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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 22 Nov 2010 15:03:10 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/22/t1290438070nj7m4gprvf7sxd7.htm/, Retrieved Fri, 28 Aug 2026 16:14:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=98569, Retrieved Fri, 28 Aug 2026 16:14:47 +0000

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471

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-       [(Partial) Autocorrelation Function] [] [2010-11-22 15:03:10] [9b9a58c480cb5dafe4bfceb51e1cfd12] [Current]

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Dataseries X:

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-3.5527136788005E-14
0.016941797155665
1.1546319456102E-14
1.1546319456102E-14
-0.016941797155689
0.016941797155665
1.1546319456102E-14
1.1546319456102E-14
1.1546319456102E-14
1.1546319456102E-14
1.1546319456102E-14
-0.016941797155689
-3.5527136788005E-14
-3.5527136788005E-14
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0.016941797155665
0.012632696758011
2.6645352591004E-14
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-4.2632564145606E-14
0.016271545440057
2.6645352591004E-14
2.6645352591004E-14
-0.016271545440073
-4.2632564145606E-14
0.016271545440057
2.6645352591004E-14
2.6645352591004E-14
-0.016271545440073
0.016271545440057
2.6645352591004E-14
2.6645352591004E-14
-0.016271545440073
-4.2632564145606E-14
-4.2632564145606E-14
-4.2632564145606E-14
0.016271545440057
2.6645352591004E-14
2.6645352591004E-14
2.6645352591004E-14
-0.016271545440073
0.016271545440057
2.6645352591004E-14
-0.016271545440073
0.016271545440057
2.6645352591004E-14
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-4.2632564145606E-14
-4.2632564145606E-14
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0.016271545440057
2.6645352591004E-14
2.6645352591004E-14
2.6645352591004E-14
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2.6645352591004E-14
2.6645352591004E-14
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0.0088466041402575
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2.6201263381154E-14
0.015934778323926
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2.6201263381154E-14
2.6201263381154E-14
0.015934778323926
-3.5971225997855E-14
-3.5971225997855E-14
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2.6201263381154E-14
0.015934778323926
-0.015934778323936
0.015934778323926
-3.5971225997855E-14
-3.5971225997855E-14
-0.015934778323936
0.015934778323926
-3.5971225997855E-14
-3.5971225997855E-14
-3.5971225997855E-14
-3.5971225997855E-14
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-3.5971225997855E-14
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2.6201263381154E-14
2.6201263381154E-14
2.6201263381154E-14
0.015934778323926
-3.5971225997855E-14
-3.5971225997855E-14
-3.5971225997855E-14
-0.015934778323936
2.6201263381154E-14
2.6201263381154E-14
2.6201263381154E-14
2.6201263381154E-14
2.6201263381154E-14
2.6201263381154E-14
2.6201263381154E-14
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0.016025984015882
3.7303493627405E-14
3.7303493627405E-14
-0.016025984015863
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3.7303493627405E-14
3.7303493627405E-14
3.7303493627405E-14
-0.016025984015863
-1.7763568394003E-14
0.016025984015882
3.7303493627405E-14
3.7303493627405E-14
-0.016025984015863
-1.7763568394003E-14
0.016025984015882
3.7303493627405E-14
-0.016025984015863
-0.0036994261844177
1.4210854715202E-14
1.4210854715202E-14
1.4210854715202E-14
1.4210854715202E-14
0.016768510513714
-2.5757174171304E-14
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1.4210854715202E-14
1.4210854715202E-14
0.016768510513714
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1.4210854715202E-14
1.4210854715202E-14
0.016768510513714
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1.4210854715202E-14
1.4210854715202E-14
0.016768510513714
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-2.5757174171304E-14
-2.5757174171304E-14
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1.4210854715202E-14
1.4210854715202E-14
1.4210854715202E-14
1.4210854715202E-14
0.016768510513714
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-2.5757174171304E-14
-0.016768510513725
1.4210854715202E-14
1.4210854715202E-14
1.4210854715202E-14
1.4210854715202E-14
1.4210854715202E-14
1.4210854715202E-14
1.4210854715202E-14
1.4210854715202E-14

