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# Fourier Analysis of PGEM (Ply Gem Holdings)

PGEM (Ply Gem Holdings) appears to have interesting cyclic behaviour every 17 weeks (.5519*sine), 26 weeks (.4568*cosine), and 21 weeks (.3668*sine).

PGEM (Ply Gem Holdings) has an average price of 14.84 (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 5/23/2013 to 4/9/2018 for PGEM (Ply Gem Holdings), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
014.84371   0
12.84499 -2.03017 (1*2π)/256256 weeks
21.10333 -.65575 (2*2π)/256128 weeks
3.94898 .85491 (3*2π)/25685 weeks
4.24593 .09391 (4*2π)/25664 weeks
5.73996 -.37491 (5*2π)/25651 weeks
6.50678 -1.02546 (6*2π)/25643 weeks
7.07615 .19374 (7*2π)/25637 weeks
8.54691 -.29695 (8*2π)/25632 weeks
9.22249 .05606 (9*2π)/25628 weeks
10.45677 .15171 (10*2π)/25626 weeks
11.065 .21686 (11*2π)/25623 weeks
12-.08011 .36682 (12*2π)/25621 weeks
13-.25856 -.05613 (13*2π)/25620 weeks
14-.15808 .00364 (14*2π)/25618 weeks
15.11814 -.55195 (15*2π)/25617 weeks
16-.18866 .23108 (16*2π)/25616 weeks
17.09507 -.00708 (17*2π)/25615 weeks
18.04828 .08985 (18*2π)/25614 weeks
19.18864 .08588 (19*2π)/25613 weeks
20.04493 .03475 (20*2π)/25613 weeks
21-.24089 .13077 (21*2π)/25612 weeks
22-.11765 -.10573 (22*2π)/25612 weeks
23.07668 .1162 (23*2π)/25611 weeks
24-.04995 .19144 (24*2π)/25611 weeks
25.10795 .03579 (25*2π)/25610 weeks
26.22119 -.04699 (26*2π)/25610 weeks
27.16661 .05975 (27*2π)/2569 weeks
28.07316 .12952 (28*2π)/2569 weeks
29-.00849 -.0319 (29*2π)/2569 weeks
30.00337 -.12076 (30*2π)/2569 weeks
31.1084 .08034 (31*2π)/2568 weeks
32-.02985 -.01127 (32*2π)/2568 weeks
33.08524 -.06648 (33*2π)/2568 weeks
34.12375 .10623 (34*2π)/2568 weeks
35-.16433 .09731 (35*2π)/2567 weeks
36.01061 -.06072 (36*2π)/2567 weeks
37-.02335 -.06976 (37*2π)/2567 weeks
38-.09431 -.00709 (38*2π)/2567 weeks
39.02455 .04487 (39*2π)/2567 weeks
40-.00891 .11054 (40*2π)/2566 weeks
41-.02616 .03392 (41*2π)/2566 weeks
42-.0057 -.05569 (42*2π)/2566 weeks
43-.15117 -.00917 (43*2π)/2566 weeks
44-.15365 .11404 (44*2π)/2566 weeks
45.05402 -.01318 (45*2π)/2566 weeks
46-.01609 -.05465 (46*2π)/2566 weeks
47.10402 -.10367 (47*2π)/2565 weeks
48.03751 .06078 (48*2π)/2565 weeks
49.15454 .01286 (49*2π)/2565 weeks
50.00855 .00005 (50*2π)/2565 weeks
51.07973 .01387 (51*2π)/2565 weeks
52-.01873 .02578 (52*2π)/2565 weeks
53.02263 .02398 (53*2π)/2565 weeks
54-.03491 .03253 (54*2π)/2565 weeks
55.0356 -.03783 (55*2π)/2565 weeks
