Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_autocorrelation.wasp
Title produced by software(Partial) Autocorrelation Function
Date of computationTue, 09 Dec 2008 12:00:23 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/09/t1228849350tqh87s7325h8604.htm/, Retrieved Wed, 22 May 2024 20:36:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=31702, Retrieved Wed, 22 May 2024 20:36:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact194
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
F RMP     [(Partial) Autocorrelation Function] [Opdracht 1 - Blok...] [2008-12-09 19:00:23] [1351baa662f198be3bff32f9007a9a6d] [Current]
Feedback Forum
2008-12-11 19:13:42 [Nathalie Daneels] [reply
Evaluatie opdracht 1 - Blok 20 (Q2 vervolg):

Ook hier moet de conclusie worden aangevuld:
We gaan de tijdreeks stationair maken aan de hand van de autocorrelatiefunctie. Stationair maken houdt in dat we de lange termijn trend en/of de seizoenaliteit uit de tijdreeks gaan halen door een aantal keer te (seizoenaal) differentiëren en/of de tijdreeks te transformeren. We moeten er al vanaf het begin mee rekening houden dat we een voldoende groot aantal time lags hanteren: In dit geval 60, aangezien we een lange tijdreeks hebben. Als de tijdreeks bv. Bestond uit 60 observaties, dan hadden we 36 kunnen nemen als aantal time lags: Dan gaan we 3 jaar in het verleden kijken ; we hebben dan 3 keer de seizoenale autocorrelatie berekent in het verleden van de seizoenale tijdreeks die je hebt.
- We gaan eerst de tijdreeks bekijken, zonder daar een transformatie/differentiatie op te hebben toegepast (Lambda = 1, D = 0 en d = 0). In de tabel zien we in de tweede kolom ‘ACF(k)’ de 1e autocorrelatie (De autocorrelatie die overeenkomt met time lag 1): het verband tussen Yt en Yt-1, de 2e autocorrelatie (De autocorrelatie die overeenkomt met time lag 2): het verband tussen Yt en Yt-2,… Er wordt dus telkens het verband getoond tussen de waarden van de tijdreeks nu en de waarden van de tijdreeks in het verleden (Yt-1, Yt-2, waarbij Yt-1, de tijdreeks 1 periode wordt vertraagd, waarbij Yt-2, de tijdreeks 2 periodes wordt vertraagd,…).
Als we vervolgens naar de grafiek kijken, kunnen we vaststellen dat er een langzaam dalende functie is van allemaal positieve correlatiecoëfficiënten, die significant verschillend zijn van 0. Er is duidelijk zichtbaar dat een hangmattenpatroon zich voordoet. We merken dat de palen van deze hangmatten allemaal positieve en significante correlatiecoëfficiënten zijn en dat ze overeenkomen met de perioden 12,24,… (Telkens om het jaar) Dit wijst op seizoenaliteit. Dit hangmattenpatroon is (vaak) een typisch patroon voor een langzaam dalende ACF. Als we voornamelijk naar de linkse kant van de grafiek gaan kijken (Naar de eerste 4 à 5 coëfficiënten, waarbij de coëfficiënt die overeenkomt met lag 0 buiten beschouwing wordt gelaten), merken we een langzaam dalend patroon van positieve coëfficiënten die significant verschillend zijn van 0: Dit wijst erop dat er een lange termijn trend aanwezig is.
Om de tijdreeks stationair te maken, gaan we stapsgewijs te werk gaan.
- Om deze lange termijntrend weg te werken, moeten we de grafiek gaan differentiëren: We gaan d gelijk stellen aan 1 (Lambda blijft 1 en D = 0). Dit betekent dat de tijdreeks niet-seizoenaal wordt gedifferentieerd, vooraleer de ACF wordt berekend. We gaan merken dat de nieuwe grafiek er helemaal anders uit gaat zien. Waar we oorspronkelijk links een langzaam dalend patroon zagen, is dat er nu niet meer doordat we de tijdreeks hebben gedifferentieerd. Er is wel nog duidelijk seizoenaliteit aanwezig in de tijdreeks: De coëfficiënten die overeenkomen met de periodes 12, 24,… zijn positief en significant verschillend van 0.
- Dit betekent dat we de tijdreeks bijkomend seizoenaal gaan moeten differentiëren: D = 1 (Lambda en d blijven 1). We kunnen opmerken dat op de nieuwe grafiek het langzaam dalend patroon van de seizoenale autocorrelatiecoëfficiënten volledig weg is. De seizoenale coëfficiënt is enkel bij time lag 12 nog significant verschillend van 0, maar wordt bij deze time lag wel negatief: Er is dus zeker geen sprake meer van een seizoenale trend. De.correlatiecoëfficiënten op de time lags 24,36,… zijn allemaal niet significant verschillend van 0 en ongeveer afwisselend positief en negatief. En de lange termijn trend was al in de 2e grafiek verdwenen. Dit betekent dat we erin geslaagd zijn om de tijdreeks stationair te maken (a.h.v. deze methode). Wat hebben we hieruit geleerd? Dat d = 1 en D = 1: Je moet de tijdreeks als volgt modelleren ‘N^d x N(12)^D x Yt = Et. Nu we weten wat D en d is kunnen we dit invullen in de formule: N x N(12) x Yt = Et. Als we dit vervolgens ingeven in de computer (die waardes van d en D en nadat we de waarde van lambda weten = 0,5) dan krijgen we een differentievergelijking (N x N(12) x Wortel (Yt) = Et) waarmee we voorspellingen kunnen doen.
