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Fourier Analysis of FTO (FRONTIER OIL CP)


FTO (FRONTIER OIL CP) appears to have interesting cyclic behaviour every 23 weeks (9.8779*sine), 15 weeks (6.4486*sine), and 18 weeks (5.6517*sine).

FTO (FRONTIER OIL CP) has an average price of 123.24 (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 10/10/2007 to 1/9/2017 for FTO (FRONTIER OIL CP), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0123.2432   0 
163.72865 50.15197 (1*2π)/276276 weeks
2-2.11606 56.75751 (2*2π)/276138 weeks
3-9.74868 9.57991 (3*2π)/27692 weeks
46.9935 1.81862 (4*2π)/27669 weeks
5-.87414 15.40079 (5*2π)/27655 weeks
6-5.21441 5.84897 (6*2π)/27646 weeks
71.93509 -.05746 (7*2π)/27639 weeks
86.86672 10.57888 (8*2π)/27635 weeks
9-6.37301 10.08862 (9*2π)/27631 weeks
10-4.3588 -.90496 (10*2π)/27628 weeks
114.19122 .85385 (11*2π)/27625 weeks
121.17054 9.87789 (12*2π)/27623 weeks
13-2.88982 4.60459 (13*2π)/27621 weeks
141.26264 .54467 (14*2π)/27620 weeks
153.77641 5.65173 (15*2π)/27618 weeks
16-2.49033 4.54959 (16*2π)/27617 weeks
17-1.19659 -1.29314 (17*2π)/27616 weeks
184.91328 1.80687 (18*2π)/27615 weeks
191.11738 6.44859 (19*2π)/27615 weeks
20-2.98393 1.99813 (20*2π)/27614 weeks
21.70985 -1.90032 (21*2π)/27613 weeks
223.175 2.61065 (22*2π)/27613 weeks
23-1.26277 2.93309 (23*2π)/27612 weeks
24-.6272 .66089 (24*2π)/27612 weeks
252.58213 .97704 (25*2π)/27611 weeks
26.38838 3.34033 (26*2π)/27611 weeks
27-1.8994 .0867 (27*2π)/27610 weeks
281.20607 -1.05624 (28*2π)/27610 weeks
292.39853 2.93616 (29*2π)/27610 weeks
30-.72216 2.58247 (30*2π)/2769 weeks
31-.77405 -.08692 (31*2π)/2769 weeks
321.55843 .29758 (32*2π)/2769 weeks
331.09852 2.48996 (33*2π)/2768 weeks
34-.71263 .38186 (34*2π)/2768 weeks
351.26171 .31911 (35*2π)/2768 weeks
361.97474 2.07966 (36*2π)/2768 weeks
37-1.19496 1.31364 (37*2π)/2767 weeks
38-.38126 -.33356 (38*2π)/2767 weeks
392.61957 .32098 (39*2π)/2767 weeks
40.50916 2.12967 (40*2π)/2767 weeks
41-.67954 1.11214 (41*2π)/2767 weeks
421.32179 -.0418 (42*2π)/2767 weeks
431.24382 .98648 (43*2π)/2766 weeks
44-.20541 1.06314 (44*2π)/2766 weeks
45.80635 -.87277 (45*2π)/2766 weeks
461.50434 .85318 (46*2π)/2766 weeks
47-.11459 1.97887 (47*2π)/2766 weeks
48-.71208 -.22997 (48*2π)/2766 weeks
49.75087 .0688 (49*2π)/2766 weeks
501.5116 1.6199 (50*2π)/2766 weeks
51-.31656 1.03284 (51*2π)/2765 weeks
52.58727 .23366 (52*2π)/2765 weeks
531.10129 1.03914 (53*2π)/2765 weeks
54-.35753 1.45326 (54*2π)/2765 weeks
55.2349 -.05822 (55*2π)/2765 weeks
561.63971 .25142 (56*2π)/2765 weeks
571.2093 2.19687 (57*2π)/2765 weeks
58-.93295 .35104 (58*2π)/2765 weeks
59.58603 -.45926 (59*2π)/2765 weeks
601.71136 .81918 (60*2π)/2765 weeks
61-.12684 1.25553 (61*2π)/2765 weeks
