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Fourier Analysis of AAD


AAD appears to have interesting cyclic behaviour every 98 weeks (83.9788*sine), 90 weeks (82.2182*sine), and 108 weeks (69.2372*sine).

AAD has an average price of 145.05 (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 3/11/1996 to 1/9/2017 for AAD, this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0145.0466   0 
1200.0915 121.8087 (1*2π)/10761,076 weeks
2105.6269 109.51 (2*2π)/1076538 weeks
378.3889 54.89655 (3*2π)/1076359 weeks
4118.8998 25.22598 (4*2π)/1076269 weeks
5158.9771 74.71851 (5*2π)/1076215 weeks
6123.1165 139.0837 (6*2π)/1076179 weeks
757.50136 147.6164 (7*2π)/1076154 weeks
813.90824 116.2253 (8*2π)/1076135 weeks
911.40322 75.56152 (9*2π)/1076120 weeks
1032.7297 69.23724 (10*2π)/1076108 weeks
1127.72426 83.97878 (11*2π)/107698 weeks
1211.6359 82.21818 (12*2π)/107690 weeks
13-1.02446 73.78729 (13*2π)/107683 weeks
14-6.13948 59.42044 (14*2π)/107677 weeks
15-2.76752 52.58437 (15*2π)/107672 weeks
16-8.69471 50.1628 (16*2π)/107667 weeks
17-11.95962 35.47118 (17*2π)/107663 weeks
18-.95187 25.89658 (18*2π)/107660 weeks
198.09327 28.09787 (19*2π)/107657 weeks
2011.91989 36.72085 (20*2π)/107654 weeks
21-.18405 45.7933 (21*2π)/107651 weeks
22-15.20759 33.32571 (22*2π)/107649 weeks
23-11.31215 15.17826 (23*2π)/107647 weeks
242.64385 8.39652 (24*2π)/107645 weeks
2515.96238 13.25789 (25*2π)/107643 weeks
2618.54022 28.01288 (26*2π)/107641 weeks
275.65512 35.29747 (27*2π)/107640 weeks
28-5.05094 27.37 (28*2π)/107638 weeks
29-5.21229 15.09608 (29*2π)/107637 weeks
306.43067 6.17155 (30*2π)/107636 weeks
3119.75837 14.7011 (31*2π)/107635 weeks
3217.57036 28.05797 (32*2π)/107634 weeks
337.19297 32.39452 (33*2π)/107633 weeks
34-.93631 27.2837 (34*2π)/107632 weeks
35-.09296 19.68022 (35*2π)/107631 weeks
364.41441 19.80329 (36*2π)/107630 weeks
372.61189 22.26086 (37*2π)/107629 weeks
38.45653 19.41594 (38*2π)/107628 weeks
392.94676 18.08072 (39*2π)/107628 weeks
403.32134 19.94437 (40*2π)/107627 weeks
411.69325 22.24767 (41*2π)/107626 weeks
42-4.39316 22.38054 (42*2π)/107626 weeks
43-8.8802 14.61415 (43*2π)/107625 weeks
44-3.56358 6.21542 (44*2π)/107624 weeks
455.28625 6.77616 (45*2π)/107624 weeks
469.34554 13.84615 (46*2π)/107623 weeks
474.03623 21.14993 (47*2π)/107623 weeks
48-5.25069 18.1337 (48*2π)/107622 weeks
49-5.55884 8.4843 (49*2π)/107622 weeks
501.63298 5.03462 (50*2π)/107622 weeks
517.20731 8.01386 (51*2π)/107621 weeks
527.64241 14.05423 (52*2π)/107621 weeks
533.06557 16.34223 (53*2π)/107620 weeks
54.05313 14.64212 (54*2π)/107620 weeks
55-1.25805 12.47423 (55*2π)/107620 weeks
56-.80925 9.15909 (56*2π)/107619 weeks
571.99691 8.26281 (57*2π)/107619 weeks
