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# Fourier Analysis of NAVI (Navient Corporation)

NAVI (Navient Corporation) appears to have interesting cyclic behaviour every 18 weeks (.3756*sine), 22 weeks (.2712*sine), and 20 weeks (.2344*sine).

NAVI (Navient Corporation) has an average price of 13.91 (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 4/17/2014 to 5/21/2018 for NAVI (Navient Corporation), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
013.9055   0
11.43986 .68232 (1*2π)/215215 weeks
2-1.68118 1.83475 (2*2π)/215108 weeks
3-.18072 -.78632 (3*2π)/21572 weeks
4.36457 -.18149 (4*2π)/21554 weeks
5.05776 .03759 (5*2π)/21543 weeks
6.09793 -.23107 (6*2π)/21536 weeks
7-.27171 -.03633 (7*2π)/21531 weeks
8.09758 .54039 (8*2π)/21527 weeks
9-.18879 .09611 (9*2π)/21524 weeks
10.04276 -.27117 (10*2π)/21522 weeks
11.07562 .23436 (11*2π)/21520 weeks
12-.01685 -.37555 (12*2π)/21518 weeks
13.1435 .04308 (13*2π)/21517 weeks
14.19492 -.11639 (14*2π)/21515 weeks
15-.11383 -.07967 (15*2π)/21514 weeks
16-.09054 .09821 (16*2π)/21513 weeks
17.06966 .00845 (17*2π)/21513 weeks
18.0895 .02187 (18*2π)/21512 weeks
19.16314 -.21183 (19*2π)/21511 weeks
20.02762 -.05782 (20*2π)/21511 weeks
21-.13573 .10433 (21*2π)/21510 weeks
22.19852 .1509 (22*2π)/21510 weeks
23-.03437 -.05948 (23*2π)/2159 weeks
24.17019 -.02606 (24*2π)/2159 weeks
25.05557 .03607 (25*2π)/2159 weeks
26-.11336 .0914 (26*2π)/2158 weeks
27.02607 -.01384 (27*2π)/2158 weeks
28-.171 -.09315 (28*2π)/2158 weeks
29.10561 .0315 (29*2π)/2157 weeks
30.16472 -.00869 (30*2π)/2157 weeks
31-.03266 .0376 (31*2π)/2157 weeks
32-.01485 .05136 (32*2π)/2157 weeks
33-.03307 .01077 (33*2π)/2157 weeks
34-.09471 -.09435 (34*2π)/2156 weeks
35.20678 .13448 (35*2π)/2156 weeks
36-.06941 -.04013 (36*2π)/2156 weeks
37.06104 .08416 (37*2π)/2156 weeks
38-.01055 -.13388 (38*2π)/2156 weeks
39-.07097 -.03346 (39*2π)/2156 weeks
40.02255 -.01598 (40*2π)/2155 weeks
41.04985 .05659 (41*2π)/2155 weeks
42-.05369 .02794 (42*2π)/2155 weeks
43.03182 -.12771 (43*2π)/2155 weeks
44-.03428 .01083 (44*2π)/2155 weeks
45-.01723 .01015 (45*2π)/2155 weeks
46-.0494 -.06363 (46*2π)/2155 weeks
47-.01439 .09505 (47*2π)/2155 weeks
48.04226 -.00746 (48*2π)/2154 weeks
49.03635 .02028 (49*2π)/2154 weeks
50.00063 .02343 (50*2π)/2154 weeks
51-.0022 .00115 (51*2π)/2154 weeks
52-.0926 -.00447 (52*2π)/2154 weeks
53.01918 .00934 (53*2π)/2154 weeks
54.03402 -.01772 (54*2π)/2154 weeks
55.01747 -.01869 (55*2π)/2154 weeks
56.03359 .00208 (56*2π)/2154 weeks
57-.02053 -.07224 (57*2π)/2154 weeks
58-.01846 .02368 (58*2π)/2154 weeks
59-.01058 .03786 (59*2π)/2154 weeks
60.02252 -.03837 (60*2π)/2154 weeks
61.04982 -.00039 (61*2π)/2154 weeks
62-.02158 -.05915 (62*2π)/2153 weeks
63-.04875 -.02811 (63*2π)/2153 weeks
64-.02117 -.00623 (64*2π)/2153 weeks