62-.23928 -.43661 (62*2π)/2764 weeks
631.19782 .30883 (63*2π)/2764 weeks
64.55878 1.62199 (64*2π)/2764 weeks
65-.84362 .39973 (65*2π)/2764 weeks
66.72607 -.60481 (66*2π)/2764 weeks
671.51436 .51499 (67*2π)/2764 weeks
68-.27656 1.64475 (68*2π)/2764 weeks
69-.48093 -.20673 (69*2π)/2764 weeks
70.93858 -.17561 (70*2π)/2764 weeks
71.70181 .91339 (71*2π)/2764 weeks
72-.69795 .47053 (72*2π)/2764 weeks
73.3361 -.27732 (73*2π)/2764 weeks
741.31061 .535 (74*2π)/2764 weeks
75-.39534 1.07193 (75*2π)/2764 weeks
76-.54683 -.38593 (76*2π)/2764 weeks
77.8331 -.62748 (77*2π)/2764 weeks
78.60581 1.26846 (78*2π)/2764 weeks
79-.25899 .40427 (79*2π)/2763 weeks
80.11948 -.58462 (80*2π)/2763 weeks
81.97862 .57173 (81*2π)/2763 weeks
82-.29612 .21929 (82*2π)/2763 weeks
83-.17232 -.56775 (83*2π)/2763 weeks
841.10763 .09432 (84*2π)/2763 weeks
85.22014 .99491 (85*2π)/2763 weeks
86-.35996 .31625 (86*2π)/2763 weeks
87.68813 -.89215 (87*2π)/2763 weeks
88.79915 .36883 (88*2π)/2763 weeks
89.28039 .58314 (89*2π)/2763 weeks
90.33583 -.30892 (90*2π)/2763 weeks
91.99485 .03258 (91*2π)/2763 weeks
92.65871 .34996 (92*2π)/2763 weeks
93-.09389 -.45465 (93*2π)/2763 weeks
941.10767 -.71145 (94*2π)/2763 weeks
951.14866 .20854 (95*2π)/2763 weeks
96.06033 .14539 (96*2π)/2763 weeks
97.22469 -.61043 (97*2π)/2763 weeks
981.0172 -.60655 (98*2π)/2763 weeks
99.40818 .38388 (99*2π)/2763 weeks
100.28994 -.51943 (100*2π)/2763 weeks
101.95404 -.38555 (101*2π)/2763 weeks
102.81321 .63561 (102*2π)/2763 weeks
103-.01835 .06159 (103*2π)/2763 weeks
104.46488 -1.0154 (104*2π)/2763 weeks
1051.59688 .04554 (105*2π)/2763 weeks
106.68149 .60288 (106*2π)/2763 weeks
107-.17063 -.20246 (107*2π)/2763 weeks
108.89161 -.46623 (108*2π)/2763 weeks
1091.12187 .42911 (109*2π)/2763 weeks
110.19379 .24009 (110*2π)/2763 weeks
111.84933 -.66968 (111*2π)/2762 weeks
1121.44542 .18645 (112*2π)/2762 weeks
113.12051 .87353 (113*2π)/2762 weeks
114.25496 -.40742 (114*2π)/2762 weeks
1151.31767 -.56907 (115*2π)/2762 weeks
1161.39302 .51859 (116*2π)/2762 weeks
117.03893 .29171 (117*2π)/2762 weeks
118.54998 -.67746 (118*2π)/2762 weeks
1191.08245 .18653 (119*2π)/2762 weeks
120.2775 .80049 (120*2π)/2762 weeks
121.39808 -.19026 (121*2π)/2762 weeks
1221.32079 -.53221 (122*2π)/2762 weeks
1231.06002 .96156 (123*2π)/2762 weeks
124-.04187 .43763 (124*2π)/2762 weeks
125.4913 -.60968 (125*2π)/2762 weeks
1261.31447 -.04399 (126*2π)/2762 weeks
127.50378 .75697 (127*2π)/2762 weeks
128.29588 -.07702 (128*2π)/2762 weeks
1291.06828 -.16599 (129*2π)/2762 weeks
130.79472 .64303 (130*2π)/2762 weeks
131.03361 .06535 (131*2π)/2762 weeks
132.76113 -.72238 (132*2π)/2762 weeks
1331.33839 .17202 (133*2π)/2762 weeks
134.4683 .67056 (134*2π)/2762 weeks
