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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 02 Jun 2010 21:52:38 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Jun/02/t1275515620ea76ifs8orsco4c.htm/, Retrieved Fri, 19 Apr 2024 17:34:32 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77331, Retrieved Fri, 19 Apr 2024 17:34:32 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W21

Estimated Impact

150

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [(Partial) Autocorrelation Function] [] [2010-06-02 21:52:38] [ba71a47f11e8062985d77fe3913d8d26] [Current]

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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	1 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77331&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77331&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77331&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	1 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.503443	-15.0949	0
2	0.009372	0.281	0.389381
3	0.036195	1.0852	0.139051
4	-0.037852	-1.1349	0.128353
5	-0.012622	-0.3784	0.352596
6	-0.00866	-0.2597	0.39759
7	0.042137	1.2634	0.103385
8	-0.013541	-0.406	0.34242
9	-0.055354	-1.6597	0.048662
10	0.108741	3.2604	0.000577
11	-0.083886	-2.5152	0.006035
12	-0.006045	-0.1813	0.428101
13	0.05459	1.6368	0.051011
14	-0.031612	-0.9478	0.171731
15	-0.002278	-0.0683	0.472776
16	-0.030978	-0.9288	0.176614
17	0.076326	2.2885	0.01117
18	-0.020907	-0.6269	0.265458
19	-0.056027	-1.6799	0.046663
20	0.086138	2.5827	0.00498
21	-0.05604	-1.6803	0.046626
22	-0.048882	-1.4656	0.071549
23	0.109634	3.2872	0.000526
24	-0.060493	-1.8138	0.035021
25	-0.023133	-0.6936	0.244052
26	0.045127	1.3531	0.088187
27	-0.024117	-0.7231	0.2349
28	0.009256	0.2775	0.390721
29	0.017916	0.5372	0.295634

