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# Fourier Analysis of ATT (Grupa Azoty SA)

ATT (Grupa Azoty SA) appears to have interesting cyclic behaviour every 44 weeks (67.4315*cosine), 47 weeks (62.445*sine), and 28 weeks (44.191*cosine).

ATT (Grupa Azoty SA) has an average price of 269.17 (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 9/22/2005 to 6/19/2017 for ATT (Grupa Azoty SA), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0269.1671   0
1-33.96434 285.9666 (1*2π)/614614 weeks
2111.9502 -105.7885 (2*2π)/614307 weeks
3132.7281 228.3463 (3*2π)/614205 weeks
4-25.21188 100.1796 (4*2π)/614154 weeks
5-28.62732 137.8773 (5*2π)/614123 weeks
6-82.47051 2.57635 (6*2π)/614102 weeks
7-9.67069 27.20079 (7*2π)/61488 weeks
8-24.14393 -25.62077 (8*2π)/61477 weeks
944.70247 38.59623 (9*2π)/61468 weeks
10-32.70808 20.74863 (10*2π)/61461 weeks
1127.97417 2.69399 (11*2π)/61456 weeks
1211.44785 35.3355 (12*2π)/61451 weeks
13-.73228 62.44499 (13*2π)/61447 weeks
14-67.43147 21.3998 (14*2π)/61444 weeks
15-8.61706 -24.71045 (15*2π)/61441 weeks
16.91443 -.61535 (16*2π)/61438 weeks
179.3198 13.09899 (17*2π)/61436 weeks
18-23.57105 2.03534 (18*2π)/61434 weeks
1921.48554 -5.49467 (19*2π)/61432 weeks
20-.46757 21.22788 (20*2π)/61431 weeks
2115.07336 21.57282 (21*2π)/61429 weeks
22-44.19104 27.17913 (22*2π)/61428 weeks
23-2.78763 -30.03889 (23*2π)/61427 weeks
24-9.83481 15.8795 (24*2π)/61426 weeks
258.02673 -25.15827 (25*2π)/61425 weeks
265.9175 29.83602 (26*2π)/61424 weeks
27-9.78361 -23.10437 (27*2π)/61423 weeks
2822.59807 18.41364 (28*2π)/61422 weeks
29-7.74621 3.19659 (29*2π)/61421 weeks
302.93334 28.23237 (30*2π)/61420 weeks
31-33.97767 -12.74627 (31*2π)/61420 weeks
3220.13908 -5.79505 (32*2π)/61419 weeks
33-15.41996 -4.05549 (33*2π)/61419 weeks
3424.70157 -4.42714 (34*2π)/61418 weeks
35-17.06656 12.73041 (35*2π)/61418 weeks
3619.17729 -15.00914 (36*2π)/61417 weeks
37-.10101 24.01611 (37*2π)/61417 weeks
381.5326 -5.05978 (38*2π)/61416 weeks
39-10.08378 18.32396 (39*2π)/61416 weeks
40-10.42548 -22.48755 (40*2π)/61415 weeks
4114.6584 1.94925 (41*2π)/61415 weeks
42.03657 -3.58657 (42*2π)/61415 weeks
4311.35007 4.41994 (43*2π)/61414 weeks
44-.15422 1.12599 (44*2π)/61414 weeks
4512.62825 2.73032 (45*2π)/61414 weeks
46-.21358 13.58712 (46*2π)/61413 weeks
47-4.96945 1.50719 (47*2π)/61413 weeks
48-1.77135 2.25058 (48*2π)/61413 weeks
49-2.51975 -8.49865 (49*2π)/61413 weeks
5014.10667 -1.21506 (50*2π)/61412 weeks
511.6502 5.80515 (51*2π)/61412 weeks
529.79921 1.5108 (52*2π)/61412 weeks
53-.11298 8.75001 (53*2π)/61412 weeks
547.56341 .27225 (54*2π)/61411 weeks
