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Fourier Analysis of KEG (Key Energy Services, Inc. Commo)


KEG (Key Energy Services, Inc. Commo) appears to have interesting cyclic behaviour every 108 weeks (177.8112*sine), 62 weeks (156.8699*sine), and 130 weeks (131.714*sine).

KEG (Key Energy Services, Inc. Commo) has an average price of 1,812.7 (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 3/17/1992 to 1/9/2017 for KEG (Key Energy Services, Inc. Commo), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
01,812.697   0 
1-816.7466 -80.21042 (1*2π)/12951,295 weeks
2-501.3993 268.7411 (2*2π)/1295648 weeks
3-437.1763 -264.1863 (3*2π)/1295432 weeks
452.78477 111.0899 (4*2π)/1295324 weeks
5488.3647 129.6919 (5*2π)/1295259 weeks
6-272.5722 183.5942 (6*2π)/1295216 weeks
7-425.5921 88.15671 (7*2π)/1295185 weeks
8195.063 -164.6313 (8*2π)/1295162 weeks
9320.8943 16.10404 (9*2π)/1295144 weeks
10-38.15357 131.714 (10*2π)/1295130 weeks
11-86.54222 -92.10818 (11*2π)/1295118 weeks
12-51.93649 -177.8112 (12*2π)/1295108 weeks
1353.21889 72.78315 (13*2π)/1295100 weeks
1480.41549 127.4528 (14*2π)/129593 weeks
15-43.33477 -1.07422 (15*2π)/129586 weeks
16-86.21677 -.52413 (16*2π)/129581 weeks
1779.07761 49.82988 (17*2π)/129576 weeks
18117.0545 -36.52797 (18*2π)/129572 weeks
19-52.77162 45.39791 (19*2π)/129568 weeks
20-6.30073 107.688 (20*2π)/129565 weeks
2119.2837 -156.8699 (21*2π)/129562 weeks
22-.24265 -15.03563 (22*2π)/129559 weeks
2312.35693 84.30538 (23*2π)/129556 weeks
24-81.74791 -16.13142 (24*2π)/129554 weeks
25-7.89863 108.6643 (25*2π)/129552 weeks
2650.33318 -40.97805 (26*2π)/129550 weeks
2776.69335 -74.00128 (27*2π)/129548 weeks
28-68.90108 121.4087 (28*2π)/129546 weeks
29-17.63243 25.91219 (29*2π)/129545 weeks
3032.51726 -36.21797 (30*2π)/129543 weeks
3170.50632 -32.13559 (31*2π)/129542 weeks
3248.02062 39.48365 (32*2π)/129540 weeks
33-53.34758 .70311 (33*2π)/129539 weeks
34-92.84853 28.73162 (34*2π)/129538 weeks
3559.48988 -25.00617 (35*2π)/129537 weeks
3632.80771 -4.9863 (36*2π)/129536 weeks
379.75586 46.27932 (37*2π)/129535 weeks
38-52.72417 39.15063 (38*2π)/129534 weeks
39-23.61652 -32.77569 (39*2π)/129533 weeks
4060.4578 .50192 (40*2π)/129532 weeks
4158.34552 13.55516 (41*2π)/129532 weeks
42-60.85807 19.07838 (42*2π)/129531 weeks
43-55.02473 8.00206 (43*2π)/129530 weeks
4473.43387 -.12189 (44*2π)/129529 weeks
457.67108 17.75739 (45*2π)/129529 weeks
4622.92357 10.80433 (46*2π)/129528 weeks
47-36.64637 -25.27225 (47*2π)/129528 weeks
48-26.32878 -13.79061 (48*2π)/129527 weeks
4943.69729 22.16551 (49*2π)/129526 weeks
502.47003 45.78508 (50*2π)/129526 weeks
51-39.94879 -4.04421 (51*2π)/129525 weeks