2008-12-11 19:19:19 [Nathalie Daneels] [reply
Ik heb hierboven de hele evaluatie gezet die bij ACF hoort en niet bij elke stap apart.
2008-12-14 12:38:11 [Bénédicte Soens] [reply
Er is een langzaam dalend patroon op te merken met bulten. Deze bulten komen voor bij 12, 24, 36,.. maanden. Dit wijst erop dat er seizoenaliteit aanwezig is in de tijdreeks. De lijnen van de autocorrelatie zijn significant verschillend van 0 aangezien ze boven het 95% betrouwbaarheidsinterval komen. Dit wijst erop dat ze niet aan toeval toe te wijzen zijn.
Het is best om 1maal te differentiëren om zo het langzaam dalend patroon weg te werken.
2008-12-16 09:36:08 [Katja van Hek] [reply
De ACF grafiek laat een duidelijk dalend patroon zien wat duidt op een trend, het hangmatten patroon duidt op de aanwezigheid van seizoenaliteit.Beide kun je verwijderen door de gevonden waarden van de VRM in te vullen nl d=1 en D=1. Op deze manier verdwijnt de trend en de seizoenaliteit uit het model.

Post a new message
Dataseries X:
235.1
280.7
264.6
240.7
201.4
240.8
241.1
223.8
206.1
174.7
203.3
220.5
299.5
347.4
338.3
327.7
351.6
396.6
438.8
395.6
363.5
378.8
357
369
464.8
479.1
431.3
366.5
326.3
355.1
331.6
261.3
249
205.5
235.6
240.9
264.9
253.8
232.3
193.8
177
213.2
207.2
180.6
188.6
175.4
199
179.6
225.8
234
200.2
183.6
178.2
203.2
208.5
191.8
172.8
148
159.4
154.5
213.2
196.4
182.8
176.4
153.6
173.2
171
151.2
161.9
157.2
201.7
236.4
356.1
398.3
403.7
384.6
365.8
368.1
367.9
347
343.3
292.9
311.5
300.9
366.9
356.9
329.7
316.2
269
289.3
266.2
253.6
233.8
228.4
253.6
260.1
306.6
309.2
309.5
271
279.9
317.9
298.4
246.7
227.3
209.1
259.9
266
320.6
308.5
282.2
262.7
263.5
313.1
284.3
252.6
250.3
246.5
312.7
333.2
446.4
511.6
515.5
506.4
483.2
522.3
509.8
460.7
405.8
375
378.5
406.8
467.8
469.8
429.8
355.8
332.7
378
360.5
334.7
319.5
323.1
363.6
352.1
411.9
388.6
416.4
360.7
338
417.2
388.4
371.1
331.5
353.7
396.7
447
533.5
565.4
542.3
488.7
467.1
531.3
496.1
444
403.4
386.3
394.1
404.1
462.1
448.1
432.3
386.3
395.2
421.9
382.9
384.2
345.5
323.4
372.6
376
462.7
487
444.2
399.3
394.9
455.4
414
375.5
347
339.4
385.8
378.8
451.8
446.1
422.5
383.1
352.8
445.3
367.5
355.1
326.2
319.8
331.8
340.9
394.1
417.2
369.9
349.2
321.4
405.7
342.9
316.5
284.2
270.9
288.8
278.8
324.4
310.9
299
273
279.3
359.2
305
282.1
250.3
246.5
257.9
266.5
315.9
318.4
295.4
266.4
245.8
362.8
324.9
294.2
289.5
295.2
290.3
272
307.4
328.7
292.9
249.1
230.4
361.5
321.7
277.2
260.7
251
257.6
241.8
287.5
292.3
274.7
254.2
230
339
318.2
287
295.8
284
271
262.7
340.6
379.4
373.3
355.2
338.4
466.9
451
422
429.2
425.9
460.7
463.6
541.4
544.2
517.5
469.4
439.4
549
533
506.1
484
457
481.5
469.5
544.7
541.2
521.5
469.7
434.4
542.6
517.3
485.7
465.8
447
426.6
411.6
467.5
484.5
451.2
417.4
379.9
484.7
455
420.8
416.5
376.3
405.6
405.8
500.8
514
475.5
430.1
414.4
538
526
488.5
520.2
504.4
568.5
610.6
818
830.9
835.9
782
762.3
856.9
820.9
769.6
752.2
724.4
723.1
719.5
817.4
803.3
752.5
689
630.4
765.5
757.7
732.2
702.6
683.3
709.5
702.2
784.8
810.9
755.6
656.8
615.1
745.3
694.1
675.7
643.7
622.1
634.6
588
689.7
673.9
647.9
568.8
545.7
632.6
643.8
593.1
579.7
546
562.9
572.5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31702&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31702&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31702&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.95829718.4830
20.91521817.65210
30.88341217.03860
40.87008816.78160
