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# Fourier Analysis of YRCW (YRC Worldwide Inc)

YRCW (YRC Worldwide Inc) appears to have interesting cyclic behaviour every 141 weeks (11853.5*sine), 176 weeks (8056.94*sine), and 192 weeks (7386.308*sine).

YRCW (YRC Worldwide Inc) has an average price of 119,593.1 (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 3/17/1980 to 9/14/2020 for YRCW (YRC Worldwide Inc), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0119,593.1   0
1-82,772.69 40,620.54 (1*2π)/21142,114 weeks
2-13,472.27 74,916.88 (2*2π)/21141,057 weeks
318,614.5 -40,857.83 (3*2π)/2114705 weeks
4-37,259.47 -5,710.819 (4*2π)/2114529 weeks
514,325.06 21,307.91 (5*2π)/2114423 weeks
612,908.22 -20,099.51 (6*2π)/2114352 weeks
7-6,088.823 11,717.13 (7*2π)/2114302 weeks
8-1,586.337 11,291.78 (8*2π)/2114264 weeks
9900.6105 -6,867.257 (9*2π)/2114235 weeks
10-5,997.158 2,674.842 (10*2π)/2114211 weeks
116,008.447 -7,386.308 (11*2π)/2114192 weeks
122,541.463 8,056.94 (12*2π)/2114176 weeks
135,819.582 -1,687.199 (13*2π)/2114163 weeks
14166.5743 6,446.725 (14*2π)/2114151 weeks
15-3,827.007 11,853.5 (15*2π)/2114141 weeks
16-1,629.123 -6,743.108 (16*2π)/2114132 weeks
17-7,311.025 4,626.036 (17*2π)/2114124 weeks
184,120.919 -2,637.488 (18*2π)/2114117 weeks
19-1,560.255 -55.5365 (19*2π)/2114111 weeks
20-3,773.648 768.6851 (20*2π)/2114106 weeks
215,112.382 -897.4584 (21*2π)/2114101 weeks
22-3,390.214 -1,721.303 (22*2π)/211496 weeks
232,704.969 2,381.462 (23*2π)/211492 weeks
241,391.401 425.5793 (24*2π)/211488 weeks
25-1,082.815 -1,637.232 (25*2π)/211485 weeks
261,192.644 4,807.833 (26*2π)/211481 weeks
271,317.44 -1,423.515 (27*2π)/211478 weeks
28-1,281.217 2,416.362 (28*2π)/211476 weeks
29-1,373.914 676.7332 (29*2π)/211473 weeks
30-3.25398 2,589.998 (30*2π)/211470 weeks
31-2,357.053 -3,751.179 (31*2π)/211468 weeks
32835.158 -3,174.025 (32*2π)/211466 weeks
333,945.11 6,256.25 (33*2π)/211464 weeks
341,373.832 -3,766.098 (34*2π)/211462 weeks
35-2,854.535 3,581.697 (35*2π)/211460 weeks
361,891.829 3,353.994 (36*2π)/211459 weeks
37218.1624 -2,512.153 (37*2π)/211457 weeks
38-2,401.044 2,625.675 (38*2π)/211456 weeks
39115.6643 2,051.657 (39*2π)/211454 weeks
40-1,516.236 -1,892.859 (40*2π)/211453 weeks
41578.0592 -90.74377 (41*2π)/211452 weeks
42-1,683.771 559.1479 (42*2π)/211450 weeks
431,330.926 -837.0745 (43*2π)/211449 weeks
442,059.064 -294.6548 (44*2π)/211448 weeks
45-1,776.854 3,180.877 (45*2π)/211447 weeks
46-1,307.431 -1,257.352 (46*2π)/211446 weeks
472,675.6 -592.9786 (47*2π)/211445 weeks
48-628.6497 1,051.444 (48*2π)/211444 weeks
49-452.6826 2,251.439 (49*2π)/211443 weeks
50-64.05379 -502.5199 (50*2π)/211442 weeks
51-633.9209 46.88827 (51*2π)/211441 weeks
52-1,564.326 712.0837 (52*2π)/211441 weeks
