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Fourier Analysis of PNTR (Pointer Telocation Ltd.)


PNTR (Pointer Telocation Ltd.) appears to have interesting cyclic behaviour every 99 weeks (87.967*cosine), 91 weeks (84.1302*sine), and 119 weeks (61.9753*cosine).

PNTR (Pointer Telocation Ltd.) has an average price of 373.12 (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 6/17/1994 to 3/20/2017 for PNTR (Pointer Telocation Ltd.), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0373.1174   0 
1409.8598 484.7574 (1*2π)/11881,188 weeks
2-40.55057 397.2417 (2*2π)/1188594 weeks
3-99.86847 119.7911 (3*2π)/1188396 weeks
49.95844 57.57202 (4*2π)/1188297 weeks
518.16278 93.85975 (5*2π)/1188238 weeks
6-6.03692 78.51321 (6*2π)/1188198 weeks
75.57274 67.21394 (7*2π)/1188170 weeks
8-9.86429 83.56164 (8*2π)/1188149 weeks
9-58.83857 62.62131 (9*2π)/1188132 weeks
10-61.97532 -19.56667 (10*2π)/1188119 weeks
1130.1978 -56.37715 (11*2π)/1188108 weeks
1287.96701 25.23964 (12*2π)/118899 weeks
1326.11322 84.13022 (13*2π)/118891 weeks
14-18.77685 40.52602 (14*2π)/118885 weeks
1513.02897 13.21115 (15*2π)/118879 weeks
1631.69987 43.75562 (16*2π)/118874 weeks
17-.12888 64.95535 (17*2π)/118870 weeks
18-26.76148 41.48462 (18*2π)/118866 weeks
19-16.7422 17.15726 (19*2π)/118863 weeks
20-3.3116 18.73772 (20*2π)/118859 weeks
21-5.47021 21.8567 (21*2π)/118857 weeks
22-3.17915 13.7408 (22*2π)/118854 weeks
2311.52617 20.94841 (23*2π)/118852 weeks
24-.98345 44.76928 (24*2π)/118850 weeks
25-35.73581 33.04593 (25*2π)/118848 weeks
26-35.09601 -9.83947 (26*2π)/118846 weeks
279.75895 -25.28875 (27*2π)/118844 weeks
2838.42713 15.39117 (28*2π)/118842 weeks
295.46366 51.87141 (29*2π)/118841 weeks
30-33.32462 28.04699 (30*2π)/118840 weeks
31-19.5414 -6.83129 (31*2π)/118838 weeks
328.46944 -.25931 (32*2π)/118837 weeks
332.74314 20.86456 (33*2π)/118836 weeks
34-12.91336 11.89779 (34*2π)/118835 weeks
351.1598 -.82996 (35*2π)/118834 weeks
3612.61593 19.53858 (36*2π)/118833 weeks
37-13.54945 32.902 (37*2π)/118832 weeks
38-32.22672 4.40256 (38*2π)/118831 weeks
39-5.61589 -20.0701 (39*2π)/118830 weeks
4021.88464 2.78133 (40*2π)/118830 weeks
413.59705 30.20759 (41*2π)/118829 weeks
42-21.56728 17.08803 (42*2π)/118828 weeks
43-13.63514 -4.03921 (43*2π)/118828 weeks
442.47516 2.20746 (44*2π)/118827 weeks
45-6.88314 16.16664 (45*2π)/118826 weeks
46-23.41677 2.67814 (46*2π)/118826 weeks
47-9.35742 -17.45378 (47*2π)/118825 weeks
4810.20935 -6.41992 (48*2π)/118825 weeks
49.55638 8.00816 (49*2π)/118824 weeks
50-8.80042 -4.73911 (50*2π)/118824 weeks
518.03217 -11.85244 (51*2π)/118823 weeks
5214.1064 5.42574 (52*2π)/118823 weeks
53.41729 9.59818 (53*2π)/118822 weeks