583.93254 9.18238 (58*2π)/107619 weeks
594.77649 11.33459 (59*2π)/107618 weeks
603.24799 14.09477 (60*2π)/107618 weeks
61-.82958 13.71638 (61*2π)/107618 weeks
62-1.96494 10.43901 (62*2π)/107617 weeks
63-1.43139 8.078 (63*2π)/107617 weeks
641.08077 6.07243 (64*2π)/107617 weeks
654.08077 7.46328 (65*2π)/107617 weeks
664.68587 10.3708 (66*2π)/107616 weeks
672.40187 13.19244 (67*2π)/107616 weeks
68-1.87408 12.76341 (68*2π)/107616 weeks
69-4.31904 8.48051 (69*2π)/107616 weeks
70-1.69603 3.97561 (70*2π)/107615 weeks
713.11562 4.17129 (71*2π)/107615 weeks
724.83951 8.41608 (72*2π)/107615 weeks
731.56889 11.32967 (73*2π)/107615 weeks
74-2.48553 9.69989 (74*2π)/107615 weeks
75-2.84047 5.31799 (75*2π)/107614 weeks
76.12264 3.53202 (76*2π)/107614 weeks
771.9549 4.41557 (77*2π)/107614 weeks
782.26435 5.41027 (78*2π)/107614 weeks
791.3069 5.61106 (79*2π)/107614 weeks
801.79498 3.92075 (80*2π)/107613 weeks
813.683 4.46836 (81*2π)/107613 weeks
823.60628 5.95068 (82*2π)/107613 weeks
832.49555 6.17572 (83*2π)/107613 weeks
841.47834 5.04171 (84*2π)/107613 weeks
852.91087 2.18172 (85*2π)/107613 weeks
867.49999 3.17475 (86*2π)/107613 weeks
878.35094 8.01752 (87*2π)/107612 weeks
884.94206 11.10513 (88*2π)/107612 weeks
89.5976 10.02825 (89*2π)/107612 weeks
90-.41662 5.42606 (90*2π)/107612 weeks
913.93225 3.0671 (91*2π)/107612 weeks
927.35661 6.68263 (92*2π)/107612 weeks
935.611 11.01695 (93*2π)/107612 weeks
941.0248 12.03894 (94*2π)/107611 weeks
95-2.18447 8.50283 (95*2π)/107611 weeks
96-.57559 5.01755 (96*2π)/107611 weeks
971.80306 4.77239 (97*2π)/107611 weeks
982.85965 5.98789 (98*2π)/107611 weeks
992.50894 7.02172 (99*2π)/107611 weeks
1002.05089 7.18304 (100*2π)/107611 weeks
1011.83633 7.70755 (101*2π)/107611 weeks
102.55435 8.34384 (102*2π)/107611 weeks
103-1.43205 7.26233 (103*2π)/107610 weeks
104-1.38294 4.33504 (104*2π)/107610 weeks
1051.33963 3.39709 (105*2π)/107610 weeks
1063.18349 5.30731 (106*2π)/107610 weeks
1072.21362 8.12067 (107*2π)/107610 weeks
108-1.60923 8.62934 (108*2π)/107610 weeks
109-3.79176 4.91264 (109*2π)/107610 weeks
110-2.13608 1.71728 (110*2π)/107610 weeks
111.60183 .45036 (111*2π)/107610 weeks
1123.72222 1.87971 (112*2π)/107610 weeks
1133.51425 4.99885 (113*2π)/107610 weeks
1141.32509 5.58847 (114*2π)/10769 weeks
115-.32597 4.46211 (115*2π)/10769 weeks
116-.16914 1.48033 (116*2π)/10769 weeks
1173.26207 .19331 (117*2π)/10769 weeks
1186.15269 2.65338 (118*2π)/10769 weeks
1195.61651 6.18311 (119*2π)/10769 weeks
1202.82254 7.47282 (120*2π)/10769 weeks
121.50836 5.71916 (121*2π)/10769 weeks
1221.70561 3.21719 (122*2π)/10769 weeks
1234.39057 4.1581 (123*2π)/10769 weeks
1244.06576 6.90621 (124*2π)/10769 weeks
1251.72213 7.85688 (125*2π)/10769 weeks