531,289.219 -616.7952 (53*2π)/211440 weeks
54-748.9984 -1,082.103 (54*2π)/211439 weeks
551,118.208 442.9572 (55*2π)/211438 weeks
561,503.775 1,402.824 (56*2π)/211438 weeks
57-1,411.181 1,965.559 (57*2π)/211437 weeks
58-1,460.86 -1,147.937 (58*2π)/211436 weeks
59-1,264.821 -241.0494 (59*2π)/211436 weeks
603,289.743 -1,400.644 (60*2π)/211435 weeks
61-242.9504 2,281.549 (61*2π)/211435 weeks
62-1,884.612 285.5954 (62*2π)/211434 weeks
63394.523 300.7159 (63*2π)/211434 weeks
64536.2078 -1,529.742 (64*2π)/211433 weeks
65-987.7161 1,096.438 (65*2π)/211433 weeks
661,039.445 -567.1503 (66*2π)/211432 weeks
671,379.331 978.378 (67*2π)/211432 weeks
68-1,230.079 1,095.333 (68*2π)/211431 weeks
69-1,404.607 -60.39519 (69*2π)/211431 weeks
701,161.857 -312.869 (70*2π)/211430 weeks
71-222.2256 -300.4219 (71*2π)/211430 weeks
72479.307 1,113.423 (72*2π)/211429 weeks
73-1,200.328 248.0484 (73*2π)/211429 weeks
74-65.92873 185.9589 (74*2π)/211429 weeks
75536.4568 -1,328.755 (75*2π)/211428 weeks
76-914.7565 546.5266 (76*2π)/211428 weeks
771,224.698 959.3293 (77*2π)/211427 weeks
7870.61971 -1,333.145 (78*2π)/211427 weeks
79-771.818 1,302.003 (79*2π)/211427 weeks
80203.119 509.1303 (80*2π)/211426 weeks
81-165.0938 -1,772.585 (81*2π)/211426 weeks
82940.5699 953.7097 (82*2π)/211426 weeks
83-237.6587 403.2825 (83*2π)/211425 weeks
84555.6817 72.12928 (84*2π)/211425 weeks
85-546.3247 755.4071 (85*2π)/211425 weeks
86223.1799 -417.964 (86*2π)/211425 weeks
87-26.60892 169.2572 (87*2π)/211424 weeks
88494.8864 1,585.607 (88*2π)/211424 weeks
89-1,534.885 -1,131.019 (89*2π)/211424 weeks
90-25.78445 -192.1202 (90*2π)/211423 weeks
912,063.055 155.5163 (91*2π)/211423 weeks
92-1,741.14 -544.0045 (92*2π)/211423 weeks
932,577.619 1,749.094 (93*2π)/211423 weeks
94-1,641.018 375.0137 (94*2π)/211422 weeks
95-454.3432 -283.7346 (95*2π)/211422 weeks
96-407.5091 528.3809 (96*2π)/211422 weeks
97765.0722 -1,180.063 (97*2π)/211422 weeks
9810.90068 -354.3064 (98*2π)/211422 weeks
991,655.919 1,900.222 (99*2π)/211421 weeks
100-1,039.689 698.763 (100*2π)/211421 weeks
101-1,268.708 -63.43221 (101*2π)/211421 weeks
1021,108 -287.1232 (102*2π)/211421 weeks
103-1,604.385 278.8391 (103*2π)/211421 weeks
1041,454.468 206.004 (104*2π)/211420 weeks
105-624.527 -203.3751 (105*2π)/211420 weeks
106-1,247.759 334.982 (106*2π)/211420 weeks
1071,241.328 -148.9025 (107*2π)/211420 weeks
108-272.8167 -1,201.708 (108*2π)/211420 weeks
109787.2006 1,237.647 (109*2π)/211419 weeks
110-421.5708 544.0687 (110*2π)/211419 weeks
111372.7336 -169.5939 (111*2π)/211419 weeks
112-519.3707 320.7608 (112*2π)/211419 weeks
113-215.5645 171.9455 (113*2π)/211419 weeks
114-261.2975 588.7568 (114*2π)/211419 weeks
115223.2859 -1,456.915 (115*2π)/211418 weeks
116-514.0313 807.6229 (116*2π)/211418 weeks
117867.6324 -142.431 (117*2π)/211418 weeks
