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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 47 weeks (156.129*sine), 62 weeks (149.229*sine), and 109 weeks (138.1245*sine).

KEG (Key Energy Services, Inc. Commo) has an average price of 1,799.04 (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 3/17/1992 to 3/20/2017 for KEG (Key Energy Services, Inc. Commo), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
01,799.038   0
1-839.3499 -56.92007 (1*2π)/13051,305 weeks
2-496.7655 291.5026 (2*2π)/1305653 weeks
3-445.3648 -228.7228 (3*2π)/1305435 weeks
483.97308 116.2067 (4*2π)/1305326 weeks
5485.6875 78.07582 (5*2π)/1305261 weeks
6-273.3719 220.0815 (6*2π)/1305218 weeks
7-384.4249 135.413 (7*2π)/1305186 weeks
8196.6314 -212.2145 (8*2π)/1305163 weeks
9307.4034 -40.63676 (9*2π)/1305145 weeks
10-38.08641 135.2955 (10*2π)/1305131 weeks
11-120.4247 -78.72857 (11*2π)/1305119 weeks
12-86.68394 -138.1245 (12*2π)/1305109 weeks
1389.6196 81.38612 (13*2π)/1305100 weeks
14106.4748 99.64556 (14*2π)/130593 weeks
15-58.31855 12.00243 (15*2π)/130587 weeks
16-67.89756 29.88921 (16*2π)/130582 weeks
17105.0637 6.17927 (17*2π)/130577 weeks
1872.36684 -71.41765 (18*2π)/130573 weeks
19-44.72763 81.33648 (19*2π)/130569 weeks
2029.23674 76.89781 (20*2π)/130565 weeks
21-69.21115 -149.229 (21*2π)/130562 weeks
22.76783 23.95547 (22*2π)/130559 weeks
2347.20211 83.32723 (23*2π)/130557 weeks
24-74.23428 34.04176 (24*2π)/130554 weeks
2567.18916 71.99817 (25*2π)/130552 weeks
2610.49141 -84.78302 (26*2π)/130550 weeks
2711.04155 -68.91472 (27*2π)/130548 weeks
2814.5951 156.129 (28*2π)/130547 weeks
29-4.46152 -2.70424 (29*2π)/130545 weeks
30.13978 -64.41235 (30*2π)/130544 weeks
3127.66999 -48.70291 (31*2π)/130542 weeks
3235.19221 33.37151 (32*2π)/130541 weeks
33-61.40918 60.87438 (33*2π)/130540 weeks
34-31.25121 66.91535 (34*2π)/130538 weeks
3534.24523 -77.10623 (35*2π)/130537 weeks
3617.66349 -1.88618 (36*2π)/130536 weeks
3727.58488 44.86536 (37*2π)/130535 weeks
38-21.76477 54.7521 (38*2π)/130534 weeks
39-33.10769 -27.3282 (39*2π)/130533 weeks
4045.41111 -46.44422 (40*2π)/130533 weeks
4122.299 -2.1233 (41*2π)/130532 weeks
42-34.2692 81.1189 (42*2π)/130531 weeks
43-11.99381 19.61324 (43*2π)/130530 weeks
4437.22719 -71.95433 (44*2π)/130530 weeks
451.52986 23.55262 (45*2π)/130529 weeks
46-5.287 2.53975 (46*2π)/130528 weeks
47-44.94251 34.83496 (47*2π)/130528 weeks
482.12667 10.21898 (48*2π)/130527 weeks
4947.32613 -24.51467 (49*2π)/130527 weeks
5016.03618 32.28667 (50*2π)/130526 weeks
51-40.3816 25.19905 (51*2π)/130526 weeks
52-15.26117 -26.83955 (52*2π)/130525 weeks
5315.76385 -10.57908 (53*2π)/130525 weeks