56-.01142 -.13184 (56*2π)/2565 weeks
57.03507 -.00992 (57*2π)/2564 weeks
58-.05232 -.04398 (58*2π)/2564 weeks
59-.00876 .04783 (59*2π)/2564 weeks
60-.04037 -.05133 (60*2π)/2564 weeks
61.06095 -.054 (61*2π)/2564 weeks
62.05463 -.04076 (62*2π)/2564 weeks
63.03231 -.04833 (63*2π)/2564 weeks
64.07305 .0525 (64*2π)/2564 weeks
65-.03477 .05068 (65*2π)/2564 weeks
66.07455 -.02042 (66*2π)/2564 weeks
67-.06084 -.01404 (67*2π)/2564 weeks
68.04503 -.01391 (68*2π)/2564 weeks
69.1191 .0125 (69*2π)/2564 weeks
70.07514 .02411 (70*2π)/2564 weeks
71.05042 -.0083 (71*2π)/2564 weeks
72.13021 .03201 (72*2π)/2564 weeks
73.03648 .0128 (73*2π)/2564 weeks
74.06874 .03167 (74*2π)/2563 weeks
75.03115 .07275 (75*2π)/2563 weeks
76.02406 .01457 (76*2π)/2563 weeks
77.01165 .0399 (77*2π)/2563 weeks
78.06844 .04223 (78*2π)/2563 weeks
79-.00108 .02289 (79*2π)/2563 weeks
80.01181 .03925 (80*2π)/2563 weeks
81.02768 .02922 (81*2π)/2563 weeks
82-.01204 .06248 (82*2π)/2563 weeks
83-.04506 .03909 (83*2π)/2563 weeks
84-.01218 .06193 (84*2π)/2563 weeks
85-.03038 .03692 (85*2π)/2563 weeks
86-.03551 .026 (86*2π)/2563 weeks
87-.06274 .00744 (87*2π)/2563 weeks
88.01731 .03605 (88*2π)/2563 weeks
89-.04471 .04096 (89*2π)/2563 weeks
90.03941 .01979 (90*2π)/2563 weeks
91-.01967 -.04253 (91*2π)/2563 weeks
92-.00928 -.03725 (92*2π)/2563 weeks
93.04629 -.00152 (93*2π)/2563 weeks
94.05743 .02158 (94*2π)/2563 weeks
95-.03444 .07564 (95*2π)/2563 weeks
96-.04952 -.02143 (96*2π)/2563 weeks
97.02722 -.01689 (97*2π)/2563 weeks
98.00726 -.01046 (98*2π)/2563 weeks
99.02871 -.07775 (99*2π)/2563 weeks
100-.02246 .00471 (100*2π)/2563 weeks
101.06977 -.02748 (101*2π)/2563 weeks
102.0598 .04617 (102*2π)/2563 weeks
103.03386 -.00641 (103*2π)/2562 weeks
104-.03443 .00511 (104*2π)/2562 weeks
105-.01542 .01095 (105*2π)/2562 weeks
106-.0416 .0264 (106*2π)/2562 weeks
107-.07942 -.01145 (107*2π)/2562 weeks
108.03782 .01271 (108*2π)/2562 weeks
109-.01461 .0264 (109*2π)/2562 weeks
110-.00404 .01812 (110*2π)/2562 weeks
111.00417 .02706 (111*2π)/2562 weeks
112.02121 .0133 (112*2π)/2562 weeks
113.05503 -.03776 (113*2π)/2562 weeks
114.00943 .00805 (114*2π)/2562 weeks
115.04223 .04071 (115*2π)/2562 weeks
116-.00122 .00773 (116*2π)/2562 weeks
117.02114 .01663 (117*2π)/2562 weeks
118.0833 -.0154 (118*2π)/2562 weeks
119.01345 .07893 (119*2π)/2562 weeks
120-.03723 -.01242 (120*2π)/2562 weeks
121-.01688 .0219 (121*2π)/2562 weeks
122.0632 .03463 (122*2π)/2562 weeks
123-.01848 -.04266 (123*2π)/2562 weeks