50.86173516.62050
60.83236716.05410
70.81215315.66420
80.77509514.94950
90.74559214.38050
100.73465214.16950
110.73915414.25630
120.74370514.34410
130.69318813.36970
140.6441612.42410
150.61139311.79210
160.59979311.56840
170.59740911.52240
180.57795411.14720
190.56895310.97360
200.54377610.4880
210.52623210.14960
220.52570110.13940
230.53771210.3710
240.55135410.63410
250.5128499.89150
260.4750369.16220
270.451488.70780
280.4465798.61330
290.448128.6430
300.4318678.32950
310.4249028.19520
320.4028217.76930
330.3883397.490
340.3888877.50060
350.401247.73880
360.4155648.01510
370.3792257.31420
380.344126.63710
390.3204116.17990
400.3139326.05490
410.3139726.05570
420.2986625.76040
430.2917155.62640
440.2712295.23130
450.2585574.98690
460.26195.05130
470.2776165.35450
480.2937845.66630
490.2637235.08650
500.2335144.50394e-06
510.2142154.13162.2e-05
520.209714.04473.2e-05
530.2113754.07682.8e-05
540.1968923.79758.5e-05
550.190393.67210.000138
560.1683633.24730.000635
570.1523882.93920.001748
580.1500172.89340.002018
590.1578023.04360.001252
600.1653633.18940.000773

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.958297 & 18.483 & 0 \tabularnewline
2 & 0.915218 & 17.6521 & 0 \tabularnewline
3 & 0.883412 & 17.0386 & 0 \tabularnewline
4 & 0.870088 & 16.7816 & 0 \tabularnewline
5 & 0.861735 & 16.6205 & 0 \tabularnewline
6 & 0.832367 & 16.0541 & 0 \tabularnewline
7 & 0.812153 & 15.6642 & 0 \tabularnewline
8 & 0.775095 & 14.9495 & 0 \tabularnewline
9 & 0.745592 & 14.3805 & 0 \tabularnewline
10 & 0.734652 & 14.1695 & 0 \tabularnewline
11 & 0.739154 & 14.2563 & 0 \tabularnewline
12 & 0.743705 & 14.3441 & 0 \tabularnewline
13 & 0.693188 & 13.3697 & 0 \tabularnewline
14 & 0.64416 & 12.4241 & 0 \tabularnewline
15 & 0.611393 & 11.7921 & 0 \tabularnewline
16 & 0.599793 & 11.5684 & 0 \tabularnewline
17 & 0.597409 & 11.5224 & 0 \tabularnewline
18 & 0.577954 & 11.1472 & 0 \tabularnewline
19 & 0.568953 & 10.9736 & 0 \tabularnewline
20 & 0.543776 & 10.488 & 0 \tabularnewline
21 & 0.526232 & 10.1496 & 0 \tabularnewline
22 & 0.525701 & 10.1394 & 0 \tabularnewline
23 & 0.537712 & 10.371 & 0 \tabularnewline
24 & 0.551354 & 10.6341 & 0 \tabularnewline
25 & 0.512849 & 9.8915 & 0 \tabularnewline
26 & 0.475036 & 9.1622 & 0 \tabularnewline
27 & 0.45148 & 8.7078 & 0 \tabularnewline
28 & 0.446579 & 8.6133 & 0 \tabularnewline
29 & 0.44812 & 8.643 & 0 \tabularnewline
30 & 0.431867 & 8.3295 & 0 \tabularnewline
31 & 0.424902 & 8.1952 & 0 \tabularnewline
32 & 0.402821 & 7.7693 & 0 \tabularnewline
33 & 0.388339 & 7.49 & 0 \tabularnewline
34 & 0.388887 & 7.5006 & 0 \tabularnewline
35 & 0.40124 & 7.7388 & 0 \tabularnewline
36 & 0.415564 & 8.0151 & 0 \tabularnewline
37 & 0.379225 & 7.3142 & 0 \tabularnewline
38 & 0.34412 & 6.6371 & 0 \tabularnewline
39 & 0.320411 & 6.1799 & 0 \tabularnewline
40 & 0.313932 & 6.0549 & 0 \tabularnewline
41 & 0.313972 & 6.0557 & 0 \tabularnewline
42 & 0.298662 & 5.7604 & 0 \tabularnewline
43 & 0.291715 & 5.6264 & 0 \tabularnewline
44 & 0.271229 & 5.2313 & 0 \tabularnewline
45 & 0.258557 & 4.9869 & 0 \tabularnewline
46 & 0.2619 & 5.0513 & 0 \tabularnewline
47 & 0.277616 & 5.3545 & 0 \tabularnewline
48 & 0.293784 & 5.6663 & 0 \tabularnewline
49 & 0.263723 & 5.0865 & 0 \tabularnewline
50 & 0.233514 & 4.5039 & 4e-06 \tabularnewline
51 & 0.214215 & 4.1316 & 2.2e-05 \tabularnewline
52 & 0.20971 & 4.0447 & 3.2e-05 \tabularnewline
53 & 0.211375 & 4.0768 & 2.8e-05 \tabularnewline
54 & 0.196892 & 3.7975 & 8.5e-05 \tabularnewline