55-1.84734 16.08847 (55*2π)/61411 weeks
56-7.02574 -4.84323 (56*2π)/61411 weeks
573.75527 2.25756 (57*2π)/61411 weeks
581.67933 -6.60196 (58*2π)/61411 weeks
5912.691 5.62481 (59*2π)/61410 weeks
60.21113 2.35232 (60*2π)/61410 weeks
619.46564 9.94238 (61*2π)/61410 weeks
62-7.85533 4.1609 (62*2π)/61410 weeks
6312.37514 5.25805 (63*2π)/61410 weeks
64-11.71442 11.37209 (64*2π)/61410 weeks
653.05774 -6.87337 (65*2π)/6149 weeks
66-4.86418 2.77244 (66*2π)/6149 weeks
6713.11411 -7.33479 (67*2π)/6149 weeks
682.36662 16.95174 (68*2π)/6149 weeks
693.05191 -2.80995 (69*2π)/6149 weeks
701.96526 12.79119 (70*2π)/6149 weeks
71.43414 -2.94685 (71*2π)/6149 weeks
72.04174 14.30561 (72*2π)/6149 weeks
73-8.09078 -3.94558 (73*2π)/6148 weeks
742.90832 4.60116 (74*2π)/6148 weeks
75.47284 -7.24915 (75*2π)/6148 weeks
7613.65061 9.38763 (76*2π)/6148 weeks
77-6.28242 4.91874 (77*2π)/6148 weeks
785.12769 4.8468 (78*2π)/6148 weeks
79-5.36973 4.63416 (79*2π)/6148 weeks
805.72345 6.78724 (80*2π)/6148 weeks
81-11.30963 5.7334 (81*2π)/6148 weeks
823.7603 -5.70598 (82*2π)/6147 weeks
83-2.94502 2.2747 (83*2π)/6147 weeks
848.66056 -3.08014 (84*2π)/6147 weeks
85-2.95927 11.4234 (85*2π)/6147 weeks
862.74113 -2.75421 (86*2π)/6147 weeks
87-2.3951 12.08921 (87*2π)/6147 weeks
88-1.98027 -5.23576 (88*2π)/6147 weeks
89-1.3042 9.57678 (89*2π)/6147 weeks
90-6.08834 -7.9067 (90*2π)/6147 weeks
913.60098 5.40983 (91*2π)/6147 weeks
92-3.45222 -6.78675 (92*2π)/6147 weeks
9312.18571 6.45484 (93*2π)/6147 weeks
94-7.21746 3.47688 (94*2π)/6147 weeks
955.56026 2.47439 (95*2π)/6146 weeks
96-9.59341 3.8147 (96*2π)/6146 weeks
975.62791 -3.62271 (97*2π)/6146 weeks
98-7.26137 7.76596 (98*2π)/6146 weeks
991.60316 -10.18197 (99*2π)/6146 weeks
100.73833 6.80301 (100*2π)/6146 weeks
1012.24422 -9.95605 (101*2π)/6146 weeks
1027.24695 13.64256 (102*2π)/6146 weeks
103-8.92604 -5.10394 (103*2π)/6146 weeks
1047.07217 7.13934 (104*2π)/6146 weeks
105-12.6149 -5.98723 (105*2π)/6146 weeks
10613.44846 1.52368 (106*2π)/6146 weeks
107-14.35474 1.44615 (107*2π)/6146 weeks
10814.12276 -8.72019 (108*2π)/6146 weeks
109-7.18823 6.3987 (109*2π)/6146 weeks
11013.81237 -10.04086 (110*2π)/6146 weeks
111-4.59294 19.87845 (111*2π)/6146 weeks
112-1.8937 -12.71948 (112*2π)/6145 weeks
1131.62104 11.96599 (113*2π)/6145 weeks
114-2.18155 -14.92619 (114*2π)/6145 weeks
1158.12951 16.02912 (115*2π)/6145 weeks
116-14.94006 -14.30708 (116*2π)/6145 weeks
11722.42845 5.16823 (117*2π)/6145 weeks
118-10.83847 .77714 (118*2π)/6145 weeks
11919.27966 3.33868 (119*2π)/6145 weeks
120-18.71324 5.47874 (120*2π)/6145 weeks
12115.74633 -8.1042 (121*2π)/6145 weeks
