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Fourier Analysis of PAFSX (Parnassus Asia Fund - Investor )


PAFSX (Parnassus Asia Fund - Investor ) appears to have interesting cyclic behaviour every 20 weeks (.1937*cosine), 17 weeks (.1639*sine), and 20 weeks (.0918*sine).

PAFSX (Parnassus Asia Fund - Investor ) has an average price of 15.91 (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 4/30/2013 to 3/13/2017 for PAFSX (Parnassus Asia Fund - Investor ), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
015.9078   0 
1-.25403 .6627 (1*2π)/203203 weeks
2.68228 -1.00977 (2*2π)/203102 weeks
3-.27229 -.68996 (3*2π)/20368 weeks
4.14018 -.05518 (4*2π)/20351 weeks
5-.27464 -.12471 (5*2π)/20341 weeks
6.22054 -.1247 (6*2π)/20334 weeks
7-.01083 -.25278 (7*2π)/20329 weeks
8.107 .04122 (8*2π)/20325 weeks
9.1639 -.30383 (9*2π)/20323 weeks
10-.19373 -.09176 (10*2π)/20320 weeks
11-.07668 .04157 (11*2π)/20318 weeks
12.06111 -.16386 (12*2π)/20317 weeks
13-.06763 -.09278 (13*2π)/20316 weeks
14-.02141 -.07035 (14*2π)/20315 weeks
15-.02673 -.04961 (15*2π)/20314 weeks
16-.01824 -.0489 (16*2π)/20313 weeks
17-.00896 -.1552 (17*2π)/20312 weeks
18-.00848 .05947 (18*2π)/20311 weeks
19.01508 -.08701 (19*2π)/20311 weeks
20-.01959 -.07106 (20*2π)/20310 weeks
21-.04519 -.00346 (21*2π)/20310 weeks
22-.01407 -.033 (22*2π)/2039 weeks
23-.02606 -.03408 (23*2π)/2039 weeks
24-.02389 .02531 (24*2π)/2038 weeks
25.01983 -.05954 (25*2π)/2038 weeks
26.01116 -.05953 (26*2π)/2038 weeks
27-.04742 -.06534 (27*2π)/2038 weeks
28-.0008 -.03232 (28*2π)/2037 weeks
29-.0056 -.01994 (29*2π)/2037 weeks
30-.01069 -.01832 (30*2π)/2037 weeks
31-.05057 -.04084 (31*2π)/2037 weeks
32-.02684 -.03197 (32*2π)/2036 weeks
33.01636 .00563 (33*2π)/2036 weeks
34.00962 -.01319 (34*2π)/2036 weeks
35-.03319 -.04721 (35*2π)/2036 weeks
36-.02713 -.03333 (36*2π)/2036 weeks
37-.04758 .03688 (37*2π)/2035 weeks
38.03886 -.02423 (38*2π)/2035 weeks
39-.00494 -.07628 (39*2π)/2035 weeks
40-.01681 .01493 (40*2π)/2035 weeks
41.02138 -.05161 (41*2π)/2035 weeks
42-.01384 -.03659 (42*2π)/2035 weeks
43-.00787 .00246 (43*2π)/2035 weeks
44.00887 -.0233 (44*2π)/2035 weeks
45-.02777 -.01913 (45*2π)/2035 weeks
46-.05641 .00492 (46*2π)/2034 weeks
47.00569 -.02992 (47*2π)/2034 weeks
48-.0173 -.03133 (48*2π)/2034 weeks
49-.03626 -.03865 (49*2π)/2034 weeks
50-.00411 .02083 (50*2π)/2034 weeks
51-.00343 -.03702 (51*2π)/2034 weeks
52-.02992 -.02878 (52*2π)/2034 weeks
53-.01644 .00871 (53*2π)/2034 weeks
54-.00448 -.03836 (54*2π)/2034 weeks
55-.00785 .00283 (55*2π)/2034 weeks
56-.00382 .01621 (56*2π)/2034 weeks
57.00318 -.00882 (57*2π)/2034 weeks
58-.02866 -.0397 (58*2π)/2034 weeks
59-.00559 -.02549 (59*2π)/2033 weeks