126-.12578 6.27282 (126*2π)/10769 weeks
127.88343 4.54627 (127*2π)/10768 weeks
1282.31555 5.52588 (128*2π)/10768 weeks
1291.36395 7.41483 (129*2π)/10768 weeks
130-1.41434 7.33584 (130*2π)/10768 weeks
131-2.68976 4.434 (131*2π)/10768 weeks
132-.67225 2.35886 (132*2π)/10768 weeks
1331.38138 3.41941 (133*2π)/10768 weeks
134.72286 5.66812 (134*2π)/10768 weeks
135-2.08689 5.40866 (135*2π)/10768 weeks
136-3.1178 2.5897 (136*2π)/10768 weeks
137-1.43702 .17154 (137*2π)/10768 weeks
1381.25455 .20605 (138*2π)/10768 weeks
1392.20711 2.15318 (139*2π)/10768 weeks
1401.01218 3.34797 (140*2π)/10768 weeks
141-.36513 2.41901 (141*2π)/10768 weeks
142.34217 .93848 (142*2π)/10768 weeks
1431.39688 1.24886 (143*2π)/10768 weeks
1441.38064 1.60124 (144*2π)/10767 weeks
1451.10419 1.81794 (145*2π)/10767 weeks
146.33911 .8314 (146*2π)/10767 weeks
1471.68664 -.41637 (147*2π)/10767 weeks
1482.88486 .27711 (148*2π)/10767 weeks
1492.75948 .97148 (149*2π)/10767 weeks
1502.31465 .82583 (150*2π)/10767 weeks
1512.2123 -.16534 (151*2π)/10767 weeks
1523.58383 -1.1855 (152*2π)/10767 weeks
1535.23868 -.77554 (153*2π)/10767 weeks
1546.35829 .18295 (154*2π)/10767 weeks
1556.84244 1.78576 (155*2π)/10767 weeks
1566.02539 2.84086 (156*2π)/10767 weeks
1575.39801 2.68439 (157*2π)/10767 weeks
1585.77996 2.27014 (158*2π)/10767 weeks
1596.80322 2.62772 (159*2π)/10767 weeks
1607.5139 4.07794 (160*2π)/10767 weeks
1616.80503 6.06824 (161*2π)/10767 weeks
1624.87257 6.41765 (162*2π)/10767 weeks
1634.11062 5.81888 (163*2π)/10767 weeks
1643.84847 5.31852 (164*2π)/10767 weeks
1654.16636 5.17579 (165*2π)/10767 weeks
1664.11907 5.81033 (166*2π)/10766 weeks
1673.29957 6.04952 (167*2π)/10766 weeks
1682.7055 5.63728 (168*2π)/10766 weeks
1692.66739 5.25968 (169*2π)/10766 weeks
1702.51869 5.28416 (170*2π)/10766 weeks
1712.00817 4.94559 (171*2π)/10766 weeks
1722.09599 4.02612 (172*2π)/10766 weeks
1733.10877 3.68503 (173*2π)/10766 weeks
1743.9461 4.65801 (174*2π)/10766 weeks
1753.20697 5.8805 (175*2π)/10766 weeks
1761.76719 5.71891 (176*2π)/10766 weeks
1771.32718 4.35262 (177*2π)/10766 weeks
1782.50899 3.54357 (178*2π)/10766 weeks
1793.36643 4.57221 (179*2π)/10766 weeks
1802.59355 5.46243 (180*2π)/10766 weeks
1811.89043 5.02648 (181*2π)/10766 weeks
1821.77589 4.77207 (182*2π)/10766 weeks
1831.95517 4.34641 (183*2π)/10766 weeks
1842.43067 4.95446 (184*2π)/10766 weeks
1851.16077 5.53461 (185*2π)/10766 weeks
186.46513 4.30403 (186*2π)/10766 weeks
187.85916 3.30782 (187*2π)/10766 weeks
1882.18912 2.97052 (188*2π)/10766 weeks
1892.98027 4.61322 (189*2π)/10766 weeks
1901.17734 5.9379 (190*2π)/10766 weeks
191-.90296 4.52446 (191*2π)/10766 weeks
192-.49189 2.14049 (192*2π)/10766 weeks
1931.43173 1.36351 (193*2π)/10766 weeks