122-14.60148 12.2355 (122*2π)/6145 weeks
12314.16441 -14.85307 (123*2π)/6145 weeks
124-6.71569 17.5094 (124*2π)/6145 weeks
1257.39529 -22.7356 (125*2π)/6145 weeks
1266.66349 20.99383 (126*2π)/6145 weeks
127-2.62223 -14.41689 (127*2π)/6145 weeks
12810.24072 21.85852 (128*2π)/6145 weeks
129-14.27505 -12.30878 (129*2π)/6145 weeks
13016.5279 11.48903 (130*2π)/6145 weeks
131-18.08668 -7.37696 (131*2π)/6145 weeks
13222.37304 3.27013 (132*2π)/6145 weeks
133-19.56482 3.21352 (133*2π)/6145 weeks
13423.76491 -8.28579 (134*2π)/6145 weeks
135-12.82045 15.20734 (135*2π)/6145 weeks
13615.44268 -10.71323 (136*2π)/6145 weeks
137-12.08846 22.87242 (137*2π)/6144 weeks
1385.12928 -19.94191 (138*2π)/6144 weeks
139-.20551 21.04162 (139*2π)/6144 weeks
140-1.24309 -21.09357 (140*2π)/6144 weeks
1418.19627 21.40766 (141*2π)/6144 weeks
142-10.25861 -17.66949 (142*2π)/6144 weeks
14319.67785 16.65702 (143*2π)/6144 weeks
144-13.83659 -6.59297 (144*2π)/6144 weeks
14518.84691 11.14309 (145*2π)/6144 weeks
146-23.09013 -2.02035 (146*2π)/6144 weeks
14719.39033 -3.45345 (147*2π)/6144 weeks
148-16.48867 8.67777 (148*2π)/6144 weeks
14915.65057 -8.50973 (149*2π)/6144 weeks
150-9.41272 13.39839 (150*2π)/6144 weeks
1519.50725 -13.62115 (151*2π)/6144 weeks
152-1.73109 17.13433 (152*2π)/6144 weeks
153-.58975 -9.3843 (153*2π)/6144 weeks
154.20305 15.62399 (154*2π)/6144 weeks
155-7.90589 -11.11599 (155*2π)/6144 weeks
1569.23545 6.73805 (156*2π)/6144 weeks
157-6.32393 -3.80682 (157*2π)/6144 weeks
1588.55676 3.45911 (158*2π)/6144 weeks
159-6.7681 .16308 (159*2π)/6144 weeks
1608.33768 .28386 (160*2π)/6144 weeks
161-3.96415 6.87252 (161*2π)/6144 weeks
162.58516 .00723 (162*2π)/6144 weeks
163-5.28061 2.60191 (163*2π)/6144 weeks
164-.07349 -5.51125 (164*2π)/6144 weeks
1652.32335 1.97464 (165*2π)/6144 weeks
166-1.05232 -.0337 (166*2π)/6144 weeks
1671.63749 -.47397 (167*2π)/6144 weeks
1681.22621 1.67978 (168*2π)/6144 weeks
1691.19263 .19857 (169*2π)/6144 weeks
170.00306 4.70439 (170*2π)/6144 weeks
171-5.50458 -1.93856 (171*2π)/6144 weeks
1722.70866 -.52893 (172*2π)/6144 weeks
173-3.65967 -2.86262 (173*2π)/6144 weeks
1748.29495 -1.40405 (174*2π)/6144 weeks
175-5.72443 4.4739 (175*2π)/6144 weeks
1766.55639 -5.78829 (176*2π)/6143 weeks
177-1.44613 8.81209 (177*2π)/6143 weeks
1781.87546 -6.73339 (178*2π)/6143 weeks
179-1.38411 10.2891 (179*2π)/6143 weeks
180-5.65676 -10.4513 (180*2π)/6143 weeks
1816.80529 5.42547 (181*2π)/6143 weeks
182-4.6155 -7.40573 (182*2π)/6143 weeks
18312.18567 3.71188 (183*2π)/6143 weeks
184-8.86075 -1.24315 (184*2π)/6143 weeks
18511.35969 -2.4194 (185*2π)/6143 weeks
