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# Fourier Analysis of CSRIX (Cohen And Steers Insti Realty Shs In)

CSRIX (Cohen And Steers Insti Realty Shs In) appears to have interesting cyclic behaviour every 17 weeks (.311*sine), 12 weeks (.2773*sine), and 10 weeks (.2484*cosine).

CSRIX (Cohen And Steers Insti Realty Shs In) has an average price of 40.87 (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 1/2/2015 to 4/16/2018 for CSRIX (Cohen And Steers Insti Realty Shs In), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
040.86587   0
1-.94516 -2.84822 (1*2π)/173173 weeks
2.27176 -.9876 (2*2π)/17387 weeks
3-.7097 .44803 (3*2π)/17358 weeks
4.27802 -.09167 (4*2π)/17343 weeks
5-.37069 .84436 (5*2π)/17335 weeks
6.12658 -.04703 (6*2π)/17329 weeks
7-.0885 .15489 (7*2π)/17325 weeks
8.52829 .08948 (8*2π)/17322 weeks
9-.3197 .00068 (9*2π)/17319 weeks
10.12571 -.31104 (10*2π)/17317 weeks
11.15111 -.01834 (11*2π)/17316 weeks
12-.07693 -.0074 (12*2π)/17314 weeks
13.19564 .04997 (13*2π)/17313 weeks
14-.2408 .27735 (14*2π)/17312 weeks
15-.07173 -.0654 (15*2π)/17312 weeks
16.04892 -.17126 (16*2π)/17311 weeks
17.18326 .04433 (17*2π)/17310 weeks
18-.24838 .14198 (18*2π)/17310 weeks
19-.07945 .10556 (19*2π)/1739 weeks
20-.14826 -.00125 (20*2π)/1739 weeks
21-.1499 -.02089 (21*2π)/1738 weeks
22.06096 .13789 (22*2π)/1738 weeks
23-.03681 -.00069 (23*2π)/1738 weeks
24-.1506 -.08478 (24*2π)/1737 weeks
25.00298 -.02115 (25*2π)/1737 weeks
26.08457 -.07205 (26*2π)/1737 weeks
27-.01713 -.079 (27*2π)/1736 weeks
28.00741 .01102 (28*2π)/1736 weeks
29-.00356 .01937 (29*2π)/1736 weeks
30.00217 .08744 (30*2π)/1736 weeks
31.12072 -.01005 (31*2π)/1736 weeks
32-.04433 -.10011 (32*2π)/1735 weeks
33-.05725 -.02471 (33*2π)/1735 weeks
34-.06389 .04771 (34*2π)/1735 weeks
35-.18552 .14268 (35*2π)/1735 weeks
36-.06762 -.12405 (36*2π)/1735 weeks
37.07716 .02944 (37*2π)/1735 weeks
38-.08719 .11989 (38*2π)/1735 weeks
39-.14002 -.00408 (39*2π)/1734 weeks
40.02593 -.08401 (40*2π)/1734 weeks
41-.12998 -.05688 (41*2π)/1734 weeks
42.04338 -.06969 (42*2π)/1734 weeks
43-.03768 -.08224 (43*2π)/1734 weeks
44.08254 -.08065 (44*2π)/1734 weeks
45-.13569 .04342 (45*2π)/1734 weeks
46-.00512 -.08167 (46*2π)/1734 weeks
47-.086 .04453 (47*2π)/1734 weeks
48.01695 .11475 (48*2π)/1734 weeks
49-.00378 -.03437 (49*2π)/1734 weeks
50.03169 .09738 (50*2π)/1733 weeks
51.01986 -.04745 (51*2π)/1733 weeks
52.08258 .04348 (52*2π)/1733 weeks
53-.00055 .06124 (53*2π)/1733 weeks
54-.01303 .05708 (54*2π)/1733 weeks
55.03519 -.09435 (55*2π)/1733 weeks
56.02345 -.01744 (56*2π)/1733 weeks
57.0118 -.07314 (57*2π)/1733 weeks
58-.02777 -.0146 (58*2π)/1733 weeks
59-.02979 -.1152 (59*2π)/1733 weeks
60-.08391 -.00289 (60*2π)/1733 weeks
61-.04238 -.15516 (61*2π)/1733 weeks
62-.07282 .06567 (62*2π)/1733 weeks
63.02042 -.08857 (63*2π)/1733 weeks
64.03511 -.04093 (64*2π)/1733 weeks
65.00584 .00185 (65*2π)/1733 weeks
66.03306 -.05215 (66*2π)/1733 weeks
67-.05073 .04543 (67*2π)/1733 weeks
68-.05591 .05255 (68*2π)/1733 weeks
69-.04865 .02277 (69*2π)/1733 weeks
70-.08185 .02902 (70*2π)/1732 weeks
71-.02641 .04095 (71*2π)/1732 weeks
72-.01395 .0155 (72*2π)/1732 weeks
73-.06107 -.01834 (73*2π)/1732 weeks
74.00575 .00854 (74*2π)/1732 weeks
75-.01528 -.05708 (75*2π)/1732 weeks
76-.02137 -.02277 (76*2π)/1732 weeks
77-.01543 .00912 (77*2π)/1732 weeks
78-.05631 .0211 (78*2π)/1732 weeks
79-.0077 -.00591 (79*2π)/1732 weeks
80.01894 .07433 (80*2π)/1732 weeks
