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# Fourier Analysis of FUEL (Rocket Fuel Inc.)

FUEL (Rocket Fuel Inc.) appears to have interesting cyclic behaviour every 18 weeks (2.4957*sine), 13 weeks (2.209*sine), and 17 weeks (1.9967*sine).

FUEL (Rocket Fuel Inc.) has an average price of 16.03 (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 9/20/2013 to 3/20/2017 for FUEL (Rocket Fuel Inc.), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
016.03467   0
111.5991 14.8073 (1*2π)/184184 weeks
24.13157 10.65671 (2*2π)/18492 weeks
3.62028 8.4983 (3*2π)/18461 weeks
4-1.18278 5.55837 (4*2π)/18446 weeks
5-.92999 2.62574 (5*2π)/18437 weeks
6.18618 2.17663 (6*2π)/18431 weeks
7.39498 1.09007 (7*2π)/18426 weeks
81.55869 .9364 (8*2π)/18423 weeks
91.70416 2.10824 (9*2π)/18420 weeks
10.94005 2.49574 (10*2π)/18418 weeks
11.27946 1.99671 (11*2π)/18417 weeks
12.57062 1.29381 (12*2π)/18415 weeks
131.15573 1.54579 (13*2π)/18414 weeks
14.80934 2.209 (14*2π)/18413 weeks
15.03021 2.09151 (15*2π)/18412 weeks
16-.30197 1.62303 (16*2π)/18412 weeks
17-.13743 1.22747 (17*2π)/18411 weeks
18-.14138 1.01805 (18*2π)/18410 weeks
19-.11937 .97299 (19*2π)/18410 weeks
20-.02724 .70963 (20*2π)/1849 weeks
21.06138 .67641 (21*2π)/1849 weeks
22.23543 .67511 (22*2π)/1848 weeks
23.33939 .83467 (23*2π)/1848 weeks
24.15157 .81939 (24*2π)/1848 weeks
25.11215 .93601 (25*2π)/1847 weeks
26-.30313 .8941 (26*2π)/1847 weeks
27-.34467 .43615 (27*2π)/1847 weeks
28-.08241 .30273 (28*2π)/1847 weeks
29-.06218 .30711 (29*2π)/1846 weeks
30.20379 .16376 (30*2π)/1846 weeks
31.11433 .38516 (31*2π)/1846 weeks
32.11283 .21776 (32*2π)/1846 weeks
33.29869 .32325 (33*2π)/1846 weeks
34.03121 .46929 (34*2π)/1845 weeks
35-.21563 -.0183 (35*2π)/1845 weeks
36.26373 -.12503 (36*2π)/1845 weeks
37.29966 .02947 (37*2π)/1845 weeks
38.24708 .06891 (38*2π)/1845 weeks
39.34858 -.21947 (39*2π)/1845 weeks
40.76855 -.22249 (40*2π)/1845 weeks
41.9788 .18121 (41*2π)/1844 weeks
42.78456 .58774 (42*2π)/1844 weeks
43.40676 .69884 (43*2π)/1844 weeks
44.11102 .40801 (44*2π)/1844 weeks
45.4204 .2451 (45*2π)/1844 weeks
46.41875 .40603 (46*2π)/1844 weeks
47.25708 .4435 (47*2π)/1844 weeks
48.32154 .28618 (48*2π)/1844 weeks
49.28468 .39514 (49*2π)/1844 weeks
50.26462 .33033 (50*2π)/1844 weeks
51.21385 .33917 (51*2π)/1844 weeks
52.10367 .28468 (52*2π)/1844 weeks
53.2051 .23593 (53*2π)/1843 weeks
54.10085 .29761 (54*2π)/1843 weeks
55.08751 .20197 (55*2π)/1843 weeks
56.14008 .11718 (56*2π)/1843 weeks
57.17168 .12237 (57*2π)/1843 weeks
58.24113 .17434 (58*2π)/1843 weeks
59-.04593 .24777 (59*2π)/1843 weeks
60-.06055 -.0171 (60*2π)/1843 weeks
61.05635 -.18099 (61*2π)/1843 weeks
62.25409 -.17705 (62*2π)/1843 weeks
63.28 -.12541 (63*2π)/1843 weeks
64.31613 -.16783 (64*2π)/1843 weeks
65.42384 -.15617 (65*2π)/1843 weeks
66.4359 -.0348 (66*2π)/1843 weeks
67.44847 -.13549 (67*2π)/1843 weeks
68.65475 -.01107 (68*2π)/1843 weeks
69.54745 .13076 (69*2π)/1843 weeks
70.5405 .14407 (70*2π)/1843 weeks
71.48807 .33382 (71*2π)/1843 weeks
72.25227 .188 (72*2π)/1843 weeks
73.39353 .07848 (73*2π)/1843 weeks
74.4693 .21805 (74*2π)/1842 weeks
75.28652 .31133 (75*2π)/1842 weeks
76.20755 .29582 (76*2π)/1842 weeks
77.02501 .18862 (77*2π)/1842 weeks
78.07657 .05626 (78*2π)/1842 weeks
79.09273 -.00725 (79*2π)/1842 weeks
80.11991 -.12192 (80*2π)/1842 weeks
81.20367 -.17603 (81*2π)/1842 weeks
82.29426 -.141 (82*2π)/1842 weeks
83.21581 -.12994 (83*2π)/1842 weeks
84.26838 -.28471 (84*2π)/1842 weeks
85.45944 -.30665 (85*2π)/1842 weeks
86.6065 -.17086 (86*2π)/1842 weeks
87.58171 .04834 (87*2π)/1842 weeks