135.08856 -.23397 (135*2π)/2762 weeks
136.86799 -.43461 (136*2π)/2762 weeks
137.62364 -.11746 (137*2π)/2762 weeks
138.2629   (138*2π)/2762 weeks
139.62364 .11746 (139*2π)/2762 weeks
140.86799 .43461 (140*2π)/2762 weeks
141.08856 .23397 (141*2π)/2762 weeks
142.4683 -.67056 (142*2π)/2762 weeks
1431.33839 -.17202 (143*2π)/2762 weeks
144.76113 .72238 (144*2π)/2762 weeks
145.03361 -.06535 (145*2π)/2762 weeks
146.79472 -.64303 (146*2π)/2762 weeks
1471.06828 .16599 (147*2π)/2762 weeks
148.29588 .07702 (148*2π)/2762 weeks
149.50378 -.75697 (149*2π)/2762 weeks
1501.31447 .04399 (150*2π)/2762 weeks
151.4913 .60968 (151*2π)/2762 weeks
152-.04187 -.43763 (152*2π)/2762 weeks
1531.06002 -.96156 (153*2π)/2762 weeks
1541.32079 .53221 (154*2π)/2762 weeks
155.39808 .19026 (155*2π)/2762 weeks
156.2775 -.80049 (156*2π)/2762 weeks
1571.08245 -.18653 (157*2π)/2762 weeks
158.54998 .67746 (158*2π)/2762 weeks
159.03893 -.29171 (159*2π)/2762 weeks
1601.39302 -.51859 (160*2π)/2762 weeks
1611.31767 .56907 (161*2π)/2762 weeks
162.25496 .40742 (162*2π)/2762 weeks
163.12051 -.87353 (163*2π)/2762 weeks
1641.44542 -.18645 (164*2π)/2762 weeks
165.84933 .66968 (165*2π)/2762 weeks
166.19379 -.24009 (166*2π)/2762 weeks
1671.12187 -.42911 (167*2π)/2762 weeks
168.89161 .46623 (168*2π)/2762 weeks
169-.17063 .20246 (169*2π)/2762 weeks
170.68149 -.60288 (170*2π)/2762 weeks
1711.59688 -.04554 (171*2π)/2762 weeks
172.46488 1.0154 (172*2π)/2762 weeks
173-.01835 -.06159 (173*2π)/2762 weeks
174.81321 -.63561 (174*2π)/2762 weeks
175.95404 .38555 (175*2π)/2762 weeks
176.28994 .51943 (176*2π)/2762 weeks
177.40818 -.38388 (177*2π)/2762 weeks
1781.0172 .60655 (178*2π)/2762 weeks
179.22469 .61043 (179*2π)/2762 weeks
180.06033 -.14539 (180*2π)/2762 weeks
1811.14866 -.20854 (181*2π)/2762 weeks
1821.10767 .71145 (182*2π)/2762 weeks
183-.09389 .45465 (183*2π)/2762 weeks
184.65871 -.34996 (184*2π)/2762 weeks
185.99485 -.03258 (185*2π)/2761 weeks
186.33583 .30892 (186*2π)/2761 weeks
187.28039 -.58314 (187*2π)/2761 weeks
188.79915 -.36883 (188*2π)/2761 weeks
189.68813 .89215 (189*2π)/2761 weeks
190-.35996 -.31625 (190*2π)/2761 weeks
191.22014 -.99491 (191*2π)/2761 weeks
1921.10763 -.09432 (192*2π)/2761 weeks
193-.17232 .56775 (193*2π)/2761 weeks
194-.29612 -.21929 (194*2π)/2761 weeks
195.97862 -.57173 (195*2π)/2761 weeks
196.11948 .58462 (196*2π)/2761 weeks
197-.25899 -.40427 (197*2π)/2761 weeks
198.60581 -1.26846 (198*2π)/2761 weeks
199.8331 .62748 (199*2π)/2761 weeks
200-.54683 .38593 (200*2π)/2761 weeks
201-.39534 -1.07193 (201*2π)/2761 weeks
2021.31061 -.535 (202*2π)/2761 weeks
203.3361 .27732 (203*2π)/2761 weeks
204-.69795 -.47053 (204*2π)/2761 weeks
205.70181 -.91339 (205*2π)/2761 weeks
206.93858 .17561 (206*2π)/2761 weeks