118-151.7495 51.50323 (118*2π)/211418 weeks
1196.13839 20.76658 (119*2π)/211418 weeks
120406.4584 469.6631 (120*2π)/211418 weeks
121-651.4406 529.9028 (121*2π)/211417 weeks
122-73.78238 -514.2924 (122*2π)/211417 weeks
123573.8275 -441.1372 (123*2π)/211417 weeks
124-633.3856 834.2263 (124*2π)/211417 weeks
1251,192.41 560.2065 (125*2π)/211417 weeks
126-999.7772 -924.9585 (126*2π)/211417 weeks
127-892.1227 1,157.241 (127*2π)/211417 weeks
1281,303.229 -646.2867 (128*2π)/211417 weeks
129-339.9486 -1,053.417 (129*2π)/211416 weeks
130-300.5956 1,550.653 (130*2π)/211416 weeks
1311,400.415 -186.2538 (131*2π)/211416 weeks
132-1,237.526 -398.8656 (132*2π)/211416 weeks
133262.0764 1,022.871 (133*2π)/211416 weeks
134234.077 -316.5388 (134*2π)/211416 weeks
135-857.4416 -31.21788 (135*2π)/211416 weeks
136818.3666 -740.1322 (136*2π)/211416 weeks
137-87.88731 962.9956 (137*2π)/211415 weeks
138802.3829 206.6024 (138*2π)/211415 weeks
139-1,233.006 -197.9516 (139*2π)/211415 weeks
14051.15043 304.7096 (140*2π)/211415 weeks
141706.851 -328.2704 (141*2π)/211415 weeks
14268.28647 -84.71731 (142*2π)/211415 weeks
143-325.787 517.6752 (143*2π)/211415 weeks
144324.9858 856.6482 (144*2π)/211415 weeks
14517.19432 -977.9387 (145*2π)/211415 weeks
146-856.7332 901.1037 (146*2π)/211414 weeks
147451.5429 -112.0381 (147*2π)/211414 weeks
148-466.2586 134.0249 (148*2π)/211414 weeks
149-147.0885 -1,155.37 (149*2π)/211414 weeks
150316.2958 610.3009 (150*2π)/211414 weeks
151988.6248 40.31949 (151*2π)/211414 weeks
152-1,005.606 482.1647 (152*2π)/211414 weeks
153192.0809 -315.1418 (153*2π)/211414 weeks
154-277.7455 20.33515 (154*2π)/211414 weeks
155470.381 206.6778 (155*2π)/211414 weeks
156-411.3163 -1,117.756 (156*2π)/211414 weeks
1571,001.566 1,129.894 (157*2π)/211413 weeks
158-164.8956 71.73515 (158*2π)/211413 weeks
159-416.8277 -113.4014 (159*2π)/211413 weeks
16045.2444 257.3394 (160*2π)/211413 weeks
161482.2296 -150.0362 (161*2π)/211413 weeks
162-762.0343 -58.15957 (162*2π)/211413 weeks
163877.0609 27.82033 (163*2π)/211413 weeks
1645.14292 714.7734 (164*2π)/211413 weeks
165-958.7186 -654.3698 (165*2π)/211413 weeks
166345.525 112.4314 (166*2π)/211413 weeks
1671,238.341 -405.3432 (167*2π)/211413 weeks
168-1,002.775 675.7755 (168*2π)/211413 weeks
169373.3031 472.5387 (169*2π)/211413 weeks
170-75.60238 -1,164.585 (170*2π)/211412 weeks
171-134.9065 799.1533 (171*2π)/211412 weeks
172934.1481 -297.8093 (172*2π)/211412 weeks
173-516.8588 -47.67429 (173*2π)/211412 weeks
174329.9103 861.2847 (174*2π)/211412 weeks
175364.8087 -575.3156 (175*2π)/211412 weeks
176-691.9991 170.0493 (176*2π)/211412 weeks
177925.664 785.83 (177*2π)/211412 weeks
178-379.9678 -575.4199 (178*2π)/211412 weeks
179-549.2255 510.9578 (179*2π)/211412 weeks
180899.0151 -251.2511 (180*2π)/211412 weeks