60-.0016 -.02968 (60*2π)/2033 weeks
61-.01643 -.00333 (61*2π)/2033 weeks
62-.03712 -.01361 (62*2π)/2033 weeks
63-.02777 -.01662 (63*2π)/2033 weeks
64.00411 -.01234 (64*2π)/2033 weeks
65-.01405 -.03055 (65*2π)/2033 weeks
66-.01731 -.00702 (66*2π)/2033 weeks
67-.01106 -.00033 (67*2π)/2033 weeks
68-.02931 -.02402 (68*2π)/2033 weeks
69-.01929 .01097 (69*2π)/2033 weeks
70-.00679 -.03265 (70*2π)/2033 weeks
71-.02338 .01119 (71*2π)/2033 weeks
72.0051 -.03162 (72*2π)/2033 weeks
73-.03611 -.00225 (73*2π)/2033 weeks
74-.01786 .00535 (74*2π)/2033 weeks
75-.01218 -.01592 (75*2π)/2033 weeks
76-.0261 -.0121 (76*2π)/2033 weeks
77-.01941 -.0013 (77*2π)/2033 weeks
78-.0204 -.01491 (78*2π)/2033 weeks
79.01141 .01601 (79*2π)/2033 weeks
80-.02839 -.02692 (80*2π)/2033 weeks
81-.01658 .00176 (81*2π)/2033 weeks
82-.01387 -.00459 (82*2π)/2032 weeks
83-.02503 -.00745 (83*2π)/2032 weeks
84-.00798 .00749 (84*2π)/2032 weeks
85-.00357 -.01856 (85*2π)/2032 weeks
86-.02828 -.00839 (86*2π)/2032 weeks
87-.02493 -.0062 (87*2π)/2032 weeks
88-.03164 -.01684 (88*2π)/2032 weeks
89-.01977 .01558 (89*2π)/2032 weeks
90-.01868 -.00477 (90*2π)/2032 weeks
91-.03385 .0225 (91*2π)/2032 weeks
92-.00411 -.00518 (92*2π)/2032 weeks
93.00841 -.01985 (93*2π)/2032 weeks
94-.01283 .01228 (94*2π)/2032 weeks
95-.0255 .00904 (95*2π)/2032 weeks
96-.00363 .00012 (96*2π)/2032 weeks
97-.00865 -.02661 (97*2π)/2032 weeks
98-.03554 .00357 (98*2π)/2032 weeks
99.00855 .00088 (99*2π)/2032 weeks
100-.04697 -.01819 (100*2π)/2032 weeks
101-.00411 .00938 (101*2π)/2032 weeks
102-.00411 -.00938 (102*2π)/2032 weeks
103-.04697 .01819 (103*2π)/2032 weeks
104.00855 -.00088 (104*2π)/2032 weeks
105-.03554 -.00357 (105*2π)/2032 weeks
106-.00865 .02661 (106*2π)/2032 weeks
107-.00363 -.00012 (107*2π)/2032 weeks
108-.0255 -.00904 (108*2π)/2032 weeks
109-.01283 -.01228 (109*2π)/2032 weeks
110.00841 .01985 (110*2π)/2032 weeks
111-.00411 .00518 (111*2π)/2032 weeks
112-.03385 -.0225 (112*2π)/2032 weeks
113-.01868 .00477 (113*2π)/2032 weeks
114-.01977 -.01558 (114*2π)/2032 weeks
115-.03164 .01684 (115*2π)/2032 weeks
116-.02493 .0062 (116*2π)/2032 weeks
117-.02828 .00839 (117*2π)/2032 weeks
118-.00357 .01856 (118*2π)/2032 weeks
119-.00798 -.00749 (119*2π)/2032 weeks
120-.02503 .00745 (120*2π)/2032 weeks
121-.01387 .00459 (121*2π)/2032 weeks
122-.01658 -.00176 (122*2π)/2032 weeks
123-.02839 .02692 (123*2π)/2032 weeks
124.01141 -.01601 (124*2π)/2032 weeks
125-.0204 .01491 (125*2π)/2032 weeks
126-.01941 .0013 (126*2π)/2032 weeks
127-.0261 .0121 (127*2π)/2032 weeks
128-.01218 .01592 (128*2π)/2032 weeks
129-.01786 -.00535 (129*2π)/2032 weeks
130-.03611 .00225 (130*2π)/2032 weeks
131.0051 .03162 (131*2π)/2032 weeks