1942.87536 2.60502 (194*2π)/10766 weeks
1952.00595 4.10044 (195*2π)/10766 weeks
196.68896 3.64272 (196*2π)/10765 weeks
197.27778 2.5193 (197*2π)/10765 weeks
198.90531 1.19636 (198*2π)/10765 weeks
1992.34995 1.06888 (199*2π)/10765 weeks
2002.9491 1.85428 (200*2π)/10765 weeks
2012.68672 2.15974 (201*2π)/10765 weeks
2022.96185 1.8954 (202*2π)/10765 weeks
2033.34698 1.95841 (203*2π)/10765 weeks
2044.15059 2.25464 (204*2π)/10765 weeks
2054.26494 3.51389 (205*2π)/10765 weeks
2063.25668 3.74035 (206*2π)/10765 weeks
2073.41161 3.21422 (207*2π)/10765 weeks
2084.14959 3.53834 (208*2π)/10765 weeks
2094.40768 4.86945 (209*2π)/10765 weeks
2103.1764 6.32845 (210*2π)/10765 weeks
211.86109 6.2285 (211*2π)/10765 weeks
212-.10632 4.13618 (212*2π)/10765 weeks
213.83433 3.01453 (213*2π)/10765 weeks
2141.60173 3.11156 (214*2π)/10765 weeks
2151.66045 3.78675 (215*2π)/10765 weeks
216.48245 3.94467 (216*2π)/10765 weeks
217-.04924 2.62492 (217*2π)/10765 weeks
218.34381 1.77379 (218*2π)/10765 weeks
219.64735 .86954 (219*2π)/10765 weeks
2202.09521 -.02151 (220*2π)/10765 weeks
2213.69911 .70665 (221*2π)/10765 weeks
2224.10198 1.89806 (222*2π)/10765 weeks
2234.0785 2.93996 (223*2π)/10765 weeks
2243.04405 3.55717 (224*2π)/10765 weeks
2252.69884 2.97778 (225*2π)/10765 weeks
2262.80788 3.16234 (226*2π)/10765 weeks
2272.54905 2.79554 (227*2π)/10765 weeks
2283.38554 2.89388 (228*2π)/10765 weeks
2293.38949 3.98557 (229*2π)/10765 weeks
2302.43791 4.8757 (230*2π)/10765 weeks
231.74249 4.82636 (231*2π)/10765 weeks
232-.62554 3.13564 (232*2π)/10765 weeks
233.16125 .8478 (233*2π)/10765 weeks
2342.3006 .5616 (234*2π)/10765 weeks
2353.25674 1.79645 (235*2π)/10765 weeks
2362.79834 3.14197 (236*2π)/10765 weeks
2371.11374 3.00227 (237*2π)/10765 weeks
2381.0025 1.27969 (238*2π)/10765 weeks
2392.05632 .64718 (239*2π)/10765 weeks
2403.09045 .55109 (240*2π)/10764 weeks
2414.158 1.26695 (241*2π)/10764 weeks
2424.23278 2.64871 (242*2π)/10764 weeks
2433.383 3.35905 (243*2π)/10764 weeks
2442.3364 3.43391 (244*2π)/10764 weeks
2451.44282 2.47576 (245*2π)/10764 weeks
2461.99762 .95884 (246*2π)/10764 weeks
2473.59435 .83505 (247*2π)/10764 weeks
2484.60883 2.05266 (248*2π)/10764 weeks
2494.02104 3.56513 (249*2π)/10764 weeks
2502.51948 3.75449 (250*2π)/10764 weeks
2511.70214 2.52231 (251*2π)/10764 weeks
2522.45202 1.28715 (252*2π)/10764 weeks
2533.7886 1.37083 (253*2π)/10764 weeks
2544.52659 2.35162 (254*2π)/10764 weeks
2554.23141 3.47458 (255*2π)/10764 weeks
2563.44364 3.95944 (256*2π)/10764 weeks
2572.66531 3.93017 (257*2π)/10764 weeks
2582.03624 3.35006 (258*2π)/10764 weeks
2592.05131 2.65 (259*2π)/10764 weeks
2602.60903 1.97461 (260*2π)/10764 weeks
2613.63576 2.11461 (261*2π)/10764 weeks
