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rwasp_autocorrelation.wasp

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(Partial) Autocorrelation Function

Date of computation

Sun, 07 Dec 2008 05:04:39 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/07/t1228651548khbc0659snthw8l.htm/, Retrieved Sun, 19 May 2024 10:46:46 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29890, Retrieved Sun, 19 May 2024 10:46:46 +0000

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Estimated Impact

198

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   [Standard Deviation-Mean Plot] [q1] [2008-12-07 11:50:18] [1b742211e88d1643c42c5773474321b2]
F RM      [Variance Reduction Matrix] [step 2] [2008-12-07 11:57:32] [1b742211e88d1643c42c5773474321b2]
F RMP         [(Partial) Autocorrelation Function] [ste^2] [2008-12-07 12:04:39] [607bd9e9685911f7e343f7bc0bf7bdf9] [Current]
F RM            [Spectral Analysis] [step 2] [2008-12-07 12:10:49] [1b742211e88d1643c42c5773474321b2] 
-                 [Spectral Analysis] [step 3] [2008-12-07 12:17:09] [1b742211e88d1643c42c5773474321b2] 
F RM                [(Partial) Autocorrelation Function] [step 3] [2008-12-07 12:22:25] [1b742211e88d1643c42c5773474321b2] 
F RM                  [ARIMA Backward Selection] [step 4] [2008-12-07 12:41:04] [1b742211e88d1643c42c5773474321b2] 

Feedback Forum

2008-12-13 11:38:07 [Nicolaj Wuyts] [reply] 
VRM: We zoeken hier de d en D-waarden met de kleinste variatie. Hoe kleiner de variatie, hoe meer zekerheid dit ons biedt. Indien er twijfel is bij de gewone variatie, moet er gekeken worden naar de getrimde variatie. 
ACF: De autocorrelatie functie geeft het herkenbaar patroon van een hanglat weer. 
Spectraal analyse: Aan de hand van de lange termijntrend kan ongeveer 70% van de gegevens verklaard worden. Ook uit het raw periodogram kunnen we afleiden dat d=1 en D=1. De lange termijntrend tekent zich af in het langzaam dalend verloop naar het einde van de grafiek toe. De seizoenale trend zit verdoken in de regelmatig wederkerende pieken.
2008-12-14 12:26:42 [Carole Thielens] [reply] 
* De analyses met de partial autocorrelation function, de variance reduction matrix en de spectraalanalyse waren wel juist, maar onvolledig. De student gebruikte elke methode om te herkennen dat er sprake is van seizonaliteit en een lange termijntrend, maar zocht niet naar de juiste waarden voor de parameters d en D om te gebruikten bij de differentiatie. Het was immers de bedoeling om d en D goed te gebruiken opdat deze niet-stationaire tijdsreeks getransformeerd kan worden tot een stationaire tijdsreeks. Enkel bij de variance reduction matrix vond de student de juiste waarden voor d en D door te kijken welke waarden gepaard gingen met de kleinste variantie. Er werd niet bij de partial autocorrelation en evenmin bij de spectraalanalyse gekeken naar het effect van deze transformatie op de tijdsreeks. 
 
Partial autocorrelation function: 
 
*Voor differentiatie is er op de autocorrelation een langzaam dalende trend waar te nemen, wat er op wijst dat het gemiddelde niet stationair is. Om deze trend te verwijderen, zullen we moeten differentiëren. Ook zien we om de 12 maanden een kleine piek, wat duidt op seizonaliteit. 
 
*Op de partial autocorrelation vallen duidelijk nog enkele lags buiten het 95% betrouwbaarheidsinterval. Zij verschillen dus significant en kunnen niet aan het toeval toegewezen worden. Dit duidt op autocorrelatie. Het is de bedoeling dat we door differentiatie de autocorrelatie wegwerken en er dus voor zorgen dat er zoveel mogelijk lags binnen het betrouwbaarheidsinterval blijven. 
 
* Door differentiatie met d=1 en D=1 worden zowel de lange termijn trend als seizonaliteit uit de tijdsreeks weggewerkt. Na differentiatie met d=1 werd de trend weggewerkt, maar zagen we nog steeds dat er zich om de 12 maanden een piek voordoet. Dit wijst erop dat er nog steeds sprake is van een uitermate seizonale trend. Wanneer we meer perioden zouden opnemen in deze autocorrelatie plot, zou ook duidelijk waarneembaar zijn dat de pieken telkens ieder jaar een beetje dalen. Dit wijst er dus op dat er een nog een langzaam dalend patroon voor seizonale coëfficiënten aanwezig is.  
Om dus de seizonaliteit ook weg te werken, wordt er gedifferentieerd met D=1, wat als gevolg heeft dat de jaarlijkse pieken zich niet meer voordoen en er een stationaire tijdsreeks ontstaat. 
2008-12-14 16:49:03 [Jasmine Hendrikx] [reply] 
Evaluatie stap 2 ACF: 
De student heeft de juiste berekening gemaakt en er is een goede bespreking gegeven. Er is inderdaad sprake van een langzaam dalende trend en seizoenaliteit. De autocorrelatiecoëfficiënten zijn ook allemaal significant verschillend van 0, aangezien ze buiten het betrouwbaarheidsinterval vallen. Hier zou nog vermeld kunnen worden dat we kunnen spreken van een positieve autocorrelatie, aangezien er een langzaam dalend patroon is. Wanneer de vorige waarde hoog is, zal de volgende waarde waarschijnlijk ook hoog zijn. Dit kunt je ook afleiden uit de formule die toegepast wordt:  
Yt= Yt-1+ Et,  
dus Yt-Et = Yt-1. 
Dit betekent dat elke voorspelling ongeveer gelijk is aan de vorige voorspelling, toch ten minste wanneer Et niet groot is. 
Wanneer je een opeenvolging hebt van zeer hoge en zeer lage pieken, dan is er sprake van negatieve autocorrelatie (= wispelturig). 
Ook is er een langzaam dalend patroon te merken in de coëfficiënten op lag 12,24, etc. Dit duidt op een seizoenale trend en dus op seizoenaliteit, zoals reeds vermeld was (er is ook een hangmatpatroon, zo is er dus telkens een stijging op lag 12,24,36). 
Aangezien we zowel kunnen spreken van een langetermijntrend als van seizoenaliteit, zullen we dus D en d gelijkstellen aan 1 (dit wordt dan ook in stap 3 gedaan). 