181-754.3959 -91.49767 (181*2π)/211412 weeks
182954.2258 -26.42565 (182*2π)/211412 weeks
183341.034 169.2669 (183*2π)/211412 weeks
184-345.7475 1,199.068 (184*2π)/211411 weeks
18528.66178 -494.9407 (185*2π)/211411 weeks
186-379.4138 353.2717 (186*2π)/211411 weeks
187-12.48439 -61.96063 (187*2π)/211411 weeks
188350.8242 -3.13347 (188*2π)/211411 weeks
189-338.8613 145.9645 (189*2π)/211411 weeks
19097.36 283.1136 (190*2π)/211411 weeks
191-241.5762 -282.2957 (191*2π)/211411 weeks
192196.9558 -305.1035 (192*2π)/211411 weeks
193349.7957 579.2452 (193*2π)/211411 weeks
194171.5083 -455.2244 (194*2π)/211411 weeks
1955.11952 933.0529 (195*2π)/211411 weeks
196-137.3854 86.79742 (196*2π)/211411 weeks
197-176.6263 -256.2895 (197*2π)/211411 weeks
19847.50382 260.1198 (198*2π)/211411 weeks
199119.8016 184.7297 (199*2π)/211411 weeks
200-177.6995 189.0418 (200*2π)/211411 weeks
201-414.7854 -366.8347 (201*2π)/211411 weeks
202361.104 283.9745 (202*2π)/211410 weeks
20399.69474 -130.6004 (203*2π)/211410 weeks
204-67.10206 13.39 (204*2π)/211410 weeks
205-414.3054 574.108 (205*2π)/211410 weeks
206550.0777 -616.8965 (206*2π)/211410 weeks
207-566.1383 -51.65809 (207*2π)/211410 weeks
208360.6231 266.5056 (208*2π)/211410 weeks
209850.6953 -203.5129 (209*2π)/211410 weeks
210-1,059.447 536.0789 (210*2π)/211410 weeks
211433.3675 -21.49011 (211*2π)/211410 weeks
21244.63948 -461.5707 (212*2π)/211410 weeks
213153.2725 233.3241 (213*2π)/211410 weeks
214409.9823 454.9809 (214*2π)/211410 weeks
215-297.0438 168.2676 (215*2π)/211410 weeks
216-376.0967 285.6214 (216*2π)/211410 weeks
217150.5111 -374.0621 (217*2π)/211410 weeks
218-472.5822 81.14944 (218*2π)/211410 weeks
219340.0649 -482.4671 (219*2π)/211410 weeks
220937.986 193.2878 (220*2π)/211410 weeks
221-657.4474 458.5073 (221*2π)/211410 weeks
22298.75468 422.8816 (222*2π)/211410 weeks
223-9.31315 -412.2677 (223*2π)/21149 weeks
224-279.8751 -216.2628 (224*2π)/21149 weeks
225299.0171 707.1624 (225*2π)/21149 weeks
22616.86033 -646.8422 (226*2π)/21149 weeks
227107.1406 75.92551 (227*2π)/21149 weeks
228121.5428 606.7078 (228*2π)/21149 weeks
229-219.1665 86.74229 (229*2π)/21149 weeks
230-271.7114 -831.1578 (230*2π)/21149 weeks
231538.5729 464.7667 (231*2π)/21149 weeks
232118.3898 -104.771 (232*2π)/21149 weeks
233120.295 -144.1641 (233*2π)/21149 weeks
234467.2134 520.92 (234*2π)/21149 weeks
235-27.8794 184.11 (235*2π)/21149 weeks
236-172.6314 371.6773 (236*2π)/21149 weeks
237-104.5328 135.6438 (237*2π)/21149 weeks
238102.943 -119.8127 (238*2π)/21149 weeks
239-471.8989 199.1433 (239*2π)/21149 weeks
240430.354 -33.71239 (240*2π)/21149 weeks
241103.7419 -139.6045 (241*2π)/21149 weeks
242-262.0159 719.2115 (242*2π)/21149 weeks
243-20.12591 -344.7759 (243*2π)/21149 weeks
244-213.7675 196.1506 (244*2π)/21149 weeks