186-7.43622 6.89099 (186*2π)/6143 weeks
1877.45349 -5.22882 (187*2π)/6143 weeks
188-4.27776 9.42294 (188*2π)/6143 weeks
1891.67824 -13.47461 (189*2π)/6143 weeks
1904.52261 7.45228 (190*2π)/6143 weeks
191-1.53841 -8.61544 (191*2π)/6143 weeks
1929.86697 11.20605 (192*2π)/6143 weeks
193-8.50347 -4.60082 (193*2π)/6143 weeks
19414.7513 2.68673 (194*2π)/6143 weeks
195-10.2226 2.67382 (195*2π)/6143 weeks
1969.78656 -2.23697 (196*2π)/6143 weeks
197-11.37781 5.01299 (197*2π)/6143 weeks
19810.92066 -10.79268 (198*2π)/6143 weeks
199-1.59592 10.54489 (199*2π)/6143 weeks
2006.55125 -9.63438 (200*2π)/6143 weeks
201-.30203 13.79716 (201*2π)/6143 weeks
202-1.41799 -11.81611 (202*2π)/6143 weeks
2038.03383 13.30835 (203*2π)/6143 weeks
204-7.70796 -5.93658 (204*2π)/6143 weeks
2058.14972 6.47565 (205*2π)/6143 weeks
206-9.95886 -6.19645 (206*2π)/6143 weeks
20715.29741 .56857 (207*2π)/6143 weeks
208-6.91695 4.86064 (208*2π)/6143 weeks
2099.40895 -1.90457 (209*2π)/6143 weeks
210-6.94037 5.95821 (210*2π)/6143 weeks
2117.3236 -4.97049 (211*2π)/6143 weeks
212-3.76038 10.396 (212*2π)/6143 weeks
2131.15465 -6.61049 (213*2π)/6143 weeks
214-.7539 5.44097 (214*2π)/6143 weeks
2152.04351 -8.64486 (215*2π)/6143 weeks
2164.74833 7.70643 (216*2π)/6143 weeks
217-1.34611 -1.86651 (217*2π)/6143 weeks
2182.28422 6.32792 (218*2π)/6143 weeks
219-.76041 -2.92191 (219*2π)/6143 weeks
2202.43663 5.93502 (220*2π)/6143 weeks
221-3.51985 -3.56025 (221*2π)/6143 weeks
222.99167 4.96744 (222*2π)/6143 weeks
223-2.75675 -6.7055 (223*2π)/6143 weeks
2248.15257 6.07616 (224*2π)/6143 weeks
225-4.3073 -3.05401 (225*2π)/6143 weeks
2267.41335 7.01121 (226*2π)/6143 weeks
227-10.6113 -2.01933 (227*2π)/6143 weeks
22810.0463 2.77074 (228*2π)/6143 weeks
229-10.88759 2.20383 (229*2π)/6143 weeks
2309.78155 -1.54281 (230*2π)/6143 weeks
231-11.21665 2.22086 (231*2π)/6143 weeks
23213.10426 -8.38975 (232*2π)/6143 weeks
233-6.94517 10.37909 (233*2π)/6143 weeks
2347.32912 -8.69234 (234*2π)/6143 weeks
235-6.06204 14.18433 (235*2π)/6143 weeks
2361.51444 -13.48468 (236*2π)/6143 weeks
2371.01296 13.931 (237*2π)/6143 weeks
238-4.41072 -13.16072 (238*2π)/6143 weeks
2395.42208 10.68735 (239*2π)/6143 weeks
240-7.90983 -13.31833 (240*2π)/6143 weeks
24113.66689 7.8732 (241*2π)/6143 weeks
242-10.32314 -3.17775 (242*2π)/6143 weeks
24311.64265 6.03466 (243*2π)/6143 weeks
244-13.75585 -1.28042 (244*2π)/6143 weeks
24513.83858 -2.39689 (245*2π)/6143 weeks
246-11.43781 4.58086 (246*2π)/6142 weeks
2478.01268 -6.96603 (247*2π)/6142 weeks
248-7.0935 3.4042 (248*2π)/6142 weeks
24910.11981 -7.03414 (249*2π)/6142 weeks
250-3.12546 8.4294 (250*2π)/6142 weeks