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.503443 & -15.0949 & 0 \tabularnewline
2 & 0.009372 & 0.281 & 0.389381 \tabularnewline
3 & 0.036195 & 1.0852 & 0.139051 \tabularnewline
4 & -0.037852 & -1.1349 & 0.128353 \tabularnewline
5 & -0.012622 & -0.3784 & 0.352596 \tabularnewline
6 & -0.00866 & -0.2597 & 0.39759 \tabularnewline
7 & 0.042137 & 1.2634 & 0.103385 \tabularnewline
8 & -0.013541 & -0.406 & 0.34242 \tabularnewline
9 & -0.055354 & -1.6597 & 0.048662 \tabularnewline
10 & 0.108741 & 3.2604 & 0.000577 \tabularnewline
11 & -0.083886 & -2.5152 & 0.006035 \tabularnewline
12 & -0.006045 & -0.1813 & 0.428101 \tabularnewline
13 & 0.05459 & 1.6368 & 0.051011 \tabularnewline
14 & -0.031612 & -0.9478 & 0.171731 \tabularnewline
15 & -0.002278 & -0.0683 & 0.472776 \tabularnewline
16 & -0.030978 & -0.9288 & 0.176614 \tabularnewline
17 & 0.076326 & 2.2885 & 0.01117 \tabularnewline
18 & -0.020907 & -0.6269 & 0.265458 \tabularnewline
19 & -0.056027 & -1.6799 & 0.046663 \tabularnewline
20 & 0.086138 & 2.5827 & 0.00498 \tabularnewline
21 & -0.05604 & -1.6803 & 0.046626 \tabularnewline
22 & -0.048882 & -1.4656 & 0.071549 \tabularnewline
23 & 0.109634 & 3.2872 & 0.000526 \tabularnewline
24 & -0.060493 & -1.8138 & 0.035021 \tabularnewline
25 & -0.023133 & -0.6936 & 0.244052 \tabularnewline
26 & 0.045127 & 1.3531 & 0.088187 \tabularnewline
27 & -0.024117 & -0.7231 & 0.2349 \tabularnewline
28 & 0.009256 & 0.2775 & 0.390721 \tabularnewline
29 & 0.017916 & 0.5372 & 0.295634 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77331&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]-0.503443[/C][C]-15.0949[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.009372[/C][C]0.281[/C][C]0.389381[/C][/ROW]
[ROW][C]3[/C][C]0.036195[/C][C]1.0852[/C][C]0.139051[/C][/ROW]
[ROW][C]4[/C][C]-0.037852[/C][C]-1.1349[/C][C]0.128353[/C][/ROW]
[ROW][C]5[/C][C]-0.012622[/C][C]-0.3784[/C][C]0.352596[/C][/ROW]
[ROW][C]6[/C][C]-0.00866[/C][C]-0.2597[/C][C]0.39759[/C][/ROW]
[ROW][C]7[/C][C]0.042137[/C][C]1.2634[/C][C]0.103385[/C][/ROW]
[ROW][C]8[/C][C]-0.013541[/C][C]-0.406[/C][C]0.34242[/C][/ROW]
[ROW][C]9[/C][C]-0.055354[/C][C]-1.6597[/C][C]0.048662[/C][/ROW]
[ROW][C]10[/C][C]0.108741[/C][C]3.2604[/C][C]0.000577[/C][/ROW]
[ROW][C]11[/C][C]-0.083886[/C][C]-2.5152[/C][C]0.006035[/C][/ROW]
[ROW][C]12[/C][C]-0.006045[/C][C]-0.1813[/C][C]0.428101[/C][/ROW]
[ROW][C]13[/C][C]0.05459[/C][C]1.6368[/C][C]0.051011[/C][/ROW]
[ROW][C]14[/C][C]-0.031612[/C][C]-0.9478[/C][C]0.171731[/C][/ROW]
[ROW][C]15[/C][C]-0.002278[/C][C]-0.0683[/C][C]0.472776[/C][/ROW]
[ROW][C]16[/C][C]-0.030978[/C][C]-0.9288[/C][C]0.176614[/C][/ROW]
[ROW][C]17[/C][C]0.076326[/C][C]2.2885[/C][C]0.01117[/C][/ROW]
[ROW][C]18[/C][C]-0.020907[/C][C]-0.6269[/C][C]0.265458[/C][/ROW]
[ROW][C]19[/C][C]-0.056027[/C][C]-1.6799[/C][C]0.046663[/C][/ROW]
[ROW][C]20[/C][C]0.086138[/C][C]2.5827[/C][C]0.00498[/C][/ROW]
[ROW][C]21[/C][C]-0.05604[/C][C]-1.6803[/C][C]0.046626[/C][/ROW]
[ROW][C]22[/C][C]-0.048882[/C][C]-1.4656[/C][C]0.071549[/C][/ROW]
[ROW][C]23[/C][C]0.109634[/C][C]3.2872[/C][C]0.000526[/C][/ROW]
[ROW][C]24[/C][C]-0.060493[/C][C]-1.8138[/C][C]0.035021[/C][/ROW]
[ROW][C]25[/C][C]-0.023133[/C][C]-0.6936[/C][C]0.244052[/C][/ROW]
[ROW][C]26[/C][C]0.045127[/C][C]1.3531[/C][C]0.088187[/C][/ROW]
[ROW][C]27[/C][C]-0.024117[/C][C]-0.7231[/C][C]0.2349[/C][/ROW]
[ROW][C]28[/C][C]0.009256[/C][C]0.2775[/C][C]0.390721[/C][/ROW]
[ROW][C]29[/C][C]0.017916[/C][C]0.5372[/C][C]0.295634[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77331&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77331&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	-0.503443	-15.0949	0
2	0.009372	0.281	0.389381
3	0.036195	1.0852	0.139051
4	-0.037852	-1.1349	0.128353
5	-0.012622	-0.3784	0.352596
6	-0.00866	-0.2597	0.39759
7	0.042137	1.2634	0.103385
8	-0.013541	-0.406	0.34242
9	-0.055354	-1.6597	0.048662
10	0.108741	3.2604	0.000577
11	-0.083886	-2.5152	0.006035
12	-0.006045	-0.1813	0.428101
13	0.05459	1.6368	0.051011
14	-0.031612	-0.9478	0.171731
15	-0.002278	-0.0683	0.472776
16	-0.030978	-0.9288	0.176614
17	0.076326	2.2885	0.01117
18	-0.020907	-0.6269	0.265458
19	-0.056027	-1.6799	0.046663
20	0.086138	2.5827	0.00498
21	-0.05604	-1.6803	0.046626
22	-0.048882	-1.4656	0.071549
23	0.109634	3.2872	0.000526
24	-0.060493	-1.8138	0.035021
25	-0.023133	-0.6936	0.244052
26	0.045127	1.3531	0.088187
27	-0.024117	-0.7231	0.2349
28	0.009256	0.2775	0.390721
29	0.017916	0.5372	0.295634