54-.49287 .13803 (54*2π)/118822 weeks
556.86936 1.78687 (55*2π)/118822 weeks
564.46698 8.96717 (56*2π)/118821 weeks
57-3.58574 6.70127 (57*2π)/118821 weeks
58-1.85079 -2.46096 (58*2π)/118820 weeks
598.37159 -2.45577 (59*2π)/118820 weeks
6011.80364 8.23381 (60*2π)/118820 weeks
612.84005 14.98774 (61*2π)/118819 weeks
62-3.81053 9.72502 (62*2π)/118819 weeks
63-1.00066 7.09522 (63*2π)/118819 weeks
64-3.60019 12.66923 (64*2π)/118819 weeks
65-15.56683 8.45528 (65*2π)/118818 weeks
66-15.91888 -7.83165 (66*2π)/118818 weeks
67-.87575 -13.97608 (67*2π)/118818 weeks
685.84052 -3.31466 (68*2π)/118817 weeks
69-3.51678 -1.66732 (69*2π)/118817 weeks
70-.4876 -15.03708 (70*2π)/118817 weeks
7117.70236 -12.97501 (71*2π)/118817 weeks
7220.5269 5.55689 (72*2π)/118817 weeks
735.77252 11.03531 (73*2π)/118816 weeks
742.22108 -1.08472 (74*2π)/118816 weeks
7516.23207 -1.10959 (75*2π)/118816 weeks
7615.30527 16.94197 (76*2π)/118816 weeks
77-5.63665 18.00663 (77*2π)/118815 weeks
78-8.94689 -3.68382 (78*2π)/118815 weeks
7912.16834 -8.20024 (79*2π)/118815 weeks
8017.41929 11.80687 (80*2π)/118815 weeks
81-.31643 16.78938 (81*2π)/118815 weeks
82-3.01007 2.41618 (82*2π)/118814 weeks
839.0765 2.99586 (83*2π)/118814 weeks
846.72888 15.36865 (84*2π)/118814 weeks
85-6.76913 14.21256 (85*2π)/118814 weeks
86-8.91133 1.97449 (86*2π)/118814 weeks
87-.77606 -2.47285 (87*2π)/118814 weeks
882.83239 .54094 (88*2π)/118814 weeks
893.26755 .19287 (89*2π)/118813 weeks
908.24715 .47674 (90*2π)/118813 weeks
9111.50992 7.84409 (91*2π)/118813 weeks
925.57369 15.10049 (92*2π)/118813 weeks
93-2.65978 13.22558 (93*2π)/118813 weeks
94-3.29569 8.00031 (94*2π)/118813 weeks
95-1.89824 9.5157 (95*2π)/118813 weeks
96-8.25507 10.2298 (96*2π)/118812 weeks
97-12.0708 .85323 (97*2π)/118812 weeks
98-3.45237 -6.88513 (98*2π)/118812 weeks
995.34399 -.07462 (99*2π)/118812 weeks
100-1.33728 7.03495 (100*2π)/118812 weeks
101-6.7637 -1.27742 (101*2π)/118812 weeks
1022.9292 -6.18634 (102*2π)/118812 weeks
1037.49766 3.43878 (103*2π)/118812 weeks
104-.79912 7.08689 (104*2π)/118811 weeks
105-4.19173 -.2741 (105*2π)/118811 weeks
1062.6207 -4.4417 (106*2π)/118811 weeks
1077.81177 .993 (107*2π)/118811 weeks
1084.88874 6.4009 (108*2π)/118811 weeks
1091.41553 5.67553 (109*2π)/118811 weeks
1101.49278 5.48708 (110*2π)/118811 weeks
111-.09199 7.21413 (111*2π)/118811 weeks
112-4.93065 6.00032 (112*2π)/118811 weeks
113-5.26029 -.43516 (113*2π)/118811 weeks
114.06285 -1.76325 (114*2π)/118810 weeks
115.74879 1.57794 (115*2π)/118810 weeks
116-1.48112 1.01034 (116*2π)/118810 weeks
117-.73766 -1.0509 (117*2π)/118810 weeks
1181.02184 -1.61928 (118*2π)/118810 weeks
1192.63322 -.85932 (119*2π)/118810 weeks