124.00146 -.00491 (124*2π)/2562 weeks
125-.03637 .03077 (125*2π)/2562 weeks
126.00386 -.00698 (126*2π)/2562 weeks
127-.04447 .0088 (127*2π)/2562 weeks
128-.11352   (128*2π)/2562 weeks
129-.04447 -.0088 (129*2π)/2562 weeks
130.00386 .00698 (130*2π)/2562 weeks
131-.03637 -.03077 (131*2π)/2562 weeks
132.00146 .00491 (132*2π)/2562 weeks
133-.01848 .04266 (133*2π)/2562 weeks
134.0632 -.03463 (134*2π)/2562 weeks
135-.01688 -.0219 (135*2π)/2562 weeks
136-.03723 .01242 (136*2π)/2562 weeks
137.01345 -.07893 (137*2π)/2562 weeks
138.0833 .0154 (138*2π)/2562 weeks
139.02114 -.01663 (139*2π)/2562 weeks
140-.00122 -.00773 (140*2π)/2562 weeks
141.04223 -.04071 (141*2π)/2562 weeks
142.00943 -.00805 (142*2π)/2562 weeks
143.05503 .03776 (143*2π)/2562 weeks
144.02121 -.0133 (144*2π)/2562 weeks
145.00417 -.02706 (145*2π)/2562 weeks
146-.00404 -.01812 (146*2π)/2562 weeks
147-.01461 -.0264 (147*2π)/2562 weeks
148.03782 -.01271 (148*2π)/2562 weeks
149-.07942 .01145 (149*2π)/2562 weeks
150-.0416 -.0264 (150*2π)/2562 weeks
151-.01542 -.01095 (151*2π)/2562 weeks
152-.03443 -.00511 (152*2π)/2562 weeks
153.03386 .00641 (153*2π)/2562 weeks
154.0598 -.04617 (154*2π)/2562 weeks
155.06977 .02748 (155*2π)/2562 weeks
156-.02246 -.00471 (156*2π)/2562 weeks
157.02871 .07775 (157*2π)/2562 weeks
158.00726 .01046 (158*2π)/2562 weeks
159.02722 .01689 (159*2π)/2562 weeks
160-.04952 .02143 (160*2π)/2562 weeks
161-.03444 -.07564 (161*2π)/2562 weeks
162.05743 -.02158 (162*2π)/2562 weeks
163.04629 .00152 (163*2π)/2562 weeks
164-.00928 .03725 (164*2π)/2562 weeks
165-.01967 .04253 (165*2π)/2562 weeks
166.03941 -.01979 (166*2π)/2562 weeks
167-.04471 -.04096 (167*2π)/2562 weeks
168.01731 -.03605 (168*2π)/2562 weeks
169-.06274 -.00744 (169*2π)/2562 weeks
170-.03551 -.026 (170*2π)/2562 weeks
171-.03038 -.03692 (171*2π)/2561 weeks
172-.01218 -.06193 (172*2π)/2561 weeks
173-.04506 -.03909 (173*2π)/2561 weeks
174-.01204 -.06248 (174*2π)/2561 weeks
175.02768 -.02922 (175*2π)/2561 weeks
176.01181 -.03925 (176*2π)/2561 weeks
177-.00108 -.02289 (177*2π)/2561 weeks
178.06844 -.04223 (178*2π)/2561 weeks
179.01165 -.0399 (179*2π)/2561 weeks
180.02406 -.01457 (180*2π)/2561 weeks
181.03115 -.07275 (181*2π)/2561 weeks
182.06874 -.03167 (182*2π)/2561 weeks
183.03648 -.0128 (183*2π)/2561 weeks
184.13021 -.03201 (184*2π)/2561 weeks
185.05042 .0083 (185*2π)/2561 weeks
186.07514 -.02411 (186*2π)/2561 weeks
187.1191 -.0125 (187*2π)/2561 weeks
188.04503 .01391 (188*2π)/2561 weeks
189-.06084 .01404 (189*2π)/2561 weeks