5431.25542 13.39 (54*2π)/130524 weeks
55-23.17831 38.21413 (55*2π)/130524 weeks
56-.74501 -26.9896 (56*2π)/130523 weeks
575.15729 -6.5651 (57*2π)/130523 weeks
5810.55403 .95116 (58*2π)/130523 weeks
59-1.73618 5.73588 (59*2π)/130522 weeks
6012.54857 38.35697 (60*2π)/130522 weeks
6114.77754 -14.4683 (61*2π)/130521 weeks
62-4.09764 -24.65571 (62*2π)/130521 weeks
63-6.4162 13.58732 (63*2π)/130521 weeks
641.30659 16.35215 (64*2π)/130520 weeks
65-7.91668 29.00286 (65*2π)/130520 weeks
664.93793 13.06528 (66*2π)/130520 weeks
6724.63976 -38.91411 (67*2π)/130519 weeks
68-12.51991 28.50617 (68*2π)/130519 weeks
69-16.56797 34.45209 (69*2π)/130519 weeks
70-3.21208 -6.13901 (70*2π)/130519 weeks
7120.00085 -33.37791 (71*2π)/130518 weeks
72-3.91203 3.77036 (72*2π)/130518 weeks
739.49961 30.95192 (73*2π)/130518 weeks
74-9.9899 10.5765 (74*2π)/130518 weeks
75-14.66382 -21.00528 (75*2π)/130517 weeks
7641.71839 -9.40415 (76*2π)/130517 weeks
77-14.51057 16.66626 (77*2π)/130517 weeks
78-25.45564 28.20999 (78*2π)/130517 weeks
7914.05821 -5.28277 (79*2π)/130517 weeks
8013.81839 -4.75882 (80*2π)/130516 weeks
811.86787 -1.01554 (81*2π)/130516 weeks
829.56897 28.59377 (82*2π)/130516 weeks
83-12.14848 11.06826 (83*2π)/130516 weeks
84-4.95186 -11.99277 (84*2π)/130516 weeks
8519.76396 -16.77778 (85*2π)/130515 weeks
86-26.1755 12.11751 (86*2π)/130515 weeks
877.23349 10.7806 (87*2π)/130515 weeks
88-3.33305 7.23493 (88*2π)/130515 weeks
893.24747 -.4235 (89*2π)/130515 weeks
903.1917 -.25617 (90*2π)/130515 weeks
91-11.38896 11.63095 (91*2π)/130514 weeks
926.13074 5.76408 (92*2π)/130514 weeks
9310.48912 -10.91677 (93*2π)/130514 weeks
9412.86211 6.94498 (94*2π)/130514 weeks
95-17.24028 -1.1201 (95*2π)/130514 weeks
96-14.1316 19.63243 (96*2π)/130514 weeks
976.74918 -12.84973 (97*2π)/130513 weeks
9814.16905 -3.86195 (98*2π)/130513 weeks
99.93958 31.5215 (99*2π)/130513 weeks
100-8.68358 -8.11023 (100*2π)/130513 weeks
101-1.20819 -2.10634 (101*2π)/130513 weeks
102-3.81097 -3.10591 (102*2π)/130513 weeks
10314.59915 2.57223 (103*2π)/130513 weeks
104-8.51213 11.84186 (104*2π)/130513 weeks
105-3.87594 .89056 (105*2π)/130512 weeks
1063.83437 -16.63356 (106*2π)/130512 weeks
107-4.15985 22.39597 (107*2π)/130512 weeks
108.86745 2.58492 (108*2π)/130512 weeks
109.95358 -12.1503 (109*2π)/130512 weeks
1107.54591 11.67525 (110*2π)/130512 weeks
111.52956 -4.99935 (111*2π)/130512 weeks
112-12.48339 -9.77673 (112*2π)/130512 weeks
113-3.33414 2.67977 (113*2π)/130512 weeks
11410.6877 -1.55624 (114*2π)/130511 weeks
1152.73041 8.45029 (115*2π)/130511 weeks
116-10.21437 8.67428 (116*2π)/130511 weeks
117-3.32735 -11.53788 (117*2π)/130511 weeks