1202.7031 .12557 (120*2π)/118810 weeks
1212.35179 -.1597 (121*2π)/118810 weeks
1224.74629 -1.17456 (122*2π)/118810 weeks
1237.44676 3.6202 (123*2π)/118810 weeks
1241.515 8.07361 (124*2π)/118810 weeks
125-3.38289 1.82928 (125*2π)/118810 weeks
1262.93595 -2.27358 (126*2π)/11889 weeks
1275.86323 4.37771 (127*2π)/11889 weeks
128-2.0668 6.69496 (128*2π)/11889 weeks
129-4.85122 -3.39305 (129*2π)/11889 weeks
1307.5493 -7.54893 (130*2π)/11889 weeks
13114.04606 5.94842 (131*2π)/11889 weeks
1321.39716 14.64023 (132*2π)/11889 weeks
133-7.81361 4.27348 (133*2π)/11889 weeks
134.73486 -3.36643 (134*2π)/11889 weeks
1355.69294 5.77652 (135*2π)/11889 weeks
136-6.68949 8.32473 (136*2π)/11889 weeks
137-8.27355 -7.39864 (137*2π)/11889 weeks
1388.9359 -9.9107 (138*2π)/11889 weeks
13913.3139 6.46964 (139*2π)/11889 weeks
140-.83591 12.40735 (140*2π)/11888 weeks
141-7.46194 .7376 (141*2π)/11888 weeks
1422.26235 -5.79292 (142*2π)/11888 weeks
1438.39147 2.51353 (143*2π)/11888 weeks
1441.43724 8.25872 (144*2π)/11888 weeks
145-3.87934 2.87018 (145*2π)/11888 weeks
146.10031 -1.5619 (146*2π)/11888 weeks
1473.38116 1.83982 (147*2π)/11888 weeks
148-.48062 4.33418 (148*2π)/11888 weeks
149-3.10397 -.09566 (149*2π)/11888 weeks
1501.34901 -3.1459 (150*2π)/11888 weeks
1514.22524 .98659 (151*2π)/11888 weeks
152-.61812 3.19834 (152*2π)/11888 weeks
153-2.47923 -3.81767 (153*2π)/11888 weeks
1546.71434 -6.57052 (154*2π)/11888 weeks
15511.41012 3.17682 (155*2π)/11888 weeks
1562.78806 9.55749 (156*2π)/11888 weeks
157-3.85516 2.7076 (157*2π)/11888 weeks
1581.65147 -3.12772 (158*2π)/11888 weeks
1596.37887 2.09766 (159*2π)/11887 weeks
160.75843 5.81369 (160*2π)/11887 weeks
161-2.22951 -.33984 (161*2π)/11887 weeks
1624.41713 -2.99241 (162*2π)/11887 weeks
1636.90046 4.01089 (163*2π)/11887 weeks
164-.16088 6.19409 (164*2π)/11887 weeks
165-1.69497 -.54011 (165*2π)/11887 weeks
1664.68819 -1.25623 (166*2π)/11887 weeks
1674.77067 5.27345 (167*2π)/11887 weeks
168-2.63217 5.58202 (168*2π)/11887 weeks
169-4.65046 -3.09486 (169*2π)/11887 weeks
1704.28719 -7.89119 (170*2π)/11887 weeks
17111.64851 -.67281 (171*2π)/11887 weeks
1727.46641 7.22405 (172*2π)/11887 weeks
1731.76279 5.40333 (173*2π)/11887 weeks
1743.82188 3.28119 (174*2π)/11887 weeks
1753.44926 7.76048 (175*2π)/11887 weeks
176-4.05418 7.2757 (176*2π)/11887 weeks
177-5.13986 -2.04852 (177*2π)/11887 weeks
1784.10752 -4.8532 (178*2π)/11887 weeks
1798.14321 3.13183 (179*2π)/11887 weeks
1801.75516 7.82703 (180*2π)/11887 weeks
181-2.93408 2.81898 (181*2π)/11887 weeks
1821.13716 -1.36617 (182*2π)/11887 weeks
1834.57656 2.49926 (183*2π)/11886 weeks
184.25251 5.00788 (184*2π)/11886 weeks
185-1.55099 .27616 (185*2π)/11886 weeks