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.503443	-15.0949	0
2	-0.32695	-9.8031	0
3	-0.183196	-5.4928	0
4	-0.154449	-4.6309	2e-06
5	-0.154941	-4.6456	2e-06
6	-0.165705	-4.9684	0
7	-0.094916	-2.8459	0.002265
8	-0.065806	-1.9731	0.024395
9	-0.143289	-4.2963	1e-05
10	-0.015461	-0.4636	0.321535
11	-0.058559	-1.7558	0.039732
12	-0.099293	-2.9771	0.001494
13	-0.04243	-1.2722	0.101816
14	-0.042564	-1.2762	0.101107
15	-0.049098	-1.4721	0.070671
16	-0.111311	-3.3375	0.00044
17	-0.027311	-0.8189	0.20654
18	0.012177	0.3651	0.357564
19	-0.05472	-1.6407	0.050606
20	0.012278	0.3681	0.356429
21	-0.002392	-0.0717	0.471423
22	-0.095783	-2.8719	0.002088
23	0.008748	0.2623	0.396572
24	-0.004724	-0.1417	0.443692
25	-0.062316	-1.8685	0.031012
26	-0.021068	-0.6317	0.263875
27	-0.051648	-1.5486	0.060917
28	-0.036835	-1.1044	0.134847
29	0.026062	0.7814	0.217377