2624.17099 3.2799 (262*2π)/10764 weeks
2633.32024 4.35604 (263*2π)/10764 weeks
2642.05555 4.01221 (264*2π)/10764 weeks
2652.01239 3.20337 (265*2π)/10764 weeks
2662.17361 2.73776 (266*2π)/10764 weeks
2673.09999 2.48683 (267*2π)/10764 weeks
2683.73991 3.67818 (268*2π)/10764 weeks
2692.93833 4.87515 (269*2π)/10764 weeks
2701.33403 5.09319 (270*2π)/10764 weeks
271.14094 3.89601 (271*2π)/10764 weeks
272.38556 2.5072 (272*2π)/10764 weeks
273.9977 1.98352 (273*2π)/10764 weeks
2741.65774 1.7971 (274*2π)/10764 weeks
2752.03793 2.08251 (275*2π)/10764 weeks
2761.98728 2.23687 (276*2π)/10764 weeks
2771.91962 2.20842 (277*2π)/10764 weeks
2781.77198 1.86529 (278*2π)/10764 weeks
2792.23859 1.22044 (279*2π)/10764 weeks
2803.29926 1.23217 (280*2π)/10764 weeks
2814.02426 1.96668 (281*2π)/10764 weeks
2824.30351 3.00921 (282*2π)/10764 weeks
2833.71616 4.02451 (283*2π)/10764 weeks
2842.8082 4.19911 (284*2π)/10764 weeks
2852.43686 3.89421 (285*2π)/10764 weeks
2862.36908 3.82703 (286*2π)/10764 weeks
2872.25162 3.77924 (287*2π)/10764 weeks
2882.42361 3.81835 (288*2π)/10764 weeks
2892.47716 4.33119 (289*2π)/10764 weeks
2901.94644 5.02279 (290*2π)/10764 weeks
291.78982 5.28054 (291*2π)/10764 weeks
292-.49782 4.38568 (292*2π)/10764 weeks
293-.46588 2.81268 (293*2π)/10764 weeks
294.76809 2.11631 (294*2π)/10764 weeks
2951.77592 2.8185 (295*2π)/10764 weeks
2961.60992 4.26078 (296*2π)/10764 weeks
297-.24811 4.75607 (297*2π)/10764 weeks
298-1.50872 3.21383 (298*2π)/10764 weeks
299-1.08335 1.52471 (299*2π)/10764 weeks
300.30124 .87522 (300*2π)/10764 weeks
3011.4428 1.59576 (301*2π)/10764 weeks
3021.12108 2.67204 (302*2π)/10764 weeks
303.34323 2.54688 (303*2π)/10764 weeks
304.22905 2.05628 (304*2π)/10764 weeks
305.34685 1.86544 (305*2π)/10764 weeks
306.46953 1.58396 (306*2π)/10764 weeks
307.77331 1.5053 (307*2π)/10764 weeks
3081.17563 1.62295 (308*2π)/10763 weeks
3091.24293 2.24456 (309*2π)/10763 weeks
310.65415 2.62712 (310*2π)/10763 weeks
311-.11836 2.4392 (311*2π)/10763 weeks
312-.57633 1.51495 (312*2π)/10763 weeks
313-.0271 .7191 (313*2π)/10763 weeks
314.5784 .57366 (314*2π)/10763 weeks
3151.12669 .84449 (315*2π)/10763 weeks
3161.01321 1.29894 (316*2π)/10763 weeks
317.71537 1.32697 (317*2π)/10763 weeks
318.33753 1.00177 (318*2π)/10763 weeks
319.49654 .23107 (319*2π)/10763 weeks
3201.38018 -.07298 (320*2π)/10763 weeks
3212.0287 .30749 (321*2π)/10763 weeks
3222.31842 .93476 (322*2π)/10763 weeks
3232.14571 1.60322 (323*2π)/10763 weeks
3241.38075 1.79434 (324*2π)/10763 weeks
3251.1495 1.1484 (325*2π)/10763 weeks
3261.5618 1.04049 (326*2π)/10763 weeks
3271.51228 1.14605 (327*2π)/10763 weeks
3281.65828 1.02465 (328*2π)/10763 weeks
3291.77532 .96162 (329*2π)/10763 weeks