55 & 0.19039 & 3.6721 & 0.000138 \tabularnewline
56 & 0.168363 & 3.2473 & 0.000635 \tabularnewline
57 & 0.152388 & 2.9392 & 0.001748 \tabularnewline
58 & 0.150017 & 2.8934 & 0.002018 \tabularnewline
59 & 0.157802 & 3.0436 & 0.001252 \tabularnewline
60 & 0.165363 & 3.1894 & 0.000773 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31702&T=1

[TABLE]
[ROW][C]Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]ACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]0.958297[/C][C]18.483[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.915218[/C][C]17.6521[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.883412[/C][C]17.0386[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.870088[/C][C]16.7816[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.861735[/C][C]16.6205[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.832367[/C][C]16.0541[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.812153[/C][C]15.6642[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.775095[/C][C]14.9495[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.745592[/C][C]14.3805[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.734652[/C][C]14.1695[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.739154[/C][C]14.2563[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.743705[/C][C]14.3441[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.693188[/C][C]13.3697[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.64416[/C][C]12.4241[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.611393[/C][C]11.7921[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.599793[/C][C]11.5684[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.597409[/C][C]11.5224[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.577954[/C][C]11.1472[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.568953[/C][C]10.9736[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.543776[/C][C]10.488[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.526232[/C][C]10.1496[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]0.525701[/C][C]10.1394[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]0.537712[/C][C]10.371[/C][C]0[/C][/ROW]
[ROW][C]24[/C][C]0.551354[/C][C]10.6341[/C][C]0[/C][/ROW]
[ROW][C]25[/C][C]0.512849[/C][C]9.8915[/C][C]0[/C][/ROW]
[ROW][C]26[/C][C]0.475036[/C][C]9.1622[/C][C]0[/C][/ROW]
[ROW][C]27[/C][C]0.45148[/C][C]8.7078[/C][C]0[/C][/ROW]
[ROW][C]28[/C][C]0.446579[/C][C]8.6133[/C][C]0[/C][/ROW]
[ROW][C]29[/C][C]0.44812[/C][C]8.643[/C][C]0[/C][/ROW]
[ROW][C]30[/C][C]0.431867[/C][C]8.3295[/C][C]0[/C][/ROW]
[ROW][C]31[/C][C]0.424902[/C][C]8.1952[/C][C]0[/C][/ROW]
[ROW][C]32[/C][C]0.402821[/C][C]7.7693[/C][C]0[/C][/ROW]
[ROW][C]33[/C][C]0.388339[/C][C]7.49[/C][C]0[/C][/ROW]
[ROW][C]34[/C][C]0.388887[/C][C]7.5006[/C][C]0[/C][/ROW]
[ROW][C]35[/C][C]0.40124[/C][C]7.7388[/C][C]0[/C][/ROW]
[ROW][C]36[/C][C]0.415564[/C][C]8.0151[/C][C]0[/C][/ROW]
[ROW][C]37[/C][C]0.379225[/C][C]7.3142[/C][C]0[/C][/ROW]
[ROW][C]38[/C][C]0.34412[/C][C]6.6371[/C][C]0[/C][/ROW]
[ROW][C]39[/C][C]0.320411[/C][C]6.1799[/C][C]0[/C][/ROW]
[ROW][C]40[/C][C]0.313932[/C][C]6.0549[/C][C]0[/C][/ROW]
[ROW][C]41[/C][C]0.313972[/C][C]6.0557[/C][C]0[/C][/ROW]
[ROW][C]42[/C][C]0.298662[/C][C]5.7604[/C][C]0[/C][/ROW]
[ROW][C]43[/C][C]0.291715[/C][C]5.6264[/C][C]0[/C][/ROW]
[ROW][C]44[/C][C]0.271229[/C][C]5.2313[/C][C]0[/C][/ROW]
[ROW][C]45[/C][C]0.258557[/C][C]4.9869[/C][C]0[/C][/ROW]
