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# Fourier Analysis of APAT (AMERICAN PATRIOT CP)

APAT (AMERICAN PATRIOT CP) appears to have interesting cyclic behaviour every 13 weeks (2.1738*sine), 14 weeks (1.9953*sine), and 21 weeks (1.4616*cosine).

APAT (AMERICAN PATRIOT CP) has an average price of 7.18 (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 9/5/2007 to 2/17/2014 for APAT (AMERICAN PATRIOT CP), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
07.18287   0
112.90938 4.68621 (1*2π)/206206 weeks
29.91176 7.5143 (2*2π)/206103 weeks
36.90343 8.82118 (3*2π)/20669 weeks
43.97628 9.34869 (4*2π)/20652 weeks
51.01656 8.88085 (5*2π)/20641 weeks
6-1.32163 7.30527 (6*2π)/20634 weeks
7-2.60913 5.24295 (7*2π)/20629 weeks
8-2.97154 3.1871 (8*2π)/20626 weeks
9-2.52472 1.39827 (9*2π)/20623 weeks
10-1.46156 .25783 (10*2π)/20621 weeks
11-.31361 -.08233 (11*2π)/20619 weeks
12.58104 .10251 (12*2π)/20617 weeks
131.15647 .62789 (13*2π)/20616 weeks
141.27895 1.36685 (14*2π)/20615 weeks
15.85041 1.99529 (15*2π)/20614 weeks
16.11889 2.17377 (16*2π)/20613 weeks
17-.55973 1.91108 (17*2π)/20612 weeks
18-1.01495 1.34756 (18*2π)/20611 weeks
19-1.12858 .63094 (19*2π)/20611 weeks
20-.87513 .00631 (20*2π)/20610 weeks
21-.42991 -.36474 (21*2π)/20610 weeks
22.06466 -.49611 (22*2π)/2069 weeks
23.51914 -.3817 (23*2π)/2069 weeks
24.79239 -.06715 (24*2π)/2069 weeks
25.81035 .28331 (25*2π)/2068 weeks
26.64883 .52987 (26*2π)/2068 weeks
27.39488 .65091 (27*2π)/2068 weeks
28.0704 .62205 (28*2π)/2067 weeks
29-.23406 .36027 (29*2π)/2067 weeks
30-.31702 -.08034 (30*2π)/2067 weeks
31-.1298 -.48474 (31*2π)/2067 weeks
32.21255 -.72903 (32*2π)/2066 weeks
33.6222 -.78747 (33*2π)/2066 weeks
341.0008 -.61878 (34*2π)/2066 weeks
351.18449 -.29674 (35*2π)/2066 weeks
361.16086 -.0064 (36*2π)/2066 weeks
371.04352 .18352 (37*2π)/2066 weeks
38.87331 .30506 (38*2π)/2065 weeks
39.64226 .30722 (39*2π)/2065 weeks
40.47385 .14415 (40*2π)/2065 weeks
41.45545 -.06067 (41*2π)/2065 weeks
42.5115 -.22609 (42*2π)/2065 weeks
43.63869 -.39921 (43*2π)/2065 weeks
44.91018 -.49014 (44*2π)/2065 weeks
451.18879 -.36708 (45*2π)/2065 weeks
461.30666 -.13514 (46*2π)/2064 weeks
471.30929 .06702 (47*2π)/2064 weeks
481.24628 .25505 (48*2π)/2064 weeks
491.07472 .38343 (49*2π)/2064 weeks
50.88065 .35713 (50*2π)/2064 weeks
51.78788 .24598 (51*2π)/2064 weeks
52.75887 .14901 (52*2π)/2064 weeks
53.75816 .02616 (53*2π)/2064 weeks
54.85619 -.10814 (54*2π)/2064 weeks
551.03705 -.14999 (55*2π)/2064 weeks
561.20327 -.08421 (56*2π)/2064 weeks
571.3287 .03798 (57*2π)/2064 weeks
581.40087 .22321 (58*2π)/2064 weeks
591.35615 .43096 (59*2π)/2063 weeks
601.21139 .56117 (60*2π)/2063 weeks