190.07455 .02042 (190*2π)/2561 weeks
191-.03477 -.05068 (191*2π)/2561 weeks
192.07305 -.0525 (192*2π)/2561 weeks
193.03231 .04833 (193*2π)/2561 weeks
194.05463 .04076 (194*2π)/2561 weeks
195.06095 .054 (195*2π)/2561 weeks
196-.04037 .05133 (196*2π)/2561 weeks
197-.00876 -.04783 (197*2π)/2561 weeks
198-.05232 .04398 (198*2π)/2561 weeks
199.03507 .00992 (199*2π)/2561 weeks
200-.01142 .13184 (200*2π)/2561 weeks
201.0356 .03783 (201*2π)/2561 weeks
202-.03491 -.03253 (202*2π)/2561 weeks
203.02263 -.02398 (203*2π)/2561 weeks
204-.01873 -.02578 (204*2π)/2561 weeks
205.07973 -.01387 (205*2π)/2561 weeks
206.00855 -.00005 (206*2π)/2561 weeks
207.15454 -.01286 (207*2π)/2561 weeks
208.03751 -.06078 (208*2π)/2561 weeks
209.10402 .10367 (209*2π)/2561 weeks
210-.01609 .05465 (210*2π)/2561 weeks
211.05402 .01318 (211*2π)/2561 weeks
212-.15365 -.11404 (212*2π)/2561 weeks
213-.15117 .00917 (213*2π)/2561 weeks
214-.0057 .05569 (214*2π)/2561 weeks
215-.02616 -.03392 (215*2π)/2561 weeks
216-.00891 -.11054 (216*2π)/2561 weeks
217.02455 -.04487 (217*2π)/2561 weeks
218-.09431 .00709 (218*2π)/2561 weeks
219-.02335 .06976 (219*2π)/2561 weeks
220.01061 .06072 (220*2π)/2561 weeks
221-.16433 -.09731 (221*2π)/2561 weeks
222.12375 -.10623 (222*2π)/2561 weeks
223.08524 .06648 (223*2π)/2561 weeks
224-.02985 .01127 (224*2π)/2561 weeks
225.1084 -.08034 (225*2π)/2561 weeks
226.00337 .12076 (226*2π)/2561 weeks
227-.00849 .0319 (227*2π)/2561 weeks
228.07316 -.12952 (228*2π)/2561 weeks
229.16661 -.05975 (229*2π)/2561 weeks
230.22119 .04699 (230*2π)/2561 weeks
231.10795 -.03579 (231*2π)/2561 weeks
232-.04995 -.19144 (232*2π)/2561 weeks
233.07668 -.1162 (233*2π)/2561 weeks
234-.11765 .10573 (234*2π)/2561 weeks
235-.24089 -.13077 (235*2π)/2561 weeks
236.04493 -.03475 (236*2π)/2561 weeks
237.18864 -.08588 (237*2π)/2561 weeks
238.04828 -.08985 (238*2π)/2561 weeks
239.09507 .00708 (239*2π)/2561 weeks
240-.18866 -.23108 (240*2π)/2561 weeks
241.11814 .55195 (241*2π)/2561 weeks
242-.15808 -.00364 (242*2π)/2561 weeks
243-.25856 .05613 (243*2π)/2561 weeks
244-.08011 -.36682 (244*2π)/2561 weeks
245.065 -.21686 (245*2π)/2561 weeks
246.45677 -.15171 (246*2π)/2561 weeks
247.22249 -.05606 (247*2π)/2561 weeks
248.54691 .29695 (248*2π)/2561 weeks
249.07615 -.19374 (249*2π)/2561 weeks
250.50678 1.02546 (250*2π)/2561 weeks
251.73996 .37491 (251*2π)/2561 weeks
252.24593 -.09391 (252*2π)/2561 weeks
253.94898 -.85491 (253*2π)/2561 weeks
2541.10333 .65575 (254*2π)/2561 weeks