[ROW][C]46[/C][C]0.2619[/C][C]5.0513[/C][C]0[/C][/ROW]
[ROW][C]47[/C][C]0.277616[/C][C]5.3545[/C][C]0[/C][/ROW]
[ROW][C]48[/C][C]0.293784[/C][C]5.6663[/C][C]0[/C][/ROW]
[ROW][C]49[/C][C]0.263723[/C][C]5.0865[/C][C]0[/C][/ROW]
[ROW][C]50[/C][C]0.233514[/C][C]4.5039[/C][C]4e-06[/C][/ROW]
[ROW][C]51[/C][C]0.214215[/C][C]4.1316[/C][C]2.2e-05[/C][/ROW]
[ROW][C]52[/C][C]0.20971[/C][C]4.0447[/C][C]3.2e-05[/C][/ROW]
[ROW][C]53[/C][C]0.211375[/C][C]4.0768[/C][C]2.8e-05[/C][/ROW]
[ROW][C]54[/C][C]0.196892[/C][C]3.7975[/C][C]8.5e-05[/C][/ROW]
[ROW][C]55[/C][C]0.19039[/C][C]3.6721[/C][C]0.000138[/C][/ROW]
[ROW][C]56[/C][C]0.168363[/C][C]3.2473[/C][C]0.000635[/C][/ROW]
[ROW][C]57[/C][C]0.152388[/C][C]2.9392[/C][C]0.001748[/C][/ROW]
[ROW][C]58[/C][C]0.150017[/C][C]2.8934[/C][C]0.002018[/C][/ROW]
[ROW][C]59[/C][C]0.157802[/C][C]3.0436[/C][C]0.001252[/C][/ROW]
[ROW][C]60[/C][C]0.165363[/C][C]3.1894[/C][C]0.000773[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31702&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31702&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.95829718.4830
20.91521817.65210
30.88341217.03860
40.87008816.78160
50.86173516.62050
60.83236716.05410
70.81215315.66420
80.77509514.94950
90.74559214.38050
100.73465214.16950
110.73915414.25630
120.74370514.34410
130.69318813.36970
140.6441612.42410
150.61139311.79210
160.59979311.56840
170.59740911.52240
180.57795411.14720
190.56895310.97360
200.54377610.4880
210.52623210.14960
220.52570110.13940
230.53771210.3710
240.55135410.63410
250.5128499.89150
260.4750369.16220
270.451488.70780
280.4465798.61330
290.448128.6430
300.4318678.32950
310.4249028.19520
320.4028217.76930
330.3883397.490
340.3888877.50060
350.401247.73880
360.4155648.01510
370.3792257.31420
380.344126.63710
390.3204116.17990
400.3139326.05490
410.3139726.05570
420.2986625.76040
430.2917155.62640
440.2712295.23130
450.2585574.98690
460.26195.05130
470.2776165.35450
480.2937845.66630
490.2637235.08650
500.2335144.50394e-06
510.2142154.13162.2e-05
520.209714.04473.2e-05
530.2113754.07682.8e-05
540.1968923.79758.5e-05
550.190393.67210.000138
560.1683633.24730.000635
570.1523882.93920.001748
580.1500172.89340.002018
590.1578023.04360.001252
600.1653633.18940.000773







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.95829718.4830
2-0.038138-0.73560.231227
30.1160082.23750.012923
40.2073453.99913.8e-05
50.0712951.37510.084967
6-0.216629-4.17821.8e-05
70.1778433.43010.000336
8-0.280159-5.40350
90.0515850.99490.160206
100.2214434.2711.2e-05
110.1890493.64620.000152
12-0.045031-0.86850.192833
13-0.550158-10.61110
140.0486850.9390.17417
150.1391522.68390.003802
160.0589661.13730.128074
170.1450152.7970.002713
180.0564151.08810.13863
190.0891681.71980.04315
20-0.085304-1.64530.050378
210.0107060.20650.418258
220.0204530.39450.346725
23-0.016396-0.31620.376
240.0564891.08950.138315
25-0.235006-4.53264e-06
260.008890.17150.431974
270.0490980.9470.172137
28-0.018295-0.35290.362198
29-0.002463-0.04750.481071
300.0294940.56890.284897
310.0502210.96860.16668
32-0.006361-0.12270.45121
330.0439290.84730.198693
340.016920.32630.372172
35-0.002393-0.04620.481607
360.0201210.38810.349091
37-0.189406-3.65310.000148
380.0123510.23820.405923
39-0.038849-0.74930.227076
40-0.033337-0.6430.260319
410.0326140.6290.264854
420.0928391.79060.037084
43-0.013284-0.25620.398966
440.0235280.45380.325119
450.0335990.6480.25868
460.0403740.77870.218321
470.0116450.22460.411208
48-0.024423-0.47110.31894