524.96901 -26.3656 (52*2π)/129525 weeks
5320.34849 -8.05165 (53*2π)/129524 weeks
5419.2453 34.72935 (54*2π)/129524 weeks
55-42.6107 1.4924 (55*2π)/129524 weeks
5610.83259 -5.92507 (56*2π)/129523 weeks
5712.24089 -2.45778 (57*2π)/129523 weeks
5813.73063 8.01858 (58*2π)/129522 weeks
5917.62078 -5.89724 (59*2π)/129522 weeks
60-32.98604 10.86768 (60*2π)/129522 weeks
61-2.2567 21.86788 (61*2π)/129521 weeks
6232.98573 8.45906 (62*2π)/129521 weeks
6313.93388 1.4154 (63*2π)/129521 weeks
6410.44499 8.06077 (64*2π)/129520 weeks
65-14.91178 -6.01577 (65*2π)/129520 weeks
66-30.90218 -6.79036 (66*2π)/129520 weeks
6740.7601 32.94084 (67*2π)/129519 weeks
686.60607 11.99485 (68*2π)/129519 weeks
69-30.69548 -10.33826 (69*2π)/129519 weeks
70-20.6192 -16.84735 (70*2π)/129519 weeks
7123.43775 18.8275 (71*2π)/129518 weeks
7225.45885 3.9102 (72*2π)/129518 weeks
73-13.21196 14.36471 (73*2π)/129518 weeks
74-23.43681 -.39614 (74*2π)/129518 weeks
7514.91919 -28.33057 (75*2π)/129517 weeks
7614.82747 41.59806 (76*2π)/129517 weeks
7710.06134 20.62094 (77*2π)/129517 weeks
78-9.95055 -26.90687 (78*2π)/129517 weeks
79-1.11665 -5.35921 (79*2π)/129516 weeks
802.74613 10.22703 (80*2π)/129516 weeks
8121.36578 11.00564 (81*2π)/129516 weeks
82-14.00636 15.09152 (82*2π)/129516 weeks
83-19.19957 -5.99486 (83*2π)/129516 weeks
84-2.31295 -13.35422 (84*2π)/129515 weeks
853.28844 36.57253 (85*2π)/129515 weeks
8612.7713 -5.51773 (86*2π)/129515 weeks
87-.7853 5.48175 (87*2π)/129515 weeks
88-1.79787 -3.44437 (88*2π)/129515 weeks
89.02628 1.5725 (89*2π)/129515 weeks
901.82995 14.96669 (90*2π)/129514 weeks
914.88829 -7.25325 (91*2π)/129514 weeks
92-4.70333 -11.96859 (92*2π)/129514 weeks
938.56099 4.73635 (93*2π)/129514 weeks
94-15.50476 18.69189 (94*2π)/129514 weeks
955.83636 17.62007 (95*2π)/129514 weeks
96-3.72409 -19.32676 (96*2π)/129513 weeks
979.33442 -5.46387 (97*2π)/129513 weeks
9815.42977 24.90038 (98*2π)/129513 weeks
99-18.97482 -4.09907 (99*2π)/129513 weeks
100-2.48542 -1.35833 (100*2π)/129513 weeks
101-3.18763 .2298 (101*2π)/129513 weeks
10212.38947 -3.8527 (102*2π)/129513 weeks
103-3.70544 15.82456 (103*2π)/129513 weeks
104-4.49905 -.41009 (104*2π)/129512 weeks
105-5.05827 -13.47422 (105*2π)/129512 weeks
1068.86744 22.76087 (106*2π)/129512 weeks
107-.02401 -2.42733 (107*2π)/129512 weeks
108-5.21665 -11.18925 (108*2π)/129512 weeks
10910.96419 7.42554 (109*2π)/129512 weeks
110-5.48604 -5.1087 (110*2π)/129512 weeks
111-15.27636 -2.04408 (111*2π)/129512 weeks
1121.28964 4.66992 (112*2π)/129512 weeks
11310.53179 -4.3538 (113*2π)/129511 weeks
1144.45199 8.39012 (114*2π)/129511 weeks
115-7.06562 10.13567 (115*2π)/129511 weeks