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 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 & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=98569&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]2 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=98569&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=98569&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	2 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.159445	-2.2549	0.012612
2	-0.214522	-3.0338	0.001368
3	-0.164913	-2.3322	0.010342
4	-0.038084	-0.5386	0.295384
5	0.17659	2.4974	0.006659
6	-0.028314	-0.4004	0.344639
7	-0.028344	-0.4008	0.344481
8	-0.007977	-0.1128	0.455149
9	-0.08411	-1.1895	0.117828
10	0.000697	0.0099	0.496072
11	0.028207	0.3989	0.345194
12	-0.015609	-0.2207	0.41276
13	0.058683	0.8299	0.20379
14	-0.010143	-0.1434	0.44304
15	-0.001186	-0.0168	0.493319
16	0.09301	1.3154	0.094948
17	-0.014177	-0.2005	0.420648
18	-0.067412	-0.9533	0.170783
19	-0.018767	-0.2654	0.395483
20	-0.004303	-0.0608	0.47577
21	-0.003052	-0.0432	0.482809
22	0.016247	0.2298	0.409252
23	-0.019972	-0.2824	0.388946

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.159445 & -2.2549 & 0.012612 \tabularnewline
2 & -0.214522 & -3.0338 & 0.001368 \tabularnewline
3 & -0.164913 & -2.3322 & 0.010342 \tabularnewline
4 & -0.038084 & -0.5386 & 0.295384 \tabularnewline
5 & 0.17659 & 2.4974 & 0.006659 \tabularnewline
6 & -0.028314 & -0.4004 & 0.344639 \tabularnewline
7 & -0.028344 & -0.4008 & 0.344481 \tabularnewline
8 & -0.007977 & -0.1128 & 0.455149 \tabularnewline
9 & -0.08411 & -1.1895 & 0.117828 \tabularnewline
10 & 0.000697 & 0.0099 & 0.496072 \tabularnewline
11 & 0.028207 & 0.3989 & 0.345194 \tabularnewline
12 & -0.015609 & -0.2207 & 0.41276 \tabularnewline
13 & 0.058683 & 0.8299 & 0.20379 \tabularnewline
14 & -0.010143 & -0.1434 & 0.44304 \tabularnewline
15 & -0.001186 & -0.0168 & 0.493319 \tabularnewline
16 & 0.09301 & 1.3154 & 0.094948 \tabularnewline
17 & -0.014177 & -0.2005 & 0.420648 \tabularnewline
18 & -0.067412 & -0.9533 & 0.170783 \tabularnewline
19 & -0.018767 & -0.2654 & 0.395483 \tabularnewline
20 & -0.004303 & -0.0608 & 0.47577 \tabularnewline
21 & -0.003052 & -0.0432 & 0.482809 \tabularnewline
22 & 0.016247 & 0.2298 & 0.409252 \tabularnewline
23 & -0.019972 & -0.2824 & 0.388946 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=98569&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]-0.159445[/C][C]-2.2549[/C][C]0.012612[/C][/ROW]
[ROW][C]2[/C][C]-0.214522[/C][C]-3.0338[/C][C]0.001368[/C][/ROW]
[ROW][C]3[/C][C]-0.164913[/C][C]-2.3322[/C][C]0.010342[/C][/ROW]
[ROW][C]4[/C][C]-0.038084[/C][C]-0.5386[/C][C]0.295384[/C][/ROW]
[ROW][C]5[/C][C]0.17659[/C][C]2.4974[/C][C]0.006659[/C][/ROW]
[ROW][C]6[/C][C]-0.028314[/C][C]-0.4004[/C][C]0.344639[/C][/ROW]
[ROW][C]7[/C][C]-0.028344[/C][C]-0.4008[/C][C]0.344481[/C][/ROW]
[ROW][C]8[/C][C]-0.007977[/C][C]-0.1128[/C][C]0.455149[/C][/ROW]
[ROW][C]9[/C][C]-0.08411[/C][C]-1.1895[/C][C]0.117828[/C][/ROW]
[ROW][C]10[/C][C]0.000697[/C][C]0.0099[/C][C]0.496072[/C][/ROW]
[ROW][C]11[/C][C]0.028207[/C][C]0.3989[/C][C]0.345194[/C][/ROW]
[ROW][C]12[/C][C]-0.015609[/C][C]-0.2207[/C][C]0.41276[/C][/ROW]
[ROW][C]13[/C][C]0.058683[/C][C]0.8299[/C][C]0.20379[/C][/ROW]
[ROW][C]14[/C][C]-0.010143[/C][C]-0.1434[/C][C]0.44304[/C][/ROW]
[ROW][C]15[/C][C]-0.001186[/C][C]-0.0168[/C][C]0.493319[/C][/ROW]
[ROW][C]16[/C][C]0.09301[/C][C]1.3154[/C][C]0.094948[/C][/ROW]
[ROW][C]17[/C][C]-0.014177[/C][C]-0.2005[/C][C]0.420648[/C][/ROW]
[ROW][C]18[/C][C]-0.067412[/C][C]-0.9533[/C][C]0.170783[/C][/ROW]
[ROW][C]19[/C][C]-0.018767[/C][C]-0.2654[/C][C]0.395483[/C][/ROW]
[ROW][C]20[/C][C]-0.004303[/C][C]-0.0608[/C][C]0.47577[/C][/ROW]
[ROW][C]21[/C][C]-0.003052[/C][C]-0.0432[/C][C]0.482809[/C][/ROW]
[ROW][C]22[/C][C]0.016247[/C][C]0.2298[/C][C]0.409252[/C][/ROW]
[ROW][C]23[/C][C]-0.019972[/C][C]-0.2824[/C][C]0.388946[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=98569&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=98569&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	-0.159445	-2.2549	0.012612
2	-0.214522	-3.0338	0.001368
3	-0.164913	-2.3322	0.010342
4	-0.038084	-0.5386	0.295384
5	0.17659	2.4974	0.006659
6	-0.028314	-0.4004	0.344639
7	-0.028344	-0.4008	0.344481
8	-0.007977	-0.1128	0.455149
9	-0.08411	-1.1895	0.117828
10	0.000697	0.0099	0.496072
11	0.028207	0.3989	0.345194
12	-0.015609	-0.2207	0.41276
13	0.058683	0.8299	0.20379
14	-0.010143	-0.1434	0.44304
15	-0.001186	-0.0168	0.493319
16	0.09301	1.3154	0.094948
17	-0.014177	-0.2005	0.420648
18	-0.067412	-0.9533	0.170783
19	-0.018767	-0.2654	0.395483
20	-0.004303	-0.0608	0.47577
21	-0.003052	-0.0432	0.482809
22	0.016247	0.2298	0.409252
23	-0.019972	-0.2824	0.388946