11813.47217 -.58659 (118*2π)/130511 weeks
11914.61482 6.53662 (119*2π)/130511 weeks
1203.63996 -6.01556 (120*2π)/130511 weeks
121-.31574 -10.75329 (121*2π)/130511 weeks
122-4.7061 -.22233 (122*2π)/130511 weeks
1233.29421 11.90279 (123*2π)/130511 weeks
12414.37784 -8.12161 (124*2π)/130511 weeks
125-5.54968 15.12337 (125*2π)/130510 weeks
1265.20276 4.39802 (126*2π)/130510 weeks
127-3.1943 -5.61521 (127*2π)/130510 weeks
12823.58529 13.9015 (128*2π)/130510 weeks
129-8.21611 -6.89858 (129*2π)/130510 weeks
130-2.07487 -2.61407 (130*2π)/130510 weeks
1314.82403 10.03767 (131*2π)/130510 weeks
1326.13947 -.98625 (132*2π)/130510 weeks
133-10.58898 .44381 (133*2π)/130510 weeks
13410.09689 11.17367 (134*2π)/130510 weeks
1356.1083 -2.35463 (135*2π)/130510 weeks
1366.23388 4.51071 (136*2π)/130510 weeks
1372.08752 1.32429 (137*2π)/130510 weeks
138-.58268 -2.04844 (138*2π)/13059 weeks
1393.92366 5.95081 (139*2π)/13059 weeks
14011.21796 4.4676 (140*2π)/13059 weeks
141.54281 7.31196 (141*2π)/13059 weeks
142-17.78805 5.2883 (142*2π)/13059 weeks
14311.02596 9.22595 (143*2π)/13059 weeks
14412.76691 2.71092 (144*2π)/13059 weeks
145-5.99232 2.14341 (145*2π)/13059 weeks
1468.25543 1.25762 (146*2π)/13059 weeks
147-6.06498 15.60117 (147*2π)/13059 weeks
148-7.52054 3.02089 (148*2π)/13059 weeks
1499.64747 -12.46458 (149*2π)/13059 weeks
150-6.57959 -2.43498 (150*2π)/13059 weeks
1512.67908 19.67071 (151*2π)/13059 weeks
152-14.05067 11.16487 (152*2π)/13059 weeks
1533.24314 -14.19216 (153*2π)/13059 weeks
15411.95815 3.36418 (154*2π)/13058 weeks
155-3.26816 9.36618 (155*2π)/13058 weeks
156-2.07617 4.27066 (156*2π)/13058 weeks
157-2.42001 1.46004 (157*2π)/13058 weeks
158-3.34191 -10.24713 (158*2π)/13058 weeks
1596.7798 -3.91571 (159*2π)/13058 weeks
160-11.71624 10.04316 (160*2π)/13058 weeks
1611.0111 11.3079 (161*2π)/13058 weeks
1629.64103 4.75403 (162*2π)/13058 weeks
1639.69275 -4.82563 (163*2π)/13058 weeks
164-13.19317 -8.54955 (164*2π)/13058 weeks
1652.82464 .0201 (165*2π)/13058 weeks
1665.43773 16.20985 (166*2π)/13058 weeks
167-7.23292 4.77193 (167*2π)/13058 weeks
168-2.15521 -15.76026 (168*2π)/13058 weeks
1691.1237 9.4662 (169*2π)/13058 weeks
17012.79977 8.17345 (170*2π)/13058 weeks
171-8.59231 1.68215 (171*2π)/13058 weeks
1721.05414 2.99183 (172*2π)/13058 weeks
173-.2646 -11.45813 (173*2π)/13058 weeks
174-7.60311 -2.82591 (174*2π)/13058 weeks
1752.78423 15.07724 (175*2π)/13057 weeks
1763.68894 2.84019 (176*2π)/13057 weeks
177-.68585 -12.40637 (177*2π)/13057 weeks
178-3.32862 -1.74516 (178*2π)/13057 weeks
179-2.583 .80773 (179*2π)/13057 weeks
1806.54258 -2.73017 (180*2π)/13057 weeks
1813.98877 3.64295 (181*2π)/13057 weeks