116-4.53821 -11.34627 (116*2π)/129511 weeks
11714.77283 -3.816 (117*2π)/129511 weeks
11814.96078 2.57175 (118*2π)/129511 weeks
119.17197 -6.6723 (119*2π)/129511 weeks
120-3.59182 -8.91198 (120*2π)/129511 weeks
121-4.30448 2.83942 (121*2π)/129511 weeks
1226.10682 11.8471 (122*2π)/129511 weeks
12312.62027 -9.47539 (123*2π)/129511 weeks
124-3.98024 16.60926 (124*2π)/129510 weeks
1255.58246 3.62741 (125*2π)/129510 weeks
126-3.49896 -5.14908 (126*2π)/129510 weeks
12724.2952 12.59156 (127*2π)/129510 weeks
128-8.86785 -6.70759 (128*2π)/129510 weeks
129-2.13391 -2.5717 (129*2π)/129510 weeks
1304.74728 10.08662 (130*2π)/129510 weeks
1316.40616 -.85783 (131*2π)/129510 weeks
132-10.626 -.56269 (132*2π)/129510 weeks
1338.97825 11.83223 (133*2π)/129510 weeks
1346.63431 -1.79267 (134*2π)/129510 weeks
1356.23208 5.01283 (135*2π)/129510 weeks
1362.70755 1.46984 (136*2π)/129510 weeks
137.4613 -2.918 (137*2π)/12959 weeks
1383.10316 5.50608 (138*2π)/12959 weeks
13911.51265 6.18737 (139*2π)/12959 weeks
1401.63864 7.02213 (140*2π)/12959 weeks
141-18.1303 -.53043 (141*2π)/12959 weeks
1426.63206 11.50129 (142*2π)/12959 weeks
14313.05537 7.51258 (143*2π)/12959 weeks
144-4.20263 .37821 (144*2π)/12959 weeks
1459.96567 3.61059 (145*2π)/12959 weeks
146-8.68804 13.2324 (146*2π)/12959 weeks
147-8.904 2.56649 (147*2π)/12959 weeks
14815.20408 -6.06334 (148*2π)/12959 weeks
149-.44562 -8.08234 (149*2π)/12959 weeks
150-3.42057 17.43365 (150*2π)/12959 weeks
151-18.98468 6.17311 (151*2π)/12959 weeks
1527.08301 -10.48555 (152*2π)/12959 weeks
15310.91566 7.38517 (153*2π)/12958 weeks
154-4.46914 7.07818 (154*2π)/12958 weeks
155-3.24825 4.75537 (155*2π)/12958 weeks
156-3.36443 3.17209 (156*2π)/12958 weeks
1573.16761 -9.48332 (157*2π)/12958 weeks
15812.38212 -1.02966 (158*2π)/12958 weeks
159-11.06244 -3.28947 (159*2π)/12958 weeks
160-9.12544 5.98756 (160*2π)/12958 weeks
161-.11182 11.28309 (161*2π)/12958 weeks
16211.10181 9.63232 (162*2π)/12958 weeks
163.45559 -13.54766 (163*2π)/12958 weeks
1646.09181 -3.35362 (164*2π)/12958 weeks
165-4.44906 14.70327 (165*2π)/12958 weeks
166-10.49388 3.15885 (166*2π)/12958 weeks
16710.88093 -12.37735 (167*2π)/12958 weeks
168-3.89978 .19875 (168*2π)/12958 weeks
1692.49068 16.62735 (169*2π)/12958 weeks
170-5.174 -1.42755 (170*2π)/12958 weeks
171-5.41489 5.89064 (171*2π)/12958 weeks
1729.32938 -2.12409 (172*2π)/12958 weeks
1734.80623 -11.10608 (173*2π)/12957 weeks
174-10.26531 5.41323 (174*2π)/12957 weeks
175-7.05878 7.73966 (175*2π)/12957 weeks
1767.99329 -2.24893 (176*2π)/12957 weeks
1772.5183 -3.99866 (177*2π)/12957 weeks
178-1.88742 -6.08181 (178*2π)/12957 weeks
1795.49597 .20699 (179*2π)/12957 weeks