65-.04758 -.01804 (65*2π)/2153 weeks
66-.01281 -.0061 (66*2π)/2153 weeks
67.03412 .00562 (67*2π)/2153 weeks
68-.02489 .0315 (68*2π)/2153 weeks
69-.03171 .0231 (69*2π)/2153 weeks
70-.03486 -.00789 (70*2π)/2153 weeks
71-.00193 .04302 (71*2π)/2153 weeks
72.03781 .02691 (72*2π)/2153 weeks
73.00218 .00542 (73*2π)/2153 weeks
74.01511 .0056 (74*2π)/2153 weeks
75.05011 -.06582 (75*2π)/2153 weeks
76-.02153 -.04135 (76*2π)/2153 weeks
77-.02884 .00266 (77*2π)/2153 weeks
78-.02723 -.00808 (78*2π)/2153 weeks
79-.04503 .00364 (79*2π)/2153 weeks
80-.00997 -.02877 (80*2π)/2153 weeks
81.03204 .00399 (81*2π)/2153 weeks
82.00109 -.01414 (82*2π)/2153 weeks
83-.03979 .03201 (83*2π)/2153 weeks
84-.00431 -.00025 (84*2π)/2153 weeks
85.04473 -.01547 (85*2π)/2153 weeks
86.02153 -.03245 (86*2π)/2153 weeks
87-.05776 .00942 (87*2π)/2152 weeks
88.01515 .00544 (88*2π)/2152 weeks
89.00063 -.05066 (89*2π)/2152 weeks
90.03508 -.02946 (90*2π)/2152 weeks
91-.02726 .01686 (91*2π)/2152 weeks
92.02657 .05595 (92*2π)/2152 weeks
93.05474 -.00938 (93*2π)/2152 weeks
94-.02054 -.00239 (94*2π)/2152 weeks
95.00877 .027 (95*2π)/2152 weeks
96-.05281 -.00311 (96*2π)/2152 weeks
97-.01519 -.00291 (97*2π)/2152 weeks
98.07249 .02994 (98*2π)/2152 weeks
99.00217 .03493 (99*2π)/2152 weeks
100.01119 -.01223 (100*2π)/2152 weeks
101.00897 .02478 (101*2π)/2152 weeks
102-.06399 -.01583 (102*2π)/2152 weeks
103.01819 -.01079 (103*2π)/2152 weeks
104-.00424 -.03138 (104*2π)/2152 weeks
105-.03308 .00244 (105*2π)/2152 weeks
106.0426 .03979 (106*2π)/2152 weeks
107-.02145 -.01751 (107*2π)/2152 weeks
108-.02145 .01751 (108*2π)/2152 weeks
109.0426 -.03979 (109*2π)/2152 weeks
110-.03308 -.00244 (110*2π)/2152 weeks
111-.00424 .03138 (111*2π)/2152 weeks
112.01819 .01079 (112*2π)/2152 weeks
113-.06399 .01583 (113*2π)/2152 weeks
114.00897 -.02478 (114*2π)/2152 weeks
115.01119 .01223 (115*2π)/2152 weeks
116.00217 -.03493 (116*2π)/2152 weeks
117.07249 -.02994 (117*2π)/2152 weeks
118-.01519 .00291 (118*2π)/2152 weeks
119-.05281 .00311 (119*2π)/2152 weeks
120.00877 -.027 (120*2π)/2152 weeks
121-.02054 .00239 (121*2π)/2152 weeks
122.05474 .00938 (122*2π)/2152 weeks
123.02657 -.05595 (123*2π)/2152 weeks
124-.02726 -.01686 (124*2π)/2152 weeks
125.03508 .02946 (125*2π)/2152 weeks
126.00063 .05066 (126*2π)/2152 weeks
127.01515 -.00544 (127*2π)/2152 weeks
128-.05776 -.00942 (128*2π)/2152 weeks
129.02153 .03245 (129*2π)/2152 weeks
130.04473 .01547 (130*2π)/2152 weeks
131-.00431 .00025 (131*2π)/2152 weeks
132-.03979 -.03201 (132*2π)/2152 weeks
133.00109 .01414 (133*2π)/2152 weeks
134.03204 -.00399 (134*2π)/2152 weeks
135-.00997 .02877 (135*2π)/2152 weeks
136-.04503 -.00364 (136*2π)/2152 weeks
137-.02723 .00808 (137*2π)/2152 weeks
138-.02884 -.00266 (138*2π)/2152 weeks
139-.02153 .04135 (139*2π)/2152 weeks