81.0066 .02631 (81*2π)/1732 weeks
82.05875 -.0273 (82*2π)/1732 weeks
83-.03854 .05338 (83*2π)/1732 weeks
84-.02552 -.01541 (84*2π)/1732 weeks
85-.01981 -.03912 (85*2π)/1732 weeks
86-.00609 .00641 (86*2π)/1732 weeks
87-.00609 -.00641 (87*2π)/1732 weeks
88-.01981 .03912 (88*2π)/1732 weeks
89-.02552 .01541 (89*2π)/1732 weeks
90-.03854 -.05338 (90*2π)/1732 weeks
91.05875 .0273 (91*2π)/1732 weeks
92.0066 -.02631 (92*2π)/1732 weeks
93.01894 -.07433 (93*2π)/1732 weeks
94-.0077 .00591 (94*2π)/1732 weeks
95-.05631 -.0211 (95*2π)/1732 weeks
96-.01543 -.00912 (96*2π)/1732 weeks
97-.02137 .02277 (97*2π)/1732 weeks
98-.01528 .05708 (98*2π)/1732 weeks
99.00575 -.00854 (99*2π)/1732 weeks
100-.06107 .01834 (100*2π)/1732 weeks
101-.01395 -.0155 (101*2π)/1732 weeks
102-.02641 -.04095 (102*2π)/1732 weeks
103-.08185 -.02902 (103*2π)/1732 weeks
104-.04865 -.02277 (104*2π)/1732 weeks
105-.05591 -.05255 (105*2π)/1732 weeks
106-.05073 -.04543 (106*2π)/1732 weeks
107.03306 .05215 (107*2π)/1732 weeks
108.00584 -.00185 (108*2π)/1732 weeks
109.03511 .04093 (109*2π)/1732 weeks
110.02042 .08857 (110*2π)/1732 weeks
111-.07282 -.06567 (111*2π)/1732 weeks
112-.04238 .15516 (112*2π)/1732 weeks
113-.08391 .00289 (113*2π)/1732 weeks
114-.02979 .1152 (114*2π)/1732 weeks
115-.02777 .0146 (115*2π)/1732 weeks
116.0118 .07314 (116*2π)/1731 weeks
117.02345 .01744 (117*2π)/1731 weeks
118.03519 .09435 (118*2π)/1731 weeks
119-.01303 -.05708 (119*2π)/1731 weeks
120-.00055 -.06124 (120*2π)/1731 weeks
121.08258 -.04348 (121*2π)/1731 weeks
122.01986 .04745 (122*2π)/1731 weeks
123.03169 -.09738 (123*2π)/1731 weeks
124-.00378 .03437 (124*2π)/1731 weeks
125.01695 -.11475 (125*2π)/1731 weeks
126-.086 -.04453 (126*2π)/1731 weeks
127-.00512 .08167 (127*2π)/1731 weeks
128-.13569 -.04342 (128*2π)/1731 weeks
129.08254 .08065 (129*2π)/1731 weeks
130-.03768 .08224 (130*2π)/1731 weeks
131.04338 .06969 (131*2π)/1731 weeks
132-.12998 .05688 (132*2π)/1731 weeks
133.02593 .08401 (133*2π)/1731 weeks
134-.14002 .00408 (134*2π)/1731 weeks
135-.08719 -.11989 (135*2π)/1731 weeks
136.07716 -.02944 (136*2π)/1731 weeks
137-.06762 .12405 (137*2π)/1731 weeks
138-.18552 -.14268 (138*2π)/1731 weeks
139-.06389 -.04771 (139*2π)/1731 weeks
140-.05725 .02471 (140*2π)/1731 weeks
141-.04433 .10011 (141*2π)/1731 weeks
142.12072 .01005 (142*2π)/1731 weeks
143.00217 -.08744 (143*2π)/1731 weeks
144-.00356 -.01937 (144*2π)/1731 weeks
145.00741 -.01102 (145*2π)/1731 weeks
146-.01713 .079 (146*2π)/1731 weeks
147.08457 .07205 (147*2π)/1731 weeks
148.00298 .02115 (148*2π)/1731 weeks
149-.1506 .08478 (149*2π)/1731 weeks
150-.03681 .00069 (150*2π)/1731 weeks
151.06096 -.13789 (151*2π)/1731 weeks
152-.1499 .02089 (152*2π)/1731 weeks
153-.14826 .00125 (153*2π)/1731 weeks
154-.07945 -.10556 (154*2π)/1731 weeks
155-.24838 -.14198 (155*2π)/1731 weeks
156.18326 -.04433 (156*2π)/1731 weeks
157.04892 .17126 (157*2π)/1731 weeks
158-.07173 .0654 (158*2π)/1731 weeks
159-.2408 -.27735 (159*2π)/1731 weeks
160.19564 -.04997 (160*2π)/1731 weeks
161-.07693 .0074 (161*2π)/1731 weeks
162.15111 .01834 (162*2π)/1731 weeks
163.12571 .31104 (163*2π)/1731 weeks
164-.3197 -.00068 (164*2π)/1731 weeks
165.52829 -.08948 (165*2π)/1731 weeks
166-.0885 -.15489 (166*2π)/1731 weeks
167.12658 .04703 (167*2π)/1731 weeks
168-.37069 -.84436 (168*2π)/1731 weeks
169.27802 .09167 (169*2π)/1731 weeks
170-.7097 -.44803 (170*2π)/1731 weeks
171.27176 .9876 (171*2π)/1731 weeks