1863.48776 -1.25037 (186*2π)/11886 weeks
1875.10048 4.19388 (187*2π)/11886 weeks
188-.24993 5.90899 (188*2π)/11886 weeks
189-2.03095 1.30515 (189*2π)/11886 weeks
1901.46882 .23351 (190*2π)/11886 weeks
191.52716 2.83813 (191*2π)/11886 weeks
192-1.79752 -.36332 (192*2π)/11886 weeks
1932.73234 -3.04296 (193*2π)/11886 weeks
1945.74078 1.60599 (194*2π)/11886 weeks
1951.63964 4.43351 (195*2π)/11886 weeks
196-.81011 .58076 (196*2π)/11886 weeks
1972.99112 -1.9708 (197*2π)/11886 weeks
1986.02107 1.45847 (198*2π)/11886 weeks
1993.63803 4.79042 (199*2π)/11886 weeks
200.18685 3.57832 (200*2π)/11886 weeks
2011.05269 -.10127 (201*2π)/11886 weeks
2025.52288 .71937 (202*2π)/11886 weeks
2035.33657 6.36289 (203*2π)/11886 weeks
204-.94227 7.60701 (204*2π)/11886 weeks
205-3.49084 2.06047 (205*2π)/11886 weeks
206.39579 -.78538 (206*2π)/11886 weeks
2072.12149 1.79341 (207*2π)/11886 weeks
208.03607 1.59182 (208*2π)/11886 weeks
2091.74381 -.73343 (209*2π)/11886 weeks
2104.84045 1.46723 (210*2π)/11886 weeks
2112.96422 5.4906 (211*2π)/11886 weeks
212-1.54131 4.65089 (212*2π)/11886 weeks
213-2.03658 .27746 (213*2π)/11886 weeks
2141.46961 -1.17843 (214*2π)/11886 weeks
2153.09992 .85699 (215*2π)/11886 weeks
2162.12532 2.05617 (216*2π)/11886 weeks
2171.49382 .89192 (217*2π)/11885 weeks
2183.75204 .25885 (218*2π)/11885 weeks
2195.56267 3.18172 (219*2π)/11885 weeks
2203.1892 6.73161 (220*2π)/11885 weeks
221-1.06156 5.92343 (221*2π)/11885 weeks
222-1.6465 2.28203 (222*2π)/11885 weeks
2231.0668 1.51954 (223*2π)/11885 weeks
2241.10243 3.9029 (224*2π)/11885 weeks
225-1.23804 3.60967 (225*2π)/11885 weeks
226-1.22222 1.94527 (226*2π)/11885 weeks
227-1.00162 2.20926 (227*2π)/11885 weeks
228-2.5901 1.41056 (228*2π)/11885 weeks
229-2.12859 -1.8822 (229*2π)/11885 weeks
2302.02953 -2.35892 (230*2π)/11885 weeks
2312.62064 1.57336 (231*2π)/11885 weeks
232-1.08506 1.35187 (232*2π)/11885 weeks
233-.46905 -2.96332 (233*2π)/11885 weeks
2344.6775 -3.27533 (234*2π)/11885 weeks
2356.54333 1.70327 (235*2π)/11885 weeks
2363.21465 4.43849 (236*2π)/11885 weeks
237.88989 2.92468 (237*2π)/11885 weeks
2381.63136 2.02556 (238*2π)/11885 weeks
2391.33042 3.02903 (239*2π)/11885 weeks
240-.44331 2.17286 (240*2π)/11885 weeks
241.45265 -.17993 (241*2π)/11885 weeks
2423.12715 .6862 (242*2π)/11885 weeks
2432.25954 3.37236 (243*2π)/11885 weeks
244-.23152 2.74793 (244*2π)/11885 weeks
245.23683 .76013 (245*2π)/11885 weeks
2461.33827 1.3448 (246*2π)/11885 weeks
247.12732 1.7737 (247*2π)/11885 weeks
248-.45805 -.55776 (248*2π)/11885 weeks
2492.84524 -2.13264 (249*2π)/11885 weeks
2505.94813 1.03365 (250*2π)/11885 weeks
2513.98594 5.61881 (251*2π)/11885 weeks
252-1.20972 5.21759 (252*2π)/11885 weeks