1823.15853 -6.10374 (182*2π)/13057 weeks
183-9.83192 5.42256 (183*2π)/13057 weeks
1849.72092 3.64921 (184*2π)/13057 weeks
1856.84217 -5.24824 (185*2π)/13057 weeks
186-6.11356 4.26699 (186*2π)/13057 weeks
1872.61528 -1.0448 (187*2π)/13057 weeks
18810.29495 .81589 (188*2π)/13057 weeks
189.09586 7.88215 (189*2π)/13057 weeks
190-3.22696 -11.32759 (190*2π)/13057 weeks
191-1.2457 9.00097 (191*2π)/13057 weeks
1923.85379 -3.40921 (192*2π)/13057 weeks
1939.33558 2.86726 (193*2π)/13057 weeks
194-4.50566 .37743 (194*2π)/13057 weeks
1956.13578 -17.3625 (195*2π)/13057 weeks
196.67452 4.37225 (196*2π)/13057 weeks
1974.64362 10.32697 (197*2π)/13057 weeks
1981.21229 3.38985 (198*2π)/13057 weeks
1998.16193 -12.66517 (199*2π)/13057 weeks
200.92541 2.17055 (200*2π)/13057 weeks
20110.6097 11.62194 (201*2π)/13056 weeks
202.21051 11.87591 (202*2π)/13056 weeks
2039.08283 -13.84072 (203*2π)/13056 weeks
204-2.76673 .1804 (204*2π)/13056 weeks
205-2.52725 4.5907 (205*2π)/13056 weeks
2066.56166 2.55006 (206*2π)/13056 weeks
2071.71871 .1639 (207*2π)/13056 weeks
2085.98213 9.09122 (208*2π)/13056 weeks
2092.75857 2.51668 (209*2π)/13056 weeks
210-.96731 3.13342 (210*2π)/13056 weeks
2118.31994 .53862 (211*2π)/13056 weeks
21210.51088 1.41153 (212*2π)/13056 weeks
213-5.52183 1.96994 (213*2π)/13056 weeks
214.1496 12.91588 (214*2π)/13056 weeks
21511.25492 -3.1892 (215*2π)/13056 weeks
216-3.38522 2.09035 (216*2π)/13056 weeks
217-.15334 4.37079 (217*2π)/13056 weeks
218-1.54335 5.96708 (218*2π)/13056 weeks
2193.72 1.835 (219*2π)/13056 weeks
2207.99235 4.78992 (220*2π)/13056 weeks
221-1.2002 2.91515 (221*2π)/13056 weeks
222-.50977 -1.7654 (222*2π)/13056 weeks
2232.10117 5.91848 (223*2π)/13056 weeks
2245.96602 1.94153 (224*2π)/13056 weeks
2251.69038 2.95387 (225*2π)/13056 weeks
2265.96266 6.76231 (226*2π)/13056 weeks
227-7.59154 -2.13202 (227*2π)/13056 weeks
228.72578 7.47665 (228*2π)/13056 weeks
2294.62049 3.30389 (229*2π)/13056 weeks
230-4.80653 -2.13453 (230*2π)/13056 weeks
2313.26634 12.01387 (231*2π)/13056 weeks
2322.91956 -.62829 (232*2π)/13056 weeks
233-3.38055 -4.22319 (233*2π)/13056 weeks
2342.13715 8.87077 (234*2π)/13056 weeks
235-3.38754 3.9379 (235*2π)/13056 weeks
2366.13435 3.53336 (236*2π)/13056 weeks
2372.87612 2.16247 (237*2π)/13056 weeks
2382.07845 -1.97232 (238*2π)/13055 weeks
239-1.24907 5.67808 (239*2π)/13055 weeks
240-2.09832 7.18089 (240*2π)/13055 weeks
241.74012 .18463 (241*2π)/13055 weeks
242-.92568 3.13075 (242*2π)/13055 weeks
2435.1889 5.2854 (243*2π)/13055 weeks
244-5.70518 1.36478 (244*2π)/13055 weeks
2453.98128 -6.173 (245*2π)/13055 weeks
2462.67499 8.8281 (246*2π)/13055 weeks
247-4.33963 2.25069 (247*2π)/13055 weeks