611.06064 .58204 (61*2π)/2063 weeks
62.96167 .5399 (62*2π)/2063 weeks
63.92065 .4791 (63*2π)/2063 weeks
64.92234 .43215 (64*2π)/2063 weeks
65.95276 .40328 (65*2π)/2063 weeks
661.01438 .41138 (66*2π)/2063 weeks
671.06579 .48065 (67*2π)/2063 weeks
681.06357 .57307 (68*2π)/2063 weeks
691.03886 .65498 (69*2π)/2063 weeks
70.99131 .76278 (70*2π)/2063 weeks
71.85655 .86059 (71*2π)/2063 weeks
72.67694 .84905 (72*2π)/2063 weeks
73.56281 .75439 (73*2π)/2063 weeks
74.5061 .65344 (74*2π)/2063 weeks
75.49881 .52854 (75*2π)/2063 weeks
76.59464 .42983 (76*2π)/2063 weeks
77.72031 .45798 (77*2π)/2063 weeks
78.75685 .55036 (78*2π)/2063 weeks
79.75814 .61081 (79*2π)/2063 weeks
80.76985 .70137 (80*2π)/2063 weeks
81.70147 .828 (81*2π)/2063 weeks
82.56482 .87768 (82*2π)/2063 weeks
83.4718 .87539 (83*2π)/2062 weeks
84.37163 .9009 (84*2π)/2062 weeks
85.22171 .86691 (85*2π)/2062 weeks
86.13036 .75384 (86*2π)/2062 weeks
87.11143 .66548 (87*2π)/2062 weeks
88.09632 .60408 (88*2π)/2062 weeks
89.10772 .54206 (89*2π)/2062 weeks
90.14053 .53565 (90*2π)/2062 weeks
91.11447 .5717 (91*2π)/2062 weeks
92.04299 .5636 (92*2π)/2062 weeks
93-.00039 .52868 (93*2π)/2062 weeks
94-.05074 .51494 (94*2π)/2062 weeks
95-.13445 .46921 (95*2π)/2062 weeks
96-.18976 .37897 (96*2π)/2062 weeks
97-.2107 .29583 (97*2π)/2062 weeks
98-.22627 .21087 (98*2π)/2062 weeks
99-.21421 .11803 (99*2π)/2062 weeks
100-.17671 .04781 (100*2π)/2062 weeks
101-.13244 .0021 (101*2π)/2062 weeks
102-.08389 -.01745 (102*2π)/2062 weeks
103-.05752   (103*2π)/2062 weeks
104-.08389 .01745 (104*2π)/2062 weeks
105-.13244 -.0021 (105*2π)/2062 weeks
106-.17671 -.04781 (106*2π)/2062 weeks
107-.21421 -.11803 (107*2π)/2062 weeks
108-.22627 -.21087 (108*2π)/2062 weeks
109-.2107 -.29583 (109*2π)/2062 weeks
110-.18976 -.37897 (110*2π)/2062 weeks
111-.13445 -.46921 (111*2π)/2062 weeks
112-.05074 -.51494 (112*2π)/2062 weeks
113-.00039 -.52868 (113*2π)/2062 weeks
114.04299 -.5636 (114*2π)/2062 weeks
115.11447 -.5717 (115*2π)/2062 weeks
116.14053 -.53565 (116*2π)/2062 weeks
117.10772 -.54206 (117*2π)/2062 weeks
118.09632 -.60408 (118*2π)/2062 weeks
119.11143 -.66548 (119*2π)/2062 weeks
120.13036 -.75384 (120*2π)/2062 weeks
121.22171 -.86691 (121*2π)/2062 weeks
122.37163 -.9009 (122*2π)/2062 weeks
123.4718 -.87539 (123*2π)/2062 weeks
124.56482 -.87768 (124*2π)/2062 weeks
125.70147 -.828 (125*2π)/2062 weeks
126.76985 -.70137 (126*2π)/2062 weeks
127.75814 -.61081 (127*2π)/2062 weeks
128.75685 -.55036 (128*2π)/2062 weeks
129.72031 -.45798 (129*2π)/2062 weeks
130.59464 -.42983 (130*2π)/2062 weeks
131.49881 -.52854 (131*2π)/2062 weeks
132.5061 -.65344 (132*2π)/2062 weeks
133.56281 -.75439 (133*2π)/2062 weeks
134.67694 -.84905 (134*2π)/2062 weeks