49-0.06699-1.29210.098569
50-0.031084-0.59950.274592
51-0.023084-0.44520.328206
52-0.061509-1.18630.118122
53-0.001646-0.03180.487343
54-0.002282-0.0440.482462
550.0011130.02150.491441
56-0.039442-0.76070.223649
57-0.0128-0.24690.402567
58-0.013281-0.25620.398983
59-0.018742-0.36150.358969
60-0.027922-0.53850.29526

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.958297 & 18.483 & 0 \tabularnewline
2 & -0.038138 & -0.7356 & 0.231227 \tabularnewline
3 & 0.116008 & 2.2375 & 0.012923 \tabularnewline
4 & 0.207345 & 3.9991 & 3.8e-05 \tabularnewline
5 & 0.071295 & 1.3751 & 0.084967 \tabularnewline
6 & -0.216629 & -4.1782 & 1.8e-05 \tabularnewline
7 & 0.177843 & 3.4301 & 0.000336 \tabularnewline
8 & -0.280159 & -5.4035 & 0 \tabularnewline
9 & 0.051585 & 0.9949 & 0.160206 \tabularnewline
10 & 0.221443 & 4.271 & 1.2e-05 \tabularnewline
11 & 0.189049 & 3.6462 & 0.000152 \tabularnewline
12 & -0.045031 & -0.8685 & 0.192833 \tabularnewline
13 & -0.550158 & -10.6111 & 0 \tabularnewline
14 & 0.048685 & 0.939 & 0.17417 \tabularnewline
15 & 0.139152 & 2.6839 & 0.003802 \tabularnewline
16 & 0.058966 & 1.1373 & 0.128074 \tabularnewline
17 & 0.145015 & 2.797 & 0.002713 \tabularnewline
18 & 0.056415 & 1.0881 & 0.13863 \tabularnewline
19 & 0.089168 & 1.7198 & 0.04315 \tabularnewline
20 & -0.085304 & -1.6453 & 0.050378 \tabularnewline
21 & 0.010706 & 0.2065 & 0.418258 \tabularnewline
22 & 0.020453 & 0.3945 & 0.346725 \tabularnewline
23 & -0.016396 & -0.3162 & 0.376 \tabularnewline
24 & 0.056489 & 1.0895 & 0.138315 \tabularnewline
25 & -0.235006 & -4.5326 & 4e-06 \tabularnewline
26 & 0.00889 & 0.1715 & 0.431974 \tabularnewline
27 & 0.049098 & 0.947 & 0.172137 \tabularnewline
28 & -0.018295 & -0.3529 & 0.362198 \tabularnewline
29 & -0.002463 & -0.0475 & 0.481071 \tabularnewline
30 & 0.029494 & 0.5689 & 0.284897 \tabularnewline
31 & 0.050221 & 0.9686 & 0.16668 \tabularnewline
32 & -0.006361 & -0.1227 & 0.45121 \tabularnewline
33 & 0.043929 & 0.8473 & 0.198693 \tabularnewline
34 & 0.01692 & 0.3263 & 0.372172 \tabularnewline
35 & -0.002393 & -0.0462 & 0.481607 \tabularnewline
36 & 0.020121 & 0.3881 & 0.349091 \tabularnewline
37 & -0.189406 & -3.6531 & 0.000148 \tabularnewline
38 & 0.012351 & 0.2382 & 0.405923 \tabularnewline
39 & -0.038849 & -0.7493 & 0.227076 \tabularnewline
40 & -0.033337 & -0.643 & 0.260319 \tabularnewline
41 & 0.032614 & 0.629 & 0.264854 \tabularnewline
42 & 0.092839 & 1.7906 & 0.037084 \tabularnewline
43 & -0.013284 & -0.2562 & 0.398966 \tabularnewline
44 & 0.023528 & 0.4538 & 0.325119 \tabularnewline
45 & 0.033599 & 0.648 & 0.25868 \tabularnewline
46 & 0.040374 & 0.7787 & 0.218321 \tabularnewline
47 & 0.011645 & 0.2246 & 0.411208 \tabularnewline
48 & -0.024423 & -0.4711 & 0.31894 \tabularnewline
49 & -0.06699 & -1.2921 & 0.098569 \tabularnewline
50 & -0.031084 & -0.5995 & 0.274592 \tabularnewline
51 & -0.023084 & -0.4452 & 0.328206 \tabularnewline
52 & -0.061509 & -1.1863 & 0.118122 \tabularnewline
53 & -0.001646 & -0.0318 & 0.487343 \tabularnewline
54 & -0.002282 & -0.044 & 0.482462 \tabularnewline
55 & 0.001113 & 0.0215 & 0.491441 \tabularnewline
56 & -0.039442 & -0.7607 & 0.223649 \tabularnewline
57 & -0.0128 & -0.2469 & 0.402567 \tabularnewline
58 & -0.013281 & -0.2562 & 0.398983 \tabularnewline
59 & -0.018742 & -0.3615 & 0.358969 \tabularnewline
60 & -0.027922 & -0.5385 & 0.29526 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31702&T=2

[TABLE]