245254.8517 -285.7438 (245*2π)/21149 weeks
246-195.7135 52.69588 (246*2π)/21149 weeks
247547.2494 35.49655 (247*2π)/21149 weeks
248133.481 661.1293 (248*2π)/21149 weeks
249-521.1867 -163.5763 (249*2π)/21148 weeks
250-407.1605 558.2953 (250*2π)/21148 weeks
251286.1153 -708.4173 (251*2π)/21148 weeks
252-253.5406 -356.7318 (252*2π)/21148 weeks
253452.2022 787.3981 (253*2π)/21148 weeks
254231.1614 -449.8306 (254*2π)/21148 weeks
255-639.351 469.6507 (255*2π)/21148 weeks
256140.5695 -79.37961 (256*2π)/21148 weeks
257151.3708 -453.9084 (257*2π)/21148 weeks
258-74.77995 37.47996 (258*2π)/21148 weeks
259465.444 431.6479 (259*2π)/21148 weeks
2603.10467 -436.3523 (260*2π)/21148 weeks
261-157.2616 711.139 (261*2π)/21148 weeks
262154.7445 -330.6616 (262*2π)/21148 weeks
263-48.6496 50.07943 (263*2π)/21148 weeks
264224.8024 135.5851 (264*2π)/21148 weeks
26599.24717 90.5621 (265*2π)/21148 weeks
266-249.9692 315.0028 (266*2π)/21148 weeks
267280.2188 -358.0474 (267*2π)/21148 weeks
268130.7099 440.4982 (268*2π)/21148 weeks
269-231.0261 244.434 (269*2π)/21148 weeks
270126.9817 83.34844 (270*2π)/21148 weeks
271-323.4351 -30.93289 (271*2π)/21148 weeks
272-208.2415 269.054 (272*2π)/21148 weeks
27371.55579 -421.3903 (273*2π)/21148 weeks
27499.96729 -354.6121 (274*2π)/21148 weeks
275336.4138 583.1383 (275*2π)/21148 weeks
276173.7276 134.6822 (276*2π)/21148 weeks
277-592.155 8.8472 (277*2π)/21148 weeks
278125.5745 -12.99849 (278*2π)/21148 weeks
279288.0965 -85.52776 (279*2π)/21148 weeks
2805.44478 115.4328 (280*2π)/21148 weeks
281-172.2017 450.9146 (281*2π)/21148 weeks
282-49.09066 -272.2919 (282*2π)/21147 weeks
283-70.29156 171.2236 (283*2π)/21147 weeks
284-86.95771 -227.4435 (284*2π)/21147 weeks
28590.75073 .88597 (285*2π)/21147 weeks
286231.8501 140.4477 (286*2π)/21147 weeks
287-115.4329 -186.9014 (287*2π)/21147 weeks
28824.22745 279.585 (288*2π)/21147 weeks
289340.7817 -17.66567 (289*2π)/21147 weeks
290-371.7545 95.0456 (290*2π)/21147 weeks
291189.2698 34.91848 (291*2π)/21147 weeks
292-7.66444 114.19 (292*2π)/21147 weeks
293-27.94995 53.86399 (293*2π)/21147 weeks
294-230.0002 -119.6293 (294*2π)/21147 weeks
29546.56992 107.0495 (295*2π)/21147 weeks
296505.184 -523.7731 (296*2π)/21147 weeks
297-342.5952 653.1774 (297*2π)/21147 weeks
298524.9103 -106.4271 (298*2π)/21147 weeks
299-215.172 125.3201 (299*2π)/21147 weeks
300-281.5171 250.5659 (300*2π)/21147 weeks
301224.2985 -87.05669 (301*2π)/21147 weeks
30239.94893 -288.8985 (302*2π)/21147 weeks
303-304.2021 408.9601 (303*2π)/21147 weeks
304514.0192 -78.24284 (304*2π)/21147 weeks
305-114.7944 -298.6409 (305*2π)/21147 weeks
306-41.56208 595.8132 (306*2π)/21147 weeks
307219.9274 -21.65224 (307*2π)/21147 weeks
308-218.7635 -32.55901 (308*2π)/21147 weeks
309-2.64902 -66.5185 (309*2π)/21147 weeks