253-1.88441 .33791 (253*2π)/11885 weeks
2542.20404 -.63041 (254*2π)/11885 weeks
2552.82967 2.97758 (255*2π)/11885 weeks
256-.77337 3.05217 (256*2π)/11885 weeks
257-.4066 -.97734 (257*2π)/11885 weeks
2584.30134 -.28256 (258*2π)/11885 weeks
2593.29269 4.98169 (259*2π)/11885 weeks
260-2.16201 3.91362 (260*2π)/11885 weeks
261-1.31444 -1.52583 (261*2π)/11885 weeks
2624.03543 -.85003 (262*2π)/11885 weeks
2633.47032 4.33299 (263*2π)/11885 weeks
264-1.6761 3.82638 (264*2π)/11885 weeks
265-1.17356 -1.4564 (265*2π)/11884 weeks
2664.20885 -.97919 (266*2π)/11884 weeks
2673.77128 4.43045 (267*2π)/11884 weeks
268-1.43153 3.79564 (268*2π)/11884 weeks
269-.14251 -.95696 (269*2π)/11884 weeks
2704.11753 1.12545 (270*2π)/11884 weeks
2711.44493 5.23126 (271*2π)/11884 weeks
272-2.77957 2.12271 (272*2π)/11884 weeks
273.69313 -2.31044 (273*2π)/11884 weeks
2745.26136 1.56973 (274*2π)/11884 weeks
2751.06555 6.09029 (275*2π)/11884 weeks
276-2.9796 1.75212 (276*2π)/11884 weeks
2771.39714 -1.51444 (277*2π)/11884 weeks
2784.1444 3.18302 (278*2π)/11884 weeks
279-.92404 5.87491 (279*2π)/11884 weeks
280-3.78438 .90339 (280*2π)/11884 weeks
281.56608 -1.80305 (281*2π)/11884 weeks
2822.907 2.04212 (282*2π)/11884 weeks
283-.89481 4.22079 (283*2π)/11884 weeks
284-3.69596 .6212 (284*2π)/11884 weeks
285-.91271 -3.33356 (285*2π)/11884 weeks
2863.60308 -1.77723 (286*2π)/11884 weeks
2873.12417 2.21159 (287*2π)/11884 weeks
288.17864 2.09274 (288*2π)/11884 weeks
289.68642 -.26533 (289*2π)/11884 weeks
2902.97661 1.02204 (290*2π)/11884 weeks
2911.19683 3.53075 (291*2π)/11884 weeks
292-1.43743 1.41508 (292*2π)/11884 weeks
293.76509 -.95268 (293*2π)/11884 weeks
2942.8756 1.03454 (294*2π)/11884 weeks
2951.00543 2.93917 (295*2π)/11884 weeks
296-.52264 .80068 (296*2π)/11884 weeks
2972.16335 -.37198 (297*2π)/11884 weeks
2983.71285 2.80101 (298*2π)/11884 weeks
299.73814 5.63067 (299*2π)/11884 weeks
300-3.20097 4.06033 (300*2π)/11884 weeks
301-3.70523 .18379 (301*2π)/11884 weeks
302-1.38469 -1.54658 (302*2π)/11884 weeks
303-.18341 -1.44585 (303*2π)/11884 weeks
3041.19023 -2.19274 (304*2π)/11884 weeks
3054.06825 -.79919 (305*2π)/11884 weeks
3063.78941 3.63481 (306*2π)/11884 weeks
307-1.19782 4.71991 (307*2π)/11884 weeks
308-3.3407 .25984 (308*2π)/11884 weeks
309.02703 -2.25395 (309*2π)/11884 weeks
3102.01768 -.0778 (310*2π)/11884 weeks
311.56476 .85599 (311*2π)/11884 weeks
312.4183 -.76076 (312*2π)/11884 weeks
3132.98949 -.8202 (313*2π)/11884 weeks
3143.64542 2.73282 (314*2π)/11884 weeks
315-.33638 4.48803 (315*2π)/11884 weeks
316-3.04483 .75959 (316*2π)/11884 weeks
317.0755 -2.29052 (317*2π)/11884 weeks
3183.02356 .22622 (318*2π)/11884 weeks
319.79679 3.01836 (319*2π)/11884 weeks