180-1.32295 3.71401 (180*2π)/12957 weeks
18110.48886 3.31416 (181*2π)/12957 weeks
182-3.53984 -11.398 (182*2π)/12957 weeks
183-2.63691 3.7747 (183*2π)/12957 weeks
1848.7418 6.56128 (184*2π)/12957 weeks
185-2.0901 -4.93962 (185*2π)/12957 weeks
1862.25057 -4.04559 (186*2π)/12957 weeks
1875.44503 7.49831 (187*2π)/12957 weeks
188-8.38983 5.32467 (188*2π)/12957 weeks
18912.1808 -3.09525 (189*2π)/12957 weeks
190-5.22613 -3.98766 (190*2π)/12957 weeks
1913.71343 -3.16547 (191*2π)/12957 weeks
192-1.07842 8.3436 (192*2π)/12957 weeks
193-7.34065 -4.88681 (193*2π)/12957 weeks
19418.22284 2.4699 (194*2π)/12957 weeks
19510.00634 -1.81425 (195*2π)/12957 weeks
196-1.88095 1.25412 (196*2π)/12957 weeks
197-6.68784 -4.25859 (197*2π)/12957 weeks
19813.22591 5.04501 (198*2π)/12957 weeks
19913.0339 -2.6318 (199*2π)/12957 weeks
2001.69289 7.39948 (200*2π)/12956 weeks
201-13.93981 -3.96088 (201*2π)/12956 weeks
2027.32819 11.30262 (202*2π)/12956 weeks
2037.5575 4.32906 (203*2π)/12956 weeks
2044.95286 -3.61441 (204*2π)/12956 weeks
2052.72701 3.17909 (205*2π)/12956 weeks
2069.86809 1.30703 (206*2π)/12956 weeks
207-.22095 2.93265 (207*2π)/12956 weeks
2081.52445 4.02368 (208*2π)/12956 weeks
2092.97394 -4.34451 (209*2π)/12956 weeks
2103.69248 .70604 (210*2π)/12956 weeks
211-.28038 13.42736 (211*2π)/12956 weeks
2129.75087 5.12768 (212*2π)/12956 weeks
213-2.63672 -7.27603 (213*2π)/12956 weeks
214-.86537 11.13016 (214*2π)/12956 weeks
2153.49917 5.00976 (215*2π)/12956 weeks
2163.06927 4.96348 (216*2π)/12956 weeks
2172.23504 -1.60718 (217*2π)/12956 weeks
2185.21314 -.15668 (218*2π)/12956 weeks
219-2.33222 6.26782 (219*2π)/12956 weeks
220-2.21556 1.74719 (220*2π)/12956 weeks
2215.85591 3.97351 (221*2π)/12956 weeks
2222.91825 -.65282 (222*2π)/12956 weeks
2231.04612 4.5386 (223*2π)/12956 weeks
2244.64914 3.72337 (224*2π)/12956 weeks
225-9.08455 6.96052 (225*2π)/12956 weeks
2265.96465 5.47002 (226*2π)/12956 weeks
2272.56129 .22182 (227*2π)/12956 weeks
228-5.80453 3.99518 (228*2π)/12956 weeks
2299.39686 7.14247 (229*2π)/12956 weeks
230-1.9538 -2.26227 (230*2π)/12956 weeks
231-5.79605 1.3817 (231*2π)/12956 weeks
2326.95089 7.63529 (232*2π)/12956 weeks
233-1.41382 4.8295 (233*2π)/12956 weeks
2345.9916 -.78997 (234*2π)/12956 weeks
2351.09254 1.01724 (235*2π)/12956 weeks
236-1.20808 -.70857 (236*2π)/12955 weeks
237.40202 7.67307 (237*2π)/12955 weeks
238.27038 7.23494 (238*2π)/12955 weeks
239-.38616 -.42943 (239*2π)/12955 weeks
240-.02558 3.57818 (240*2π)/12955 weeks
2415.36477 2.59123 (241*2π)/12955 weeks
242-6.07304 2.90277 (242*2π)/12955 weeks
2431.33536 -6.5119 (243*2π)/12955 weeks
2444.57579 8.50822 (244*2π)/12955 weeks