140.05011 .06582 (140*2π)/2152 weeks
141.01511 -.0056 (141*2π)/2152 weeks
142.00218 -.00542 (142*2π)/2152 weeks
143.03781 -.02691 (143*2π)/2152 weeks
144-.00193 -.04302 (144*2π)/2151 weeks
145-.03486 .00789 (145*2π)/2151 weeks
146-.03171 -.0231 (146*2π)/2151 weeks
147-.02489 -.0315 (147*2π)/2151 weeks
148.03412 -.00562 (148*2π)/2151 weeks
149-.01281 .0061 (149*2π)/2151 weeks
150-.04758 .01804 (150*2π)/2151 weeks
151-.02117 .00623 (151*2π)/2151 weeks
152-.04875 .02811 (152*2π)/2151 weeks
153-.02158 .05915 (153*2π)/2151 weeks
154.04982 .00039 (154*2π)/2151 weeks
155.02252 .03837 (155*2π)/2151 weeks
156-.01058 -.03786 (156*2π)/2151 weeks
157-.01846 -.02368 (157*2π)/2151 weeks
158-.02053 .07224 (158*2π)/2151 weeks
159.03359 -.00208 (159*2π)/2151 weeks
160.01747 .01869 (160*2π)/2151 weeks
161.03402 .01772 (161*2π)/2151 weeks
162.01918 -.00934 (162*2π)/2151 weeks
163-.0926 .00447 (163*2π)/2151 weeks
164-.0022 -.00115 (164*2π)/2151 weeks
165.00063 -.02343 (165*2π)/2151 weeks
166.03635 -.02028 (166*2π)/2151 weeks
167.04226 .00746 (167*2π)/2151 weeks
168-.01439 -.09505 (168*2π)/2151 weeks
169-.0494 .06363 (169*2π)/2151 weeks
170-.01723 -.01015 (170*2π)/2151 weeks
171-.03428 -.01083 (171*2π)/2151 weeks
172.03182 .12771 (172*2π)/2151 weeks
173-.05369 -.02794 (173*2π)/2151 weeks
174.04985 -.05659 (174*2π)/2151 weeks
175.02255 .01598 (175*2π)/2151 weeks
176-.07097 .03346 (176*2π)/2151 weeks
177-.01055 .13388 (177*2π)/2151 weeks
178.06104 -.08416 (178*2π)/2151 weeks
179-.06941 .04013 (179*2π)/2151 weeks
180.20678 -.13448 (180*2π)/2151 weeks
181-.09471 .09435 (181*2π)/2151 weeks
182-.03307 -.01077 (182*2π)/2151 weeks
183-.01485 -.05136 (183*2π)/2151 weeks
184-.03266 -.0376 (184*2π)/2151 weeks
185.16472 .00869 (185*2π)/2151 weeks
186.10561 -.0315 (186*2π)/2151 weeks
187-.171 .09315 (187*2π)/2151 weeks
188.02607 .01384 (188*2π)/2151 weeks
189-.11336 -.0914 (189*2π)/2151 weeks
190.05557 -.03607 (190*2π)/2151 weeks
191.17019 .02606 (191*2π)/2151 weeks
192-.03437 .05948 (192*2π)/2151 weeks
193.19852 -.1509 (193*2π)/2151 weeks
194-.13573 -.10433 (194*2π)/2151 weeks
195.02762 .05782 (195*2π)/2151 weeks
196.16314 .21183 (196*2π)/2151 weeks
197.0895 -.02187 (197*2π)/2151 weeks
198.06966 -.00845 (198*2π)/2151 weeks
199-.09054 -.09821 (199*2π)/2151 weeks
200-.11383 .07967 (200*2π)/2151 weeks
201.19492 .11639 (201*2π)/2151 weeks
202.1435 -.04308 (202*2π)/2151 weeks
203-.01685 .37555 (203*2π)/2151 weeks
204.07562 -.23436 (204*2π)/2151 weeks
205.04276 .27117 (205*2π)/2151 weeks
206-.18879 -.09611 (206*2π)/2151 weeks
207.09758 -.54039 (207*2π)/2151 weeks
208-.27171 .03633 (208*2π)/2151 weeks
209.09793 .23107 (209*2π)/2151 weeks
210.05776 -.03759 (210*2π)/2151 weeks
211.36457 .18149 (211*2π)/2151 weeks
212-.18072 .78632 (212*2π)/2151 weeks
213-1.68118 -1.83475 (213*2π)/2151 weeks