3302.34664 1.11392 (330*2π)/10763 weeks
3312.34057 2.05783 (331*2π)/10763 weeks
3321.38549 2.34771 (332*2π)/10763 weeks
333.69619 1.68947 (333*2π)/10763 weeks
3341.04255 .63415 (334*2π)/10763 weeks
3352.40411 .59106 (335*2π)/10763 weeks
3362.9006 2.1935 (336*2π)/10763 weeks
3371.57904 3.14813 (337*2π)/10763 weeks
338.23576 2.71401 (338*2π)/10763 weeks
339-.38756 1.40998 (339*2π)/10763 weeks
340.48032 .07704 (340*2π)/10763 weeks
3411.71745 .46311 (341*2π)/10763 weeks
3421.74054 1.19059 (342*2π)/10763 weeks
3431.26947 1.35828 (343*2π)/10763 weeks
3441.07925 .82895 (344*2π)/10763 weeks
3451.6549 .56367 (345*2π)/10763 weeks
3462.08398 .99671 (346*2π)/10763 weeks
3471.72684 1.29894 (347*2π)/10763 weeks
3481.79653 .84426 (348*2π)/10763 weeks
3492.66417 1.02132 (349*2π)/10763 weeks
3502.89213 2.22725 (350*2π)/10763 weeks
3511.96078 3.32377 (351*2π)/10763 weeks
352.17277 3.07176 (352*2π)/10763 weeks
353-.344 1.41733 (353*2π)/10763 weeks
354.83352 .29532 (354*2π)/10763 weeks
3552.29388 1.09277 (355*2π)/10763 weeks
3561.90807 2.92599 (356*2π)/10763 weeks
357-.13067 3.3608 (357*2π)/10763 weeks
358-1.64688 1.76371 (358*2π)/10763 weeks
359-1.14674 -.35228 (359*2π)/10763 weeks
360.61183 -.79675 (360*2π)/10763 weeks
3611.35478 .17356 (361*2π)/10763 weeks
362.71144 .82791 (362*2π)/10763 weeks
363-.1171 .1289 (363*2π)/10763 weeks
364.44489 -1.13927 (364*2π)/10763 weeks
3651.73613 -1.1038 (365*2π)/10763 weeks
3662.11729 -.30848 (366*2π)/10763 weeks
3671.67929 .0085 (367*2π)/10763 weeks
3681.49756 -.66499 (368*2π)/10763 weeks
3692.53039 -1.1853 (369*2π)/10763 weeks
3703.6947 -.39952 (370*2π)/10763 weeks
3713.77765 1.08202 (371*2π)/10763 weeks
3722.49323 1.98353 (372*2π)/10763 weeks
3731.32926 1.08918 (373*2π)/10763 weeks
3741.78679 -.05535 (374*2π)/10763 weeks
3753.10866 -.09913 (375*2π)/10763 weeks
3763.77935 1.32752 (376*2π)/10763 weeks
3772.67317 2.72399 (377*2π)/10763 weeks
378.90573 2.29034 (378*2π)/10763 weeks
379.52291 .59152 (379*2π)/10763 weeks
3801.98396 -.25857 (380*2π)/10763 weeks
3813.00341 .71305 (381*2π)/10763 weeks
3822.6518 1.97182 (382*2π)/10763 weeks
3831.22518 2.2464 (383*2π)/10763 weeks
384.47382 .88148 (384*2π)/10763 weeks
3851.52949 .02874 (385*2π)/10763 weeks
3862.34243 .7036 (386*2π)/10763 weeks
3871.90914 1.69994 (387*2π)/10763 weeks
388.56463 1.51567 (388*2π)/10763 weeks
389.36718 .04772 (389*2π)/10763 weeks
3901.4452 -.4682 (390*2π)/10763 weeks
3912.0791 .11795 (391*2π)/10763 weeks
3921.69106 .76081 (392*2π)/10763 weeks
393.61153 .47763 (393*2π)/10763 weeks
394.59492 -1.09023 (394*2π)/10763 weeks
3951.97431 -1.83462 (395*2π)/10763 weeks
3963.0859 -1.28793 (396*2π)/10763 weeks
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