2482.99284 -2.34319 (248*2π)/13055 weeks
249-1.14608 -2.12435 (249*2π)/13055 weeks
2506.80649 5.62651 (250*2π)/13055 weeks
2512.35988 6.38952 (251*2π)/13055 weeks
252-7.4827 5.59845 (252*2π)/13055 weeks
2532.19557 -5.99754 (253*2π)/13055 weeks
2547.68278 8.82745 (254*2π)/13055 weeks
255-2.57188 6.81432 (255*2π)/13055 weeks
256-.05516 -5.36063 (256*2π)/13055 weeks
2572.39677 2.74706 (257*2π)/13055 weeks
258-1.98268 9.83712 (258*2π)/13055 weeks
2592.08846 -2.17224 (259*2π)/13055 weeks
260-4.21827 -.23559 (260*2π)/13055 weeks
2615.75161 .68745 (261*2π)/13055 weeks
2623.05121 9.55047 (262*2π)/13055 weeks
263-9.82901 1.73339 (263*2π)/13055 weeks
264-4.86846 -2.43008 (264*2π)/13055 weeks
26514.3021 6.84587 (265*2π)/13055 weeks
2663.78194 2.15023 (266*2π)/13055 weeks
267-.66774 5.0811 (267*2π)/13055 weeks
268-4.57649 -1.62421 (268*2π)/13055 weeks
269-6.31885 .06722 (269*2π)/13055 weeks
2708.05502 7.53099 (270*2π)/13055 weeks
2716.5765 3.2821 (271*2π)/13055 weeks
272-16.44906 -.50518 (272*2π)/13055 weeks
2731.68846 4.60066 (273*2π)/13055 weeks
2745.185 2.70426 (274*2π)/13055 weeks
2754.39525 2.40538 (275*2π)/13055 weeks
2761.12289 3.75426 (276*2π)/13055 weeks
277-6.01698 .45245 (277*2π)/13055 weeks
278-4.49899 4.56712 (278*2π)/13055 weeks
2792.60439 -1.11791 (279*2π)/13055 weeks
280-1.85842 -2.6095 (280*2π)/13055 weeks
281-2.01415 13.22627 (281*2π)/13055 weeks
282.89562 2.86002 (282*2π)/13055 weeks
283-1.59333 -5.69284 (283*2π)/13055 weeks
2843.90748 -.67097 (284*2π)/13055 weeks
285-5.45633 3.11386 (285*2π)/13055 weeks
286.18465 3.27545 (286*2π)/13055 weeks
287-2.30259 3.80236 (287*2π)/13055 weeks
2882.33121 -2.37372 (288*2π)/13055 weeks
289.75503 -2.20839 (289*2π)/13055 weeks
290-5.67445 8.22861 (290*2π)/13055 weeks
291-1.62056 7.54992 (291*2π)/13054 weeks
2928.92998 -12.15675 (292*2π)/13054 weeks
293-5.74725 -2.99465 (293*2π)/13054 weeks
2942.36268 6.90544 (294*2π)/13054 weeks
295-6.96146 8.11382 (295*2π)/13054 weeks
296.80553 -2.84373 (296*2π)/13054 weeks
2975.41593 -3.89258 (297*2π)/13054 weeks
2981.76738 7.4187 (298*2π)/13054 weeks
299-5.06128 4.58495 (299*2π)/13054 weeks
300-3.3358 .21504 (300*2π)/13054 weeks
301-3.8597 -5.60884 (301*2π)/13054 weeks
3024.80434 1.34001 (302*2π)/13054 weeks
303-1.96485 .72229 (303*2π)/13054 weeks
304-6.85639 -.36361 (304*2π)/13054 weeks
3053.75252 -3.12735 (305*2π)/13054 weeks
3061.90514 -3.51212 (306*2π)/13054 weeks
3074.1771 3.056 (307*2π)/13054 weeks
308-4.85672 11.1717 (308*2π)/13054 weeks
3092.76593 -7.59764 (309*2π)/13054 weeks
3105.40564 -8.94988 (310*2π)/13054 weeks
3111.47369 5.95947 (311*2π)/13054 weeks
3122.87659 6.38259 (312*2π)/13054 weeks