320-1.79398 .97884 (320*2π)/11884 weeks
321-.07248 -1.10381 (321*2π)/11884 weeks
3221.16422 .47236 (322*2π)/11884 weeks
323-.88014 .88001 (323*2π)/11884 weeks
324-.88623 -2.06873 (324*2π)/11884 weeks
3252.79495 -2.0863 (325*2π)/11884 weeks
3262.7124 1.85713 (326*2π)/11884 weeks
327-1.33582 1.28572 (327*2π)/11884 weeks
328-.22051 -3.10266 (328*2π)/11884 weeks
3294.80633 -1.73275 (329*2π)/11884 weeks
3303.40278 4.00786 (330*2π)/11884 weeks
331-2.87148 2.75104 (331*2π)/11884 weeks
332-2.12392 -3.84564 (332*2π)/11884 weeks
3334.31467 -4.0175 (333*2π)/11884 weeks
3345.39222 1.45665 (334*2π)/11884 weeks
3351.50953 2.87938 (335*2π)/11884 weeks
336.49265 .45147 (336*2π)/11884 weeks
3372.22716 .15037 (337*2π)/11884 weeks
3382.16003 1.77962 (338*2π)/11884 weeks
339.58199 2.05264 (339*2π)/11884 weeks
340-.35385 .7631 (340*2π)/11883 weeks
341.43166 -.38873 (341*2π)/11883 weeks
3421.00956 .11988 (342*2π)/11883 weeks
343-.03551 -.38079 (343*2π)/11883 weeks
3441.44152 -2.70258 (344*2π)/11883 weeks
3454.91906 -1.19832 (345*2π)/11883 weeks
3464.4244 2.56742 (346*2π)/11883 weeks
3471.49119 3.08417 (347*2π)/11883 weeks
348.71438 1.73806 (348*2π)/11883 weeks
349.81469 1.50266 (349*2π)/11883 weeks
350.16198 1.3456 (350*2π)/11883 weeks
351-.37342 .06207 (351*2π)/11883 weeks
3521.0672 -1.73473 (352*2π)/11883 weeks
3534.25501 -.73514 (353*2π)/11883 weeks
3544.08017 3.5891 (354*2π)/11883 weeks
355-.66154 4.39549 (355*2π)/11883 weeks
356-2.19224 .21958 (356*2π)/11883 weeks
357.77492 -1.39428 (357*2π)/11883 weeks
3581.69112 .37334 (358*2π)/11883 weeks
359.45017 .25497 (359*2π)/11883 weeks
3601.35995 -1.58624 (360*2π)/11883 weeks
3614.20181 -.46399 (361*2π)/11883 weeks
3623.64934 2.87753 (362*2π)/11883 weeks
363.66795 3.13081 (363*2π)/11883 weeks
364.31414 .99836 (364*2π)/11883 weeks
3651.79533 1.38934 (365*2π)/11883 weeks
366.54888 2.90696 (366*2π)/11883 weeks
367-1.61739 1.25391 (367*2π)/11883 weeks
368-.01392 -1.52894 (368*2π)/11883 weeks
3692.88715 -.03152 (369*2π)/11883 weeks
3701.51119 2.7573 (370*2π)/11883 weeks
371-1.00055 1.49419 (371*2π)/11883 weeks
372.10401 -.4959 (372*2π)/11883 weeks
3731.48688 .75138 (373*2π)/11883 weeks
374-.52392 1.85426 (374*2π)/11883 weeks
375-1.9278 -1.14359 (375*2π)/11883 weeks
3761.44989 -3.29377 (376*2π)/11883 weeks
3774.25384 -.30917 (377*2π)/11883 weeks
3782.07717 2.56842 (378*2π)/11883 weeks
379-.40554 1.04672 (379*2π)/11883 weeks
380.79742 -.99192 (380*2π)/11883 weeks
3812.54482 .13933 (381*2π)/11883 weeks
3821.26867 1.51935 (382*2π)/11883 weeks
383.33636 -.10853 (383*2π)/11883 weeks
3842.6506 -.86201 (384*2π)/11883 weeks
3853.68044 2.28375 (385*2π)/11883 weeks
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