135.85655 -.86059 (135*2π)/2062 weeks
136.99131 -.76278 (136*2π)/2062 weeks
1371.03886 -.65498 (137*2π)/2062 weeks
1381.06357 -.57307 (138*2π)/2061 weeks
1391.06579 -.48065 (139*2π)/2061 weeks
1401.01438 -.41138 (140*2π)/2061 weeks
141.95276 -.40328 (141*2π)/2061 weeks
142.92234 -.43215 (142*2π)/2061 weeks
143.92065 -.4791 (143*2π)/2061 weeks
144.96167 -.5399 (144*2π)/2061 weeks
1451.06064 -.58204 (145*2π)/2061 weeks
1461.21139 -.56117 (146*2π)/2061 weeks
1471.35615 -.43096 (147*2π)/2061 weeks
1481.40087 -.22321 (148*2π)/2061 weeks
1491.3287 -.03798 (149*2π)/2061 weeks
1501.20327 .08421 (150*2π)/2061 weeks
1511.03705 .14999 (151*2π)/2061 weeks
152.85619 .10814 (152*2π)/2061 weeks
153.75816 -.02616 (153*2π)/2061 weeks
154.75887 -.14901 (154*2π)/2061 weeks
155.78788 -.24598 (155*2π)/2061 weeks
156.88065 -.35713 (156*2π)/2061 weeks
1571.07472 -.38343 (157*2π)/2061 weeks
1581.24628 -.25505 (158*2π)/2061 weeks
1591.30929 -.06702 (159*2π)/2061 weeks
1601.30666 .13514 (160*2π)/2061 weeks
1611.18879 .36708 (161*2π)/2061 weeks
162.91018 .49014 (162*2π)/2061 weeks
163.63869 .39921 (163*2π)/2061 weeks
164.5115 .22609 (164*2π)/2061 weeks
165.45545 .06067 (165*2π)/2061 weeks
166.47385 -.14415 (166*2π)/2061 weeks
167.64226 -.30722 (167*2π)/2061 weeks
168.87331 -.30506 (168*2π)/2061 weeks
1691.04352 -.18352 (169*2π)/2061 weeks
1701.16086 .0064 (170*2π)/2061 weeks
1711.18449 .29674 (171*2π)/2061 weeks
1721.0008 .61878 (172*2π)/2061 weeks
173.6222 .78747 (173*2π)/2061 weeks
174.21255 .72903 (174*2π)/2061 weeks
175-.1298 .48474 (175*2π)/2061 weeks
176-.31702 .08034 (176*2π)/2061 weeks
177-.23406 -.36027 (177*2π)/2061 weeks
178.0704 -.62205 (178*2π)/2061 weeks
179.39488 -.65091 (179*2π)/2061 weeks
180.64883 -.52987 (180*2π)/2061 weeks
181.81035 -.28331 (181*2π)/2061 weeks
182.79239 .06715 (182*2π)/2061 weeks
183.51914 .3817 (183*2π)/2061 weeks
184.06466 .49611 (184*2π)/2061 weeks
185-.42991 .36474 (185*2π)/2061 weeks
186-.87513 -.00631 (186*2π)/2061 weeks
187-1.12858 -.63094 (187*2π)/2061 weeks
188-1.01495 -1.34756 (188*2π)/2061 weeks
189-.55973 -1.91108 (189*2π)/2061 weeks
190.11889 -2.17377 (190*2π)/2061 weeks
191.85041 -1.99529 (191*2π)/2061 weeks
1921.27895 -1.36685 (192*2π)/2061 weeks
1931.15647 -.62789 (193*2π)/2061 weeks
194.58104 -.10251 (194*2π)/2061 weeks
195-.31361 .08233 (195*2π)/2061 weeks
196-1.46156 -.25783 (196*2π)/2061 weeks
197-2.52472 -1.39827 (197*2π)/2061 weeks
198-2.97154 -3.1871 (198*2π)/2061 weeks
199-2.60913 -5.24295 (199*2π)/2061 weeks
200-1.32163 -7.30527 (200*2π)/2061 weeks
2011.01656 -8.88085 (201*2π)/2061 weeks
2023.97628 -9.34869 (202*2π)/2061 weeks
2036.90343 -8.82118 (203*2π)/2061 weeks
2049.91176 -7.5143 (204*2π)/2061 weeks