245-4.31074 3.13345 (245*2π)/12955 weeks
2461.81439 -3.12595 (246*2π)/12955 weeks
247-1.72471 -.62779 (247*2π)/12955 weeks
2487.73739 4.77832 (248*2π)/12955 weeks
2492.44377 6.1634 (249*2π)/12955 weeks
250-6.77528 6.75287 (250*2π)/12955 weeks
2511.22747 -6.17201 (251*2π)/12955 weeks
2528.61585 8.01327 (252*2π)/12955 weeks
253-2.32501 6.84842 (253*2π)/12955 weeks
254-1.00146 -5.40547 (254*2π)/12955 weeks
2552.38301 2.88197 (255*2π)/12955 weeks
256-1.50448 9.98397 (256*2π)/12955 weeks
2571.8366 -2.39466 (257*2π)/12955 weeks
258-4.30317 -.10955 (258*2π)/12955 weeks
2595.78253 .68426 (259*2π)/12955 weeks
2602.98058 9.66872 (260*2π)/12955 weeks
261-9.83161 1.36719 (261*2π)/12955 weeks
262-5.04839 -2.92592 (262*2π)/12955 weeks
26313.59833 8.08488 (263*2π)/12955 weeks
2644.28879 2.70916 (264*2π)/12955 weeks
265-.4801 5.24997 (265*2π)/12955 weeks
266-3.52659 -2.15193 (266*2π)/12955 weeks
267-6.28256 -1.7042 (267*2π)/12955 weeks
2686.30899 8.82487 (268*2π)/12955 weeks
2697.48094 5.57422 (269*2π)/12955 weeks
270-14.82344 -4.65791 (270*2π)/12955 weeks
271-.55037 4.39112 (271*2π)/12955 weeks
2724.09742 4.26112 (272*2π)/12955 weeks
2734.52716 4.14608 (273*2π)/12955 weeks
2741.75968 4.94674 (274*2π)/12955 weeks
275-4.05291 -1.05238 (275*2π)/12955 weeks
276-5.82102 2.83837 (276*2π)/12955 weeks
2773.05949 .77203 (277*2π)/12955 weeks
2781.26864 -4.10345 (278*2π)/12955 weeks
279-7.20169 10.55534 (279*2π)/12955 weeks
280-1.33317 5.54311 (280*2π)/12955 weeks
2811.29618 -4.28633 (281*2π)/12955 weeks
2825.44013 1.57861 (282*2π)/12955 weeks
283-4.38597 -.30495 (283*2π)/12955 weeks
284-1.05296 2.9396 (284*2π)/12955 weeks
285-4.42902 2.75852 (285*2π)/12955 weeks
2863.05137 .63472 (286*2π)/12955 weeks
2874.75451 -1.21469 (287*2π)/12955 weeks
288-7.72448 2.26578 (288*2π)/12954 weeks
289-10.04535 6.34246 (289*2π)/12954 weeks
29013.6658 -.00543 (290*2π)/12954 weeks
2912.12716 -6.88959 (291*2π)/12954 weeks
292.63815 5.34852 (292*2π)/12954 weeks
293-10.59166 1.76103 (293*2π)/12954 weeks
294-.41454 -1.03178 (294*2π)/12954 weeks
2957.87851 .6244 (295*2π)/12954 weeks
296-.62686 7.39915 (296*2π)/12954 weeks
297-5.76182 2.47887 (297*2π)/12954 weeks
298-4.16738 .77175 (298*2π)/12954 weeks
299.65904 -6.44209 (299*2π)/12954 weeks
3001.91574 4.22807 (300*2π)/12954 weeks
301-.61062 1.4103 (301*2π)/12954 weeks
302-4.83437 -6.1567 (302*2π)/12954 weeks
3032.21327 -.55208 (303*2π)/12954 weeks
3045.49298 -2.4853 (304*2π)/12954 weeks
3054.4255 3.71838 (305*2π)/12954 weeks
306-13.37511 1.05548 (306*2π)/12954 weeks
3071.40775 -1.02108 (307*2π)/12954 weeks
30812.73356 -.13057 (308*2π)/12954 weeks
3091.98563 2.32547 (309*2π)/12954 weeks
310-1.57952 8.6825 (310*2π)/12954 weeks