132-.02338 -.01119 (132*2π)/2032 weeks
133-.00679 .03265 (133*2π)/2032 weeks
134-.01929 -.01097 (134*2π)/2032 weeks
135-.02931 .02402 (135*2π)/2032 weeks
136-.01106 .00033 (136*2π)/2031 weeks
137-.01731 .00702 (137*2π)/2031 weeks
138-.01405 .03055 (138*2π)/2031 weeks
139.00411 .01234 (139*2π)/2031 weeks
140-.02777 .01662 (140*2π)/2031 weeks
141-.03712 .01361 (141*2π)/2031 weeks
142-.01643 .00333 (142*2π)/2031 weeks
143-.0016 .02968 (143*2π)/2031 weeks
144-.00559 .02549 (144*2π)/2031 weeks
145-.02866 .0397 (145*2π)/2031 weeks
146.00318 .00882 (146*2π)/2031 weeks
147-.00382 -.01621 (147*2π)/2031 weeks
148-.00785 -.00283 (148*2π)/2031 weeks
149-.00448 .03836 (149*2π)/2031 weeks
150-.01644 -.00871 (150*2π)/2031 weeks
151-.02992 .02878 (151*2π)/2031 weeks
152-.00343 .03702 (152*2π)/2031 weeks
153-.00411 -.02083 (153*2π)/2031 weeks
154-.03626 .03865 (154*2π)/2031 weeks
155-.0173 .03133 (155*2π)/2031 weeks
156.00569 .02992 (156*2π)/2031 weeks
157-.05641 -.00492 (157*2π)/2031 weeks
158-.02777 .01913 (158*2π)/2031 weeks
159.00887 .0233 (159*2π)/2031 weeks
160-.00787 -.00246 (160*2π)/2031 weeks
161-.01384 .03659 (161*2π)/2031 weeks
162.02138 .05161 (162*2π)/2031 weeks
163-.01681 -.01493 (163*2π)/2031 weeks
164-.00494 .07628 (164*2π)/2031 weeks
165.03886 .02423 (165*2π)/2031 weeks
166-.04758 -.03688 (166*2π)/2031 weeks
167-.02713 .03333 (167*2π)/2031 weeks
168-.03319 .04721 (168*2π)/2031 weeks
169.00962 .01319 (169*2π)/2031 weeks
170.01636 -.00563 (170*2π)/2031 weeks
171-.02684 .03197 (171*2π)/2031 weeks
172-.05057 .04084 (172*2π)/2031 weeks
173-.01069 .01832 (173*2π)/2031 weeks
174-.0056 .01994 (174*2π)/2031 weeks
175-.0008 .03232 (175*2π)/2031 weeks
176-.04742 .06534 (176*2π)/2031 weeks
177.01116 .05953 (177*2π)/2031 weeks
178.01983 .05954 (178*2π)/2031 weeks
179-.02389 -.02531 (179*2π)/2031 weeks
180-.02606 .03408 (180*2π)/2031 weeks
181-.01407 .033 (181*2π)/2031 weeks
182-.04519 .00346 (182*2π)/2031 weeks
183-.01959 .07106 (183*2π)/2031 weeks
184.01508 .08701 (184*2π)/2031 weeks
185-.00848 -.05947 (185*2π)/2031 weeks
186-.00896 .1552 (186*2π)/2031 weeks
187-.01824 .0489 (187*2π)/2031 weeks
188-.02673 .04961 (188*2π)/2031 weeks
189-.02141 .07035 (189*2π)/2031 weeks
190-.06763 .09278 (190*2π)/2031 weeks
191.06111 .16386 (191*2π)/2031 weeks
192-.07668 -.04157 (192*2π)/2031 weeks
193-.19373 .09176 (193*2π)/2031 weeks
194.1639 .30383 (194*2π)/2031 weeks
195.107 -.04122 (195*2π)/2031 weeks
196-.01083 .25278 (196*2π)/2031 weeks
197.22054 .1247 (197*2π)/2031 weeks
198-.27464 .12471 (198*2π)/2031 weeks
199.14018 .05518 (199*2π)/2031 weeks
200-.27229 .68996 (200*2π)/2031 weeks
201.68228 1.00977 (201*2π)/2031 weeks

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