[ROW][C]Partial Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]PACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]0.958297[/C][C]18.483[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.038138[/C][C]-0.7356[/C][C]0.231227[/C][/ROW]
[ROW][C]3[/C][C]0.116008[/C][C]2.2375[/C][C]0.012923[/C][/ROW]
[ROW][C]4[/C][C]0.207345[/C][C]3.9991[/C][C]3.8e-05[/C][/ROW]
[ROW][C]5[/C][C]0.071295[/C][C]1.3751[/C][C]0.084967[/C][/ROW]
[ROW][C]6[/C][C]-0.216629[/C][C]-4.1782[/C][C]1.8e-05[/C][/ROW]
[ROW][C]7[/C][C]0.177843[/C][C]3.4301[/C][C]0.000336[/C][/ROW]
[ROW][C]8[/C][C]-0.280159[/C][C]-5.4035[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.051585[/C][C]0.9949[/C][C]0.160206[/C][/ROW]
[ROW][C]10[/C][C]0.221443[/C][C]4.271[/C][C]1.2e-05[/C][/ROW]
[ROW][C]11[/C][C]0.189049[/C][C]3.6462[/C][C]0.000152[/C][/ROW]
[ROW][C]12[/C][C]-0.045031[/C][C]-0.8685[/C][C]0.192833[/C][/ROW]
[ROW][C]13[/C][C]-0.550158[/C][C]-10.6111[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.048685[/C][C]0.939[/C][C]0.17417[/C][/ROW]
[ROW][C]15[/C][C]0.139152[/C][C]2.6839[/C][C]0.003802[/C][/ROW]
[ROW][C]16[/C][C]0.058966[/C][C]1.1373[/C][C]0.128074[/C][/ROW]
[ROW][C]17[/C][C]0.145015[/C][C]2.797[/C][C]0.002713[/C][/ROW]
[ROW][C]18[/C][C]0.056415[/C][C]1.0881[/C][C]0.13863[/C][/ROW]
[ROW][C]19[/C][C]0.089168[/C][C]1.7198[/C][C]0.04315[/C][/ROW]
[ROW][C]20[/C][C]-0.085304[/C][C]-1.6453[/C][C]0.050378[/C][/ROW]
[ROW][C]21[/C][C]0.010706[/C][C]0.2065[/C][C]0.418258[/C][/ROW]
[ROW][C]22[/C][C]0.020453[/C][C]0.3945[/C][C]0.346725[/C][/ROW]
[ROW][C]23[/C][C]-0.016396[/C][C]-0.3162[/C][C]0.376[/C][/ROW]
[ROW][C]24[/C][C]0.056489[/C][C]1.0895[/C][C]0.138315[/C][/ROW]
[ROW][C]25[/C][C]-0.235006[/C][C]-4.5326[/C][C]4e-06[/C][/ROW]
[ROW][C]26[/C][C]0.00889[/C][C]0.1715[/C][C]0.431974[/C][/ROW]
[ROW][C]27[/C][C]0.049098[/C][C]0.947[/C][C]0.172137[/C][/ROW]
[ROW][C]28[/C][C]-0.018295[/C][C]-0.3529[/C][C]0.362198[/C][/ROW]
[ROW][C]29[/C][C]-0.002463[/C][C]-0.0475[/C][C]0.481071[/C][/ROW]
[ROW][C]30[/C][C]0.029494[/C][C]0.5689[/C][C]0.284897[/C][/ROW]
[ROW][C]31[/C][C]0.050221[/C][C]0.9686[/C][C]0.16668[/C][/ROW]
[ROW][C]32[/C][C]-0.006361[/C][C]-0.1227[/C][C]0.45121[/C][/ROW]
[ROW][C]33[/C][C]0.043929[/C][C]0.8473[/C][C]0.198693[/C][/ROW]
[ROW][C]34[/C][C]0.01692[/C][C]0.3263[/C][C]0.372172[/C][/ROW]
[ROW][C]35[/C][C]-0.002393[/C][C]-0.0462[/C][C]0.481607[/C][/ROW]
[ROW][C]36[/C][C]0.020121[/C][C]0.3881[/C][C]0.349091[/C][/ROW]
[ROW][C]37[/C][C]-0.189406[/C][C]-3.6531[/C][C]0.000148[/C][/ROW]
[ROW][C]38[/C][C]0.012351[/C][C]0.2382[/C][C]0.405923[/C][/ROW]
[ROW][C]39[/C][C]-0.038849[/C][C]-0.7493[/C][C]0.227076[/C][/ROW]
[ROW][C]40[/C][C]-0.033337[/C][C]-0.643[/C][C]0.260319[/C][/ROW]
[ROW][C]41[/C][C]0.032614[/C][C]0.629[/C][C]0.264854[/C][/ROW]
[ROW][C]42[/C][C]0.092839[/C][C]1.7906[/C][C]0.037084[/C][/ROW]
[ROW][C]43[/C][C]-0.013284[/C][C]-0.2562[/C][C]0.398966[/C][/ROW]
[ROW][C]44[/C][C]0.023528[/C][C]0.4538[/C][C]0.325119[/C][/ROW]
[ROW][C]45[/C][C]0.033599[/C][C]0.648[/C][C]0.25868[/C][/ROW]
[ROW][C]46[/C][C]0.040374[/C][C]0.7787[/C][C]0.218321[/C][/ROW]
[ROW][C]47[/C][C]0.011645[/C][C]0.2246[/C][C]0.411208[/C][/ROW]
[ROW][C]48[/C][C]-0.024423[/C][C]-0.4711[/C][C]0.31894[/C][/ROW]
[ROW][C]49[/C][C]-0.06699[/C][C]-1.2921[/C][C]0.098569[/C][/ROW]
[ROW][C]50[/C][C]-0.031084[/C][C]-0.5995[/C][C]0.274592[/C][/ROW]
[ROW][C]51[/C][C]-0.023084[/C][C]-0.4452[/C][C]0.328206[/C][/ROW]
[ROW][C]52[/C][C]-0.061509[/C][C]-1.1863[/C][C]0.118122[/C][/ROW]