2516.34367 -5.19701 (251*2π)/6142 weeks
252-5.01536 7.2559 (252*2π)/6142 weeks
2533.82349 -8.34117 (253*2π)/6142 weeks
254-3.54256 8.25436 (254*2π)/6142 weeks
2552.75725 -8.60817 (255*2π)/6142 weeks
256-.85282 7.43929 (256*2π)/6142 weeks
2573.60507 -11.85987 (257*2π)/6142 weeks
2583.13318 9.31986 (258*2π)/6142 weeks
259.02736 -9.28044 (259*2π)/6142 weeks
2602.35649 12.5296 (260*2π)/6142 weeks
261-5.81342 -11.949 (261*2π)/6142 weeks
2629.3694 10.31039 (262*2π)/6142 weeks
263-9.75479 -9.81397 (263*2π)/6142 weeks
26413.83233 5.77935 (264*2π)/6142 weeks
265-12.64651 -6.01528 (265*2π)/6142 weeks
26618.276 1.36531 (266*2π)/6142 weeks
267-13.08255 3.13336 (267*2π)/6142 weeks
26816.38909 -2.7177 (268*2π)/6142 weeks
269-14.73397 9.19524 (269*2π)/6142 weeks
27012.58674 -11.63402 (270*2π)/6142 weeks
271-7.33339 12.35356 (271*2π)/6142 weeks
2728.10414 -15.0676 (272*2π)/6142 weeks
273-1.98559 14.4025 (273*2π)/6142 weeks
2741.62184 -15.47175 (274*2π)/6142 weeks
2756.89295 15.09226 (275*2π)/6142 weeks
276-4.14161 -8.3539 (276*2π)/6142 weeks
2776.73032 10.44223 (277*2π)/6142 weeks
278-8.87771 -7.14727 (278*2π)/6142 weeks
2798.75206 3.68599 (279*2π)/6142 weeks
280-6.91584 -1.62374 (280*2π)/6142 weeks
2818.33944 -.33548 (281*2π)/6142 weeks
282-2.21106 2.00885 (282*2π)/6142 weeks
2833.82282 -1.53463 (283*2π)/6142 weeks
2842.05654 1.62525 (284*2π)/6142 weeks
285-.27935 5.71843 (285*2π)/6142 weeks
286-2.74938 -1.68726 (286*2π)/6142 weeks
2871.41763 2.6232 (287*2π)/6142 weeks
288-.37866 -5.59813 (288*2π)/6142 weeks
2894.32647 7.16736 (289*2π)/6142 weeks
290-6.41025 -6.61288 (290*2π)/6142 weeks
29111.57189 6.03309 (291*2π)/6142 weeks
292-9.96519 -2.56322 (292*2π)/6142 weeks
29314.77498 4.07422 (293*2π)/6142 weeks
294-18.36056 3.52687 (294*2π)/6142 weeks
29516.03324 -7.09068 (295*2π)/6142 weeks
296-15.36396 9.48666 (296*2π)/6142 weeks
29716.87053 -15.87022 (297*2π)/6142 weeks
298-11.89547 20.21781 (298*2π)/6142 weeks
2997.8693 -24.70548 (299*2π)/6142 weeks
3001.007 27.8325 (300*2π)/6142 weeks
301-4.63303 -23.5476 (301*2π)/6142 weeks
30210.61548 25.84161 (302*2π)/6142 weeks
303-18.05761 -23.06429 (303*2π)/6142 weeks
30420.04423 16.89606 (304*2π)/6142 weeks
305-25.04689 -14.83161 (305*2π)/6142 weeks
30631.33725 8.6701 (306*2π)/6142 weeks
307-29.08081   (307*2π)/6142 weeks
30831.33725 -8.6701 (308*2π)/6142 weeks
309-25.04689 14.83161 (309*2π)/6142 weeks
31020.04423 -16.89606 (310*2π)/6142 weeks
311-18.05761 23.06429 (311*2π)/6142 weeks
31210.61548 -25.84161 (312*2π)/6142 weeks
313-4.63303 23.5476 (313*2π)/6142 weeks
3141.007 -27.8325 (314*2π)/6142 weeks
3157.8693 24.70548 (315*2π)/6142 weeks