207-.48093 .20673 (207*2π)/2761 weeks
208-.27656 -1.64475 (208*2π)/2761 weeks
2091.51436 -.51499 (209*2π)/2761 weeks
210.72607 .60481 (210*2π)/2761 weeks
211-.84362 -.39973 (211*2π)/2761 weeks
212.55878 -1.62199 (212*2π)/2761 weeks
2131.19782 -.30883 (213*2π)/2761 weeks
214-.23928 .43661 (214*2π)/2761 weeks
215-.12684 -1.25553 (215*2π)/2761 weeks
2161.71136 -.81918 (216*2π)/2761 weeks
217.58603 .45926 (217*2π)/2761 weeks
218-.93295 -.35104 (218*2π)/2761 weeks
2191.2093 -2.19687 (219*2π)/2761 weeks
2201.63971 -.25142 (220*2π)/2761 weeks
221.2349 .05822 (221*2π)/2761 weeks
222-.35753 -1.45326 (222*2π)/2761 weeks
2231.10129 -1.03914 (223*2π)/2761 weeks
224.58727 -.23366 (224*2π)/2761 weeks
225-.31656 -1.03284 (225*2π)/2761 weeks
2261.5116 -1.6199 (226*2π)/2761 weeks
227.75087 -.0688 (227*2π)/2761 weeks
228-.71208 .22997 (228*2π)/2761 weeks
229-.11459 -1.97887 (229*2π)/2761 weeks
2301.50434 -.85318 (230*2π)/2761 weeks
231.80635 .87277 (231*2π)/2761 weeks
232-.20541 -1.06314 (232*2π)/2761 weeks
2331.24382 -.98648 (233*2π)/2761 weeks
2341.32179 .0418 (234*2π)/2761 weeks
235-.67954 -1.11214 (235*2π)/2761 weeks
236.50916 -2.12967 (236*2π)/2761 weeks
2372.61957 -.32098 (237*2π)/2761 weeks
238-.38126 .33356 (238*2π)/2761 weeks
239-1.19496 -1.31364 (239*2π)/2761 weeks
2401.97474 -2.07966 (240*2π)/2761 weeks
2411.26171 -.31911 (241*2π)/2761 weeks
242-.71263 -.38186 (242*2π)/2761 weeks
2431.09852 -2.48996 (243*2π)/2761 weeks
2441.55843 -.29758 (244*2π)/2761 weeks
245-.77405 .08692 (245*2π)/2761 weeks
246-.72216 -2.58247 (246*2π)/2761 weeks
2472.39853 -2.93616 (247*2π)/2761 weeks
2481.20607 1.05624 (248*2π)/2761 weeks
249-1.8994 -.0867 (249*2π)/2761 weeks
250.38838 -3.34033 (250*2π)/2761 weeks
2512.58213 -.97704 (251*2π)/2761 weeks
252-.6272 -.66089 (252*2π)/2761 weeks
253-1.26277 -2.93309 (253*2π)/2761 weeks
2543.175 -2.61065 (254*2π)/2761 weeks
255.70985 1.90032 (255*2π)/2761 weeks
256-2.98393 -1.99813 (256*2π)/2761 weeks
2571.11738 -6.44859 (257*2π)/2761 weeks
2584.91328 -1.80687 (258*2π)/2761 weeks
259-1.19659 1.29314 (259*2π)/2761 weeks
260-2.49033 -4.54959 (260*2π)/2761 weeks
2613.77641 -5.65173 (261*2π)/2761 weeks
2621.26264 -.54467 (262*2π)/2761 weeks
263-2.88982 -4.60459 (263*2π)/2761 weeks
2641.17054 -9.87789 (264*2π)/2761 weeks
2654.19122 -.85385 (265*2π)/2761 weeks
266-4.3588 .90496 (266*2π)/2761 weeks
267-6.37301 -10.08862 (267*2π)/2761 weeks
2686.86672 -10.57888 (268*2π)/2761 weeks
2691.93509 .05746 (269*2π)/2761 weeks
270-5.21441 -5.84897 (270*2π)/2761 weeks
271-.87414 -15.40079 (271*2π)/2761 weeks
2726.9935 -1.81862 (272*2π)/2761 weeks
273-9.74868 -9.57991 (273*2π)/2761 weeks
274-2.11606 -56.75751 (274*2π)/2761 weeks

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