[ROW][C]53[/C][C]-0.001646[/C][C]-0.0318[/C][C]0.487343[/C][/ROW]
[ROW][C]54[/C][C]-0.002282[/C][C]-0.044[/C][C]0.482462[/C][/ROW]
[ROW][C]55[/C][C]0.001113[/C][C]0.0215[/C][C]0.491441[/C][/ROW]
[ROW][C]56[/C][C]-0.039442[/C][C]-0.7607[/C][C]0.223649[/C][/ROW]
[ROW][C]57[/C][C]-0.0128[/C][C]-0.2469[/C][C]0.402567[/C][/ROW]
[ROW][C]58[/C][C]-0.013281[/C][C]-0.2562[/C][C]0.398983[/C][/ROW]
[ROW][C]59[/C][C]-0.018742[/C][C]-0.3615[/C][C]0.358969[/C][/ROW]
[ROW][C]60[/C][C]-0.027922[/C][C]-0.5385[/C][C]0.29526[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31702&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31702&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.95829718.4830
2-0.038138-0.73560.231227
30.1160082.23750.012923
40.2073453.99913.8e-05
50.0712951.37510.084967
6-0.216629-4.17821.8e-05
70.1778433.43010.000336
8-0.280159-5.40350
90.0515850.99490.160206
100.2214434.2711.2e-05
110.1890493.64620.000152
12-0.045031-0.86850.192833
13-0.550158-10.61110
140.0486850.9390.17417
150.1391522.68390.003802
160.0589661.13730.128074
170.1450152.7970.002713
180.0564151.08810.13863
190.0891681.71980.04315
20-0.085304-1.64530.050378
210.0107060.20650.418258
220.0204530.39450.346725
23-0.016396-0.31620.376
240.0564891.08950.138315
25-0.235006-4.53264e-06
260.008890.17150.431974
270.0490980.9470.172137
28-0.018295-0.35290.362198
29-0.002463-0.04750.481071
300.0294940.56890.284897
310.0502210.96860.16668
32-0.006361-0.12270.45121
330.0439290.84730.198693
340.016920.32630.372172
35-0.002393-0.04620.481607
360.0201210.38810.349091
37-0.189406-3.65310.000148
380.0123510.23820.405923
39-0.038849-0.74930.227076
40-0.033337-0.6430.260319
410.0326140.6290.264854
420.0928391.79060.037084
43-0.013284-0.25620.398966
440.0235280.45380.325119
450.0335990.6480.25868
460.0403740.77870.218321
470.0116450.22460.411208
48-0.024423-0.47110.31894
49-0.06699-1.29210.098569
50-0.031084-0.59950.274592
51-0.023084-0.44520.328206
52-0.061509-1.18630.118122
53-0.001646-0.03180.487343
54-0.002282-0.0440.482462
550.0011130.02150.491441
56-0.039442-0.76070.223649
57-0.0128-0.24690.402567
58-0.013281-0.25620.398983
59-0.018742-0.36150.358969
60-0.027922-0.53850.29526



Parameters (Session):
par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;
Parameters (R input):
par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;
R code (references can be found in the software module):
if (par1 == 'Default') {
par1 = 10*log10(length(x))
} else {
par1 <- as.numeric(par1)
}
par2 <- as.numeric(par2)
par3 <- as.numeric(par3)
par4 <- as.numeric(par4)
par5 <- as.numeric(par5)
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='pic1.png')
racf <- acf(x,par1,main='Autocorrelation',xlab='lags',ylab='ACF')
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')
dev.off()
(myacf <- c(racf$acf))
(mypacf <- c(rpacf$acf))
lengthx <- length(x)
sqrtn <- sqrt(lengthx)
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,hyperlink('basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 2:(par1+1)) {
a<-table.row.start(a)
a<-table.element(a,i-1,header=TRUE)
a<-table.element(a,round(myacf[i],6))
mytstat <- myacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Partial Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,hyperlink('basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:par1) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,round(mypacf[i],6))
mytstat <- mypacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')