316-11.89547 -20.21781 (316*2π)/6142 weeks
31716.87053 15.87022 (317*2π)/6142 weeks
318-15.36396 -9.48666 (318*2π)/6142 weeks
31916.03324 7.09068 (319*2π)/6142 weeks
320-18.36056 -3.52687 (320*2π)/6142 weeks
32114.77498 -4.07422 (321*2π)/6142 weeks
322-9.96519 2.56322 (322*2π)/6142 weeks
32311.57189 -6.03309 (323*2π)/6142 weeks
324-6.41025 6.61288 (324*2π)/6142 weeks
3254.32647 -7.16736 (325*2π)/6142 weeks
326-.37866 5.59813 (326*2π)/6142 weeks
3271.41763 -2.6232 (327*2π)/6142 weeks
328-2.74938 1.68726 (328*2π)/6142 weeks
329-.27935 -5.71843 (329*2π)/6142 weeks
3302.05654 -1.62525 (330*2π)/6142 weeks
3313.82282 1.53463 (331*2π)/6142 weeks
332-2.21106 -2.00885 (332*2π)/6142 weeks
3338.33944 .33548 (333*2π)/6142 weeks
334-6.91584 1.62374 (334*2π)/6142 weeks
3358.75206 -3.68599 (335*2π)/6142 weeks
336-8.87771 7.14727 (336*2π)/6142 weeks
3376.73032 -10.44223 (337*2π)/6142 weeks
338-4.14161 8.3539 (338*2π)/6142 weeks
3396.89295 -15.09226 (339*2π)/6142 weeks
3401.62184 15.47175 (340*2π)/6142 weeks
341-1.98559 -14.4025 (341*2π)/6142 weeks
3428.10414 15.0676 (342*2π)/6142 weeks
343-7.33339 -12.35356 (343*2π)/6142 weeks
34412.58674 11.63402 (344*2π)/6142 weeks
345-14.73397 -9.19524 (345*2π)/6142 weeks
34616.38909 2.7177 (346*2π)/6142 weeks
347-13.08255 -3.13336 (347*2π)/6142 weeks
34818.276 -1.36531 (348*2π)/6142 weeks
349-12.64651 6.01528 (349*2π)/6142 weeks
35013.83233 -5.77935 (350*2π)/6142 weeks
351-9.75479 9.81397 (351*2π)/6142 weeks
3529.3694 -10.31039 (352*2π)/6142 weeks
353-5.81342 11.949 (353*2π)/6142 weeks
3542.35649 -12.5296 (354*2π)/6142 weeks
355.02736 9.28044 (355*2π)/6142 weeks
3563.13318 -9.31986 (356*2π)/6142 weeks
3573.60507 11.85987 (357*2π)/6142 weeks
358-.85282 -7.43929 (358*2π)/6142 weeks
3592.75725 8.60817 (359*2π)/6142 weeks
360-3.54256 -8.25436 (360*2π)/6142 weeks
3613.82349 8.34117 (361*2π)/6142 weeks
362-5.01536 -7.2559 (362*2π)/6142 weeks
3636.34367 5.19701 (363*2π)/6142 weeks
364-3.12546 -8.4294 (364*2π)/6142 weeks
36510.11981 7.03414 (365*2π)/6142 weeks
366-7.0935 -3.4042 (366*2π)/6142 weeks
3678.01268 6.96603 (367*2π)/6142 weeks
368-11.43781 -4.58086 (368*2π)/6142 weeks
36913.83858 2.39689 (369*2π)/6142 weeks
370-13.75585 1.28042 (370*2π)/6142 weeks
37111.64265 -6.03466 (371*2π)/6142 weeks
372-10.32314 3.17775 (372*2π)/6142 weeks
37313.66689 -7.8732 (373*2π)/6142 weeks
374-7.90983 13.31833 (374*2π)/6142 weeks
3755.42208 -10.68735 (375*2π)/6142 weeks
376-4.41072 13.16072 (376*2π)/6142 weeks
3771.01296 -13.931 (377*2π)/6142 weeks
3781.51444 13.48468 (378*2π)/6142 weeks
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