313-8.81515 .65482 (313*2π)/13054 weeks
314-1.539 -3.24724 (314*2π)/13054 weeks
31510.38994 .11596 (315*2π)/13054 weeks
3161.82951 10.38101 (316*2π)/13054 weeks
317-5.54931 -2.53338 (317*2π)/13054 weeks
318-8.53522 -3.82322 (318*2π)/13054 weeks
3195.40863 .79173 (319*2π)/13054 weeks
3208.18853 1.5752 (320*2π)/13054 weeks
321.63682 5.42806 (321*2π)/13054 weeks
322-8.59658 -3.44513 (322*2π)/13054 weeks
323.90005 -3.20741 (323*2π)/13054 weeks
3246.44122 -2.17265 (324*2π)/13054 weeks
3254.31596 9.44724 (325*2π)/13054 weeks
326-1.1935 -.84198 (326*2π)/13054 weeks
327-4.43237 -7.86093 (327*2π)/13054 weeks
3283.28888 6.97085 (328*2π)/13054 weeks
3296.73222 3.82985 (329*2π)/13054 weeks
330.99213 -.30096 (330*2π)/13054 weeks
331-6.34478 -3.36429 (331*2π)/13054 weeks
3322.99197 .3723 (332*2π)/13054 weeks
3338.65964 5.35565 (333*2π)/13054 weeks
334-4.25069 3.58391 (334*2π)/13054 weeks
335-.91434 -3.35888 (335*2π)/13054 weeks
336.339 -3.02313 (336*2π)/13054 weeks
3371.8145 6.27285 (337*2π)/13054 weeks
3384.47744 4.11966 (338*2π)/13054 weeks
339-3.49282 -.06774 (339*2π)/13054 weeks
3404.9001 -4.02811 (340*2π)/13054 weeks
3412.54188 2.47543 (341*2π)/13054 weeks
3423.96188 6.51505 (342*2π)/13054 weeks
343-.10644 -.88713 (343*2π)/13054 weeks
344-2.98657 -.48446 (344*2π)/13054 weeks
345-3.07809 -2.42714 (345*2π)/13054 weeks
3465.01894 5.37641 (346*2π)/13054 weeks
3471.93323 9.2018 (347*2π)/13054 weeks
348-.79469 -5.83479 (348*2π)/13054 weeks
3491.60305 -1.0886 (349*2π)/13054 weeks
350-2.57963 -.37711 (350*2π)/13054 weeks
351.65324 2.83218 (351*2π)/13054 weeks
3523.70537 8.68434 (352*2π)/13054 weeks
3531.0572 -3.23413 (353*2π)/13054 weeks
354-1.76898 -4.86531 (354*2π)/13054 weeks
3553.93768 4.69389 (355*2π)/13054 weeks
356-1.54718 1.86989 (356*2π)/13054 weeks
357-.18107 5.48624 (357*2π)/13054 weeks
3586.05335 -1.08153 (358*2π)/13054 weeks
3594.40014 -1.50101 (359*2π)/13054 weeks
360-4.02192 4.24489 (360*2π)/13054 weeks
3611.44282 .72858 (361*2π)/13054 weeks
362-2.74165 1.21338 (362*2π)/13054 weeks
3633.983 -1.39746 (363*2π)/13054 weeks
364-.10508 4.27714 (364*2π)/13054 weeks
365.21241 2.5175 (365*2π)/13054 weeks
366-1.77918 -3.2346 (366*2π)/13054 weeks
3671.056 -.24826 (367*2π)/13054 weeks
3687.72099 .82805 (368*2π)/13054 weeks
369.78787 2.23771 (369*2π)/13054 weeks
370-4.04308 .68759 (370*2π)/13054 weeks
3713.82446 1.98549 (371*2π)/13054 weeks
3725.43435 4.34332 (372*2π)/13054 weeks
3732.30242 .54074 (373*2π)/13053 weeks
374.27156 2.24431 (374*2π)/13053 weeks
375-1.61883 2.79071 (375*2π)/13053 weeks
3762.50749 1.73997 (376*2π)/13053 weeks
3772.21853 -.18779 (377*2π)/13053 weeks
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