541 weeks
177-.1112 .0819 (177*2π)/2541 weeks
178-.30654 .07455 (178*2π)/2541 weeks
179-.28635 .28441 (179*2π)/2541 weeks
180-.137 .07417 (180*2π)/2541 weeks
181-.37851 .13321 (181*2π)/2541 weeks
182-.19677 .36216 (182*2π)/2541 weeks
183-.42533 .28273 (183*2π)/2541 weeks
184-.22249 .37227 (184*2π)/2541 weeks
185-.17917 .20056 (185*2π)/2541 weeks
186-.3159 .44885 (186*2π)/2541 weeks
187.03247 .16345 (187*2π)/2541 weeks
188-.45985 .1131 (188*2π)/2541 weeks
189-.16755 .31167 (189*2π)/2541 weeks
190-.34249 .17928 (190*2π)/2541 weeks
191-.11301 .23444 (191*2π)/2541 weeks
192-.33658 .05988 (192*2π)/2541 weeks
193-.19523 .40475 (193*2π)/2541 weeks
194-.31701 .41386 (194*2π)/2541 weeks
195-.19451 .17838 (195*2π)/2541 weeks
196-.223 .19595 (196*2π)/2541 weeks
197-.15282 .41134 (197*2π)/2541 weeks
198-.31917 .51786 (198*2π)/2541 weeks
199-.0937 .29147 (199*2π)/2541 weeks
200-.08009 .22173 (200*2π)/2541 weeks
201-.35219 .22742 (201*2π)/2541 weeks
202-.25017 .51126 (202*2π)/2541 weeks
203-.07999 .16412 (203*2π)/2541 weeks
204-.26568 .20266 (204*2π)/2541 weeks
205-.53167 .52913 (205*2π)/2541 weeks
206-.4502 .2725 (206*2π)/2541 weeks
207-.48927 .42197 (207*2π)/2541 weeks
208-.20716 .5354 (208*2π)/2541 weeks
209-.504 .74453 (209*2π)/2541 weeks
210-.19948 .29548 (210*2π)/2541 weeks
211-.01603 .30749 (211*2π)/2541 weeks
212.01555 .80543 (212*2π)/2541 weeks
213-.12359 .32025 (213*2π)/2541 weeks
214-.70774 .17705 (214*2π)/2541 weeks
215.3399 .64644 (215*2π)/2541 weeks
216-.56463 .37776 (216*2π)/2541 weeks
217-.10742 .62098 (217*2π)/2541 weeks
218-.88272 .60165 (218*2π)/2541 weeks
219.213 .13524 (219*2π)/2541 weeks
220-.61503 .84729 (220*2π)/2541 weeks
221-.25367 .98234 (221*2π)/2541 weeks
222-.3695 .77459 (222*2π)/2541 weeks
223-.12139 1.25679 (223*2π)/2541 weeks
224-.02705 .58739 (224*2π)/2541 weeks
225-.06483 .9399 (225*2π)/2541 weeks
226.05814 .94157 (226*2π)/2541 weeks
227-.18534 .6119 (227*2π)/2541 weeks
228-.22508 .20056 (228*2π)/2541 weeks
229-.68414 1.01375 (229*2π)/2541 weeks
230-.50345 .56849 (230*2π)/2541 weeks
231-.1507 1.20936 (231*2π)/2541 weeks
232-1.31089 1.1704 (232*2π)/2541 weeks
233.07845 1.28758 (233*2π)/2541 weeks
234-.64848 1.51062 (234*2π)/2541 weeks
235-.13939 1.01036 (235*2π)/2541 weeks
236.51595 1.74014 (236*2π)/2541 weeks
237-.31787 1.51164 (237*2π)/2541 weeks
238.2489 1.04053 (238*2π)/2541 weeks
239-.10975 1.62348 (239*2π)/2541 weeks
240.05249 .36914 (240*2π)/2541 weeks
241-.20769 2.18572 (241*2π)/2541 weeks
242-.62895 .53863 (242*2π)/2541 weeks
243.03378 2.12197 (243*2π)/2541 weeks
244-.71734 2.52633 (244*2π)/2541 weeks
245-.41814 1.93798 (245*2π)/2541 weeks
246-1.28171 3.35156 (246*2π)/2541 weeks
247-.06177 3.97796 (247*2π)/2541 weeks
2481.40772 1.66253 (248*2π)/2541 weeks
249-1.42764 6.63901 (249*2π)/2541 weeks
250-.64023 .55154 (250*2π)/2541 weeks
2512.92123 10.16545 (251*2π)/2541 weeks
2522.07319 13.67884 (252*2π)/2541 weeks

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