88.38447 .06804 (88*2π)/1842 weeks
89.41425 -.05075 (89*2π)/1842 weeks
90.45784 -.06658 (90*2π)/1842 weeks
91.4694 .01435 (91*2π)/1842 weeks
92.42902   (92*2π)/1842 weeks
93.4694 -.01435 (93*2π)/1842 weeks
94.45784 .06658 (94*2π)/1842 weeks
95.41425 .05075 (95*2π)/1842 weeks
96.38447 -.06804 (96*2π)/1842 weeks
97.58171 -.04834 (97*2π)/1842 weeks
98.6065 .17086 (98*2π)/1842 weeks
99.45944 .30665 (99*2π)/1842 weeks
100.26838 .28471 (100*2π)/1842 weeks
101.21581 .12994 (101*2π)/1842 weeks
102.29426 .141 (102*2π)/1842 weeks
103.20367 .17603 (103*2π)/1842 weeks
104.11991 .12192 (104*2π)/1842 weeks
105.09273 .00725 (105*2π)/1842 weeks
106.07657 -.05626 (106*2π)/1842 weeks
107.02501 -.18862 (107*2π)/1842 weeks
108.20755 -.29582 (108*2π)/1842 weeks
109.28652 -.31133 (109*2π)/1842 weeks
110.4693 -.21805 (110*2π)/1842 weeks
111.39353 -.07848 (111*2π)/1842 weeks
112.25227 -.188 (112*2π)/1842 weeks
113.48807 -.33382 (113*2π)/1842 weeks
114.5405 -.14407 (114*2π)/1842 weeks
115.54745 -.13076 (115*2π)/1842 weeks
116.65475 .01107 (116*2π)/1842 weeks
117.44847 .13549 (117*2π)/1842 weeks
118.4359 .0348 (118*2π)/1842 weeks
119.42384 .15617 (119*2π)/1842 weeks
120.31613 .16783 (120*2π)/1842 weeks
121.28 .12541 (121*2π)/1842 weeks
122.25409 .17705 (122*2π)/1842 weeks
123.05635 .18099 (123*2π)/1841 weeks
124-.06055 .0171 (124*2π)/1841 weeks
125-.04593 -.24777 (125*2π)/1841 weeks
126.24113 -.17434 (126*2π)/1841 weeks
127.17168 -.12237 (127*2π)/1841 weeks
128.14008 -.11718 (128*2π)/1841 weeks
129.08751 -.20197 (129*2π)/1841 weeks
130.10085 -.29761 (130*2π)/1841 weeks
131.2051 -.23593 (131*2π)/1841 weeks
132.10367 -.28468 (132*2π)/1841 weeks
133.21385 -.33917 (133*2π)/1841 weeks
134.26462 -.33033 (134*2π)/1841 weeks
135.28468 -.39514 (135*2π)/1841 weeks
136.32154 -.28618 (136*2π)/1841 weeks
137.25708 -.4435 (137*2π)/1841 weeks
138.41875 -.40603 (138*2π)/1841 weeks
139.4204 -.2451 (139*2π)/1841 weeks
140.11102 -.40801 (140*2π)/1841 weeks
141.40676 -.69884 (141*2π)/1841 weeks
142.78456 -.58774 (142*2π)/1841 weeks
143.9788 -.18121 (143*2π)/1841 weeks
144.76855 .22249 (144*2π)/1841 weeks
145.34858 .21947 (145*2π)/1841 weeks
146.24708 -.06891 (146*2π)/1841 weeks
147.29966 -.02947 (147*2π)/1841 weeks
148.26373 .12503 (148*2π)/1841 weeks
149-.21563 .0183 (149*2π)/1841 weeks
150.03121 -.46929 (150*2π)/1841 weeks
151.29869 -.32325 (151*2π)/1841 weeks
152.11283 -.21776 (152*2π)/1841 weeks
153.11433 -.38516 (153*2π)/1841 weeks
154.20379 -.16376 (154*2π)/1841 weeks
155-.06218 -.30711 (155*2π)/1841 weeks
156-.08241 -.30273 (156*2π)/1841 weeks
157-.34467 -.43615 (157*2π)/1841 weeks
158-.30313 -.8941 (158*2π)/1841 weeks
159.11215 -.93601 (159*2π)/1841 weeks
160.15157 -.81939 (160*2π)/1841 weeks
161.33939 -.83467 (161*2π)/1841 weeks
162.23543 -.67511 (162*2π)/1841 weeks
163.06138 -.67641 (163*2π)/1841 weeks
164-.02724 -.70963 (164*2π)/1841 weeks
165-.11937 -.97299 (165*2π)/1841 weeks
166-.14138 -1.01805 (166*2π)/1841 weeks
167-.13743 -1.22747 (167*2π)/1841 weeks
168-.30197 -1.62303 (168*2π)/1841 weeks
169.03021 -2.09151 (169*2π)/1841 weeks
170.80934 -2.209 (170*2π)/1841 weeks
1711.15573 -1.54579 (171*2π)/1841 weeks
172.57062 -1.29381 (172*2π)/1841 weeks
173.27946 -1.99671 (173*2π)/1841 weeks
174.94005 -2.49574 (174*2π)/1841 weeks
1751.70416 -2.10824 (175*2π)/1841 weeks
1761.55869 -.9364 (176*2π)/1841 weeks
177.39498 -1.09007 (177*2π)/1841 weeks
178.18618 -2.17663 (178*2π)/1841 weeks
179-.92999 -2.62574 (179*2π)/1841 weeks
180-1.18278 -5.55837 (180*2π)/1841 weeks
181.62028 -8.4983 (181*2π)/1841 weeks
1824.13157 -10.65671 (182*2π)/1841 weeks