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29890&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29890&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29890&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

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

\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=29890&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=29890&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29890&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 k	ACF(k)	T-STAT	P-value
1	0.958297	18.483	0
2	0.915218	17.6521	0
3	0.883412	17.0386	0
4	0.870088	16.7816	0
5	0.861735	16.6205	0
6	0.832367	16.0541	0
7	0.812153	15.6642	0
8	0.775095	14.9495	0
9	0.745592	14.3805	0
10	0.734652	14.1695	0
11	0.739154	14.2563	0
12	0.743705	14.3441	0
13	0.693188	13.3697	0
14	0.64416	12.4241	0
15	0.611393	11.7921	0
16	0.599793	11.5684	0
17	0.597409	11.5224	0
18	0.577954	11.1472	0
19	0.568953	10.9736	0
20	0.543776	10.488	0
21	0.526232	10.1496	0
22	0.525701	10.1394	0
23	0.537712	10.371	0
24	0.551354	10.6341	0
25	0.512849	9.8915	0
26	0.475036	9.1622	0
27	0.45148	8.7078	0
28	0.446579	8.6133	0
29	0.44812	8.643	0
30	0.431867	8.3295	0
31	0.424902	8.1952	0
32	0.402821	7.7693	0
33	0.388339	7.49	0
34	0.388887	7.5006	0
35	0.40124	7.7388	0
36	0.415564	8.0151	0
37	0.379225	7.3142	0
38	0.34412	6.6371	0
39	0.320411	6.1799	0
40	0.313932	6.0549	0
41	0.313972	6.0557	0
42	0.298662	5.7604	0
43	0.291715	5.6264	0
44	0.271229	5.2313	0
45	0.258557	4.9869	0
46	0.2619	5.0513	0
47	0.277616	5.3545	0
48	0.293784	5.6663	0
49	0.263723	5.0865	0
50	0.233514	4.5039	4e-06
51	0.214215	4.1316	2.2e-05
52	0.20971	4.0447	3.2e-05
53	0.211375	4.0768	2.8e-05
54	0.196892	3.7975	8.5e-05
55	0.19039	3.6721	0.000138
56	0.168363	3.2473	0.000635
57	0.152388	2.9392	0.001748
58	0.150017	2.8934	0.002018
59	0.157802	3.0436	0.001252
60	0.165363	3.1894	0.000773

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

\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=29890&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=29890&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29890&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 k	PACF(k)	T-STAT	P-value
1	0.958297	18.483	0
2	-0.038138	-0.7356	0.231227
3	0.116008	2.2375	0.012923
4	0.207345	3.9991	3.8e-05
5	0.071295	1.3751	0.084967
6	-0.216629	-4.1782	1.8e-05
7	0.177843	3.4301	0.000336
8	-0.280159	-5.4035	0
9	0.051585	0.9949	0.160206
10	0.221443	4.271	1.2e-05
11	0.189049	3.6462	0.000152
12	-0.045031	-0.8685	0.192833
13	-0.550158	-10.6111	0
14	0.048685	0.939	0.17417
15	0.139152	2.6839	0.003802
16	0.058966	1.1373	0.128074
17	0.145015	2.797	0.002713
18	0.056415	1.0881	0.13863
19	0.089168	1.7198	0.04315
20	-0.085304	-1.6453	0.050378
21	0.010706	0.2065	0.418258
22	0.020453	0.3945	0.346725
23	-0.016396	-0.3162	0.376
24	0.056489	1.0895	0.138315
25	-0.235006	-4.5326	4e-06
26	0.00889	0.1715	0.431974
27	0.049098	0.947	0.172137
28	-0.018295	-0.3529	0.362198
29	-0.002463	-0.0475	0.481071
30	0.029494	0.5689	0.284897
31	0.050221	0.9686	0.16668
32	-0.006361	-0.1227	0.45121
33	0.043929	0.8473	0.198693
34	0.01692	0.3263	0.372172
35	-0.002393	-0.0462	0.481607
36	0.020121	0.3881	0.349091
37	-0.189406	-3.6531	0.000148
38	0.012351	0.2382	0.405923
39	-0.038849	-0.7493	0.227076
40	-0.033337	-0.643	0.260319
41	0.032614	0.629	0.264854
42	0.092839	1.7906	0.037084
43	-0.013284	-0.2562	0.398966
44	0.023528	0.4538	0.325119
45	0.033599	0.648	0.25868
46	0.040374	0.7787	0.218321
47	0.011645	0.2246	0.411208
48	-0.024423	-0.4711	0.31894
49	-0.06699	-1.2921	0.098569
50	-0.031084	-0.5995	0.274592
51	-0.023084	-0.4452	0.328206
52	-0.061509	-1.1863	0.118122
53	-0.001646	-0.0318	0.487343
54	-0.002282	-0.044	0.482462
55	0.001113	0.0215	0.491441
56	-0.039442	-0.7607	0.223649
57	-0.0128	-0.2469	0.402567
58	-0.013281	-0.2562	0.398983
59	-0.018742	-0.3615	0.358969
60	-0.027922	-0.5385	0.29526

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code