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.503443 & -15.0949 & 0 \tabularnewline
2 & -0.32695 & -9.8031 & 0 \tabularnewline
3 & -0.183196 & -5.4928 & 0 \tabularnewline
4 & -0.154449 & -4.6309 & 2e-06 \tabularnewline
5 & -0.154941 & -4.6456 & 2e-06 \tabularnewline
6 & -0.165705 & -4.9684 & 0 \tabularnewline
7 & -0.094916 & -2.8459 & 0.002265 \tabularnewline
8 & -0.065806 & -1.9731 & 0.024395 \tabularnewline
9 & -0.143289 & -4.2963 & 1e-05 \tabularnewline
10 & -0.015461 & -0.4636 & 0.321535 \tabularnewline
11 & -0.058559 & -1.7558 & 0.039732 \tabularnewline
12 & -0.099293 & -2.9771 & 0.001494 \tabularnewline
13 & -0.04243 & -1.2722 & 0.101816 \tabularnewline
14 & -0.042564 & -1.2762 & 0.101107 \tabularnewline
15 & -0.049098 & -1.4721 & 0.070671 \tabularnewline
16 & -0.111311 & -3.3375 & 0.00044 \tabularnewline
17 & -0.027311 & -0.8189 & 0.20654 \tabularnewline
18 & 0.012177 & 0.3651 & 0.357564 \tabularnewline
19 & -0.05472 & -1.6407 & 0.050606 \tabularnewline
20 & 0.012278 & 0.3681 & 0.356429 \tabularnewline
21 & -0.002392 & -0.0717 & 0.471423 \tabularnewline
22 & -0.095783 & -2.8719 & 0.002088 \tabularnewline
23 & 0.008748 & 0.2623 & 0.396572 \tabularnewline
24 & -0.004724 & -0.1417 & 0.443692 \tabularnewline
25 & -0.062316 & -1.8685 & 0.031012 \tabularnewline
26 & -0.021068 & -0.6317 & 0.263875 \tabularnewline
27 & -0.051648 & -1.5486 & 0.060917 \tabularnewline
28 & -0.036835 & -1.1044 & 0.134847 \tabularnewline
29 & 0.026062 & 0.7814 & 0.217377 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77331&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]-0.503443[/C][C]-15.0949[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.32695[/C][C]-9.8031[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]-0.183196[/C][C]-5.4928[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]-0.154449[/C][C]-4.6309[/C][C]2e-06[/C][/ROW]
[ROW][C]5[/C][C]-0.154941[/C][C]-4.6456[/C][C]2e-06[/C][/ROW]
[ROW][C]6[/C][C]-0.165705[/C][C]-4.9684[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]-0.094916[/C][C]-2.8459[/C][C]0.002265[/C][/ROW]
[ROW][C]8[/C][C]-0.065806[/C][C]-1.9731[/C][C]0.024395[/C][/ROW]
[ROW][C]9[/C][C]-0.143289[/C][C]-4.2963[/C][C]1e-05[/C][/ROW]
[ROW][C]10[/C][C]-0.015461[/C][C]-0.4636[/C][C]0.321535[/C][/ROW]
[ROW][C]11[/C][C]-0.058559[/C][C]-1.7558[/C][C]0.039732[/C][/ROW]
[ROW][C]12[/C][C]-0.099293[/C][C]-2.9771[/C][C]0.001494[/C][/ROW]
[ROW][C]13[/C][C]-0.04243[/C][C]-1.2722[/C][C]0.101816[/C][/ROW]
[ROW][C]14[/C][C]-0.042564[/C][C]-1.2762[/C][C]0.101107[/C][/ROW]
[ROW][C]15[/C][C]-0.049098[/C][C]-1.4721[/C][C]0.070671[/C][/ROW]
[ROW][C]16[/C][C]-0.111311[/C][C]-3.3375[/C][C]0.00044[/C][/ROW]
[ROW][C]17[/C][C]-0.027311[/C][C]-0.8189[/C][C]0.20654[/C][/ROW]
[ROW][C]18[/C][C]0.012177[/C][C]0.3651[/C][C]0.357564[/C][/ROW]
[ROW][C]19[/C][C]-0.05472[/C][C]-1.6407[/C][C]0.050606[/C][/ROW]
[ROW][C]20[/C][C]0.012278[/C][C]0.3681[/C][C]0.356429[/C][/ROW]
[ROW][C]21[/C][C]-0.002392[/C][C]-0.0717[/C][C]0.471423[/C][/ROW]
[ROW][C]22[/C][C]-0.095783[/C][C]-2.8719[/C][C]0.002088[/C][/ROW]
[ROW][C]23[/C][C]0.008748[/C][C]0.2623[/C][C]0.396572[/C][/ROW]
[ROW][C]24[/C][C]-0.004724[/C][C]-0.1417[/C][C]0.443692[/C][/ROW]
[ROW][C]25[/C][C]-0.062316[/C][C]-1.8685[/C][C]0.031012[/C][/ROW]
[ROW][C]26[/C][C]-0.021068[/C][C]-0.6317[/C][C]0.263875[/C][/ROW]
[ROW][C]27[/C][C]-0.051648[/C][C]-1.5486[/C][C]0.060917[/C][/ROW]
[ROW][C]28[/C][C]-0.036835[/C][C]-1.1044[/C][C]0.134847[/C][/ROW]
[ROW][C]29[/C][C]0.026062[/C][C]0.7814[/C][C]0.217377[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77331&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77331&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	-0.503443	-15.0949	0
2	-0.32695	-9.8031	0
3	-0.183196	-5.4928	0
4	-0.154449	-4.6309	2e-06
5	-0.154941	-4.6456	2e-06
6	-0.165705	-4.9684	0
7	-0.094916	-2.8459	0.002265
8	-0.065806	-1.9731	0.024395
9	-0.143289	-4.2963	1e-05
10	-0.015461	-0.4636	0.321535
11	-0.058559	-1.7558	0.039732
12	-0.099293	-2.9771	0.001494
13	-0.04243	-1.2722	0.101816
14	-0.042564	-1.2762	0.101107
15	-0.049098	-1.4721	0.070671
16	-0.111311	-3.3375	0.00044
17	-0.027311	-0.8189	0.20654
18	0.012177	0.3651	0.357564
19	-0.05472	-1.6407	0.050606
20	0.012278	0.3681	0.356429
21	-0.002392	-0.0717	0.471423
22	-0.095783	-2.8719	0.002088
23	0.008748	0.2623	0.396572
24	-0.004724	-0.1417	0.443692
25	-0.062316	-1.8685	0.031012
26	-0.021068	-0.6317	0.263875
27	-0.051648	-1.5486	0.060917
28	-0.036835	-1.1044	0.134847
29	0.026062	0.7814	0.217377

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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 (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
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