311-3.75254 -4.69458 (311*2π)/12954 weeks
3121.69124 -7.34656 (312*2π)/12954 weeks
3137.25588 6.18784 (313*2π)/12954 weeks
314-6.87166 9.15482 (314*2π)/12954 weeks
315-1.19232 1.12454 (315*2π)/12954 weeks
3161.70755 -10.73385 (316*2π)/12954 weeks
3171.56676 -2.07996 (317*2π)/12954 weeks
3182.79839 6.68982 (318*2π)/12954 weeks
319-4.93245 7.29104 (319*2π)/12954 weeks
320-.31184 -6.36963 (320*2π)/12954 weeks
3212.90427 -4.79386 (321*2π)/12954 weeks
3228.35734 1.70356 (322*2π)/12954 weeks
323-5.51055 5.50615 (323*2π)/12954 weeks
324-3.31263 2.83662 (324*2π)/12954 weeks
32510.63056 -4.59366 (325*2π)/12954 weeks
326.37644 -2.07497 (326*2π)/12954 weeks
327-2.91544 4.99268 (327*2π)/12954 weeks
328-2.04404 5.79498 (328*2π)/12954 weeks
3294.63502 -4.6776 (329*2π)/12954 weeks
3305.76029 -2.41691 (330*2π)/12954 weeks
331-1.46227 8.82301 (331*2π)/12954 weeks
332-4.07185 -.38285 (332*2π)/12954 weeks
3331.22804 -.25937 (333*2π)/12954 weeks
3348.00444 .79745 (334*2π)/12954 weeks
3351.49437 -.99657 (335*2π)/12954 weeks
336-3.59347 4.00942 (336*2π)/12954 weeks
337-.66998 -4.67268 (337*2π)/12954 weeks
3384.82675 2.66926 (338*2π)/12954 weeks
3394.52501 2.21006 (339*2π)/12954 weeks
340-4.49454 3.05059 (340*2π)/12954 weeks
341-1.83227 4.26178 (341*2π)/12954 weeks
342-.49507 1.6709 (342*2π)/12954 weeks
3438.65059 -.98103 (343*2π)/12954 weeks
3444.04594 3.47417 (344*2π)/12954 weeks
345-8.71821 -1.77934 (345*2π)/12954 weeks
346.83165 .57507 (346*2π)/12954 weeks
347-.16631 3.8982 (347*2π)/12954 weeks
3484.50215 1.66102 (348*2π)/12954 weeks
3496.75974 1.73321 (349*2π)/12954 weeks
350-5.38315 -2.43692 (350*2π)/12954 weeks
351-3.44967 .46911 (351*2π)/12954 weeks
3527.21981 2.20763 (352*2π)/12954 weeks
353-.26042 3.63415 (353*2π)/12954 weeks
3543.50169 2.8484 (354*2π)/12954 weeks
3551.79117 -5.18517 (355*2π)/12954 weeks
356.17073 -.76486 (356*2π)/12954 weeks
357-1.21556 7.83967 (357*2π)/12954 weeks
358.67263 -.16714 (358*2π)/12954 weeks
359-1.57035 2.90591 (359*2π)/12954 weeks
3602.30475 -2.69273 (360*2π)/12954 weeks
3611.79552 4.72051 (361*2π)/12954 weeks
362.40886 1.60622 (362*2π)/12954 weeks
363-3.35779 -1.58761 (363*2π)/12954 weeks
3642.07234 -.12658 (364*2π)/12954 weeks
3656.7389 -1.87851 (365*2π)/12954 weeks
366.27353 3.42008 (366*2π)/12954 weeks
367-3.12747 3.4504 (367*2π)/12954 weeks
3685.03415 .58582 (368*2π)/12954 weeks
3695.90288 2.15469 (369*2π)/12954 weeks
370.697 .37097 (370*2π)/12954 weeks
371-.0585 2.95356 (371*2π)/12953 weeks
372-1.04592 3.63111 (372*2π)/12953 weeks
3732.42518 .91468 (373*2π)/12953 weeks
3741.03478 -.09129 (374*2π)/12953 weeks
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