31047.47859 321.3271 (310*2π)/21147 weeks
311303.5994 -72.28625 (311*2π)/21147 weeks
312-462.315 -1.18345 (312*2π)/21147 weeks
31397.77895 331.791 (313*2π)/21147 weeks
314195.7014 -102.305 (314*2π)/21147 weeks
315-475.1625 -189.1435 (315*2π)/21147 weeks
31639.18239 227.0207 (316*2π)/21147 weeks
317447.4542 -432.9172 (317*2π)/21147 weeks
3181.20627 151.0219 (318*2π)/21147 weeks
31980.04171 503.2012 (319*2π)/21147 weeks
320-214.4214 17.73895 (320*2π)/21147 weeks
32171.90884 -348.8164 (321*2π)/21147 weeks
322-91.32996 424.9138 (322*2π)/21147 weeks
32390.87426 -70.828 (323*2π)/21147 weeks
324-169.9563 -37.83598 (324*2π)/21147 weeks
32536.81733 -39.64149 (325*2π)/21147 weeks
326-9.84012 98.6974 (326*2π)/21146 weeks
327-110.3391 -180.2953 (327*2π)/21146 weeks
328369.3844 -230.1627 (328*2π)/21146 weeks
329126.0377 376.3794 (329*2π)/21146 weeks
330-51.91158 135.4484 (330*2π)/21146 weeks
331-74.19617 60.34437 (331*2π)/21146 weeks
332-127.2119 -158.0428 (332*2π)/21146 weeks
333262.3454 -37.09636 (333*2π)/21146 weeks
334211.0063 165.5717 (334*2π)/21146 weeks
335-76.56991 421.6084 (335*2π)/21146 weeks
336-279.6912 -23.96173 (336*2π)/21146 weeks
337-283.4165 -18.48539 (337*2π)/21146 weeks
33865.3343 -380.8899 (338*2π)/21146 weeks
339228.8306 -210.8965 (339*2π)/21146 weeks
340412.4582 325.4987 (340*2π)/21146 weeks
341-74.12306 33.8912 (341*2π)/21146 weeks
342-86.66936 548.7608 (342*2π)/21146 weeks
343-322.3282 -468.5104 (343*2π)/21146 weeks
344415.07 -68.4343 (344*2π)/21146 weeks
345-49.51215 300.446 (345*2π)/21146 weeks
346104.1103 282.7976 (346*2π)/21146 weeks
347-473.123 -179.3985 (347*2π)/21146 weeks
348-4.1115 -205.7691 (348*2π)/21146 weeks
349211.3685 81.54285 (349*2π)/21146 weeks
350117.8069 -349.4892 (350*2π)/21146 weeks
35132.48468 290.0721 (351*2π)/21146 weeks
352176.3614 -101.2168 (352*2π)/21146 weeks
353268.3582 221.5076 (353*2π)/21146 weeks
354-348.0132 123.0968 (354*2π)/21146 weeks
355289.4555 -6.19205 (355*2π)/21146 weeks
356-260.1935 101.4937 (356*2π)/21146 weeks
357171.9841 19.64815 (357*2π)/21146 weeks
358-18.32617 -92.61358 (358*2π)/21146 weeks
359-118.0405 158.4855 (359*2π)/21146 weeks
360260.7149 -35.77405 (360*2π)/21146 weeks
361-124.2315 -3.38386 (361*2π)/21146 weeks
3621.77363 82.817 (362*2π)/21146 weeks
363140.9932 -5.06088 (363*2π)/21146 weeks
364-60.26825 -96.61763 (364*2π)/21146 weeks
365233.0516 275.0905 (365*2π)/21146 weeks
366-40.80378 -120.8446 (366*2π)/21146 weeks
367-155.3083 239.2879 (367*2π)/21146 weeks
368195.0836 46.32952 (368*2π)/21146 weeks
369-91.26412 -332.6517 (369*2π)/21146 weeks
370-66.68682 330.6027 (370*2π)/21146 weeks
371541.9631 -50.35989 (371*2π)/21146 weeks
372-319.369 222.5126 (372*2π)/21146 weeks
373-154.7591 33.3913 (373*2π)/21146 weeks
374144.8683 -5.20045 (374*2π)/21146 weeks
37553.05349 -22.52906