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.159445	-2.2549	0.012612
2	-0.246204	-3.4819	0.000306
3	-0.269573	-3.8123	9.2e-05
4	-0.222724	-3.1498	0.000942
5	-0.002781	-0.0393	0.484332
6	-0.108525	-1.5348	0.06321
7	-0.064284	-0.9091	0.182192
8	-0.025761	-0.3643	0.358003
9	-0.12915	-1.8265	0.034636
10	-0.121006	-1.7113	0.044289
11	-0.083935	-1.187	0.118314
12	-0.13677	-1.9342	0.027249
13	-0.05284	-0.7473	0.227891
14	-0.05152	-0.7286	0.233548
15	-0.041472	-0.5865	0.279101
16	0.090911	1.2857	0.100022
17	0.06476	0.9158	0.180426
18	-0.015706	-0.2221	0.412224
19	0.016165	0.2286	0.409702
20	-0.005033	-0.0712	0.471664
21	-0.071835	-1.0159	0.155452
22	-0.017327	-0.245	0.403339
23	-0.030982	-0.4382	0.330875

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.159445 & -2.2549 & 0.012612 \tabularnewline
2 & -0.246204 & -3.4819 & 0.000306 \tabularnewline
3 & -0.269573 & -3.8123 & 9.2e-05 \tabularnewline
4 & -0.222724 & -3.1498 & 0.000942 \tabularnewline
5 & -0.002781 & -0.0393 & 0.484332 \tabularnewline
6 & -0.108525 & -1.5348 & 0.06321 \tabularnewline
7 & -0.064284 & -0.9091 & 0.182192 \tabularnewline
8 & -0.025761 & -0.3643 & 0.358003 \tabularnewline
9 & -0.12915 & -1.8265 & 0.034636 \tabularnewline
10 & -0.121006 & -1.7113 & 0.044289 \tabularnewline
11 & -0.083935 & -1.187 & 0.118314 \tabularnewline
12 & -0.13677 & -1.9342 & 0.027249 \tabularnewline
13 & -0.05284 & -0.7473 & 0.227891 \tabularnewline
14 & -0.05152 & -0.7286 & 0.233548 \tabularnewline
15 & -0.041472 & -0.5865 & 0.279101 \tabularnewline
16 & 0.090911 & 1.2857 & 0.100022 \tabularnewline
17 & 0.06476 & 0.9158 & 0.180426 \tabularnewline
18 & -0.015706 & -0.2221 & 0.412224 \tabularnewline
19 & 0.016165 & 0.2286 & 0.409702 \tabularnewline
20 & -0.005033 & -0.0712 & 0.471664 \tabularnewline
21 & -0.071835 & -1.0159 & 0.155452 \tabularnewline
22 & -0.017327 & -0.245 & 0.403339 \tabularnewline
23 & -0.030982 & -0.4382 & 0.330875 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=98569&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]-0.159445[/C][C]-2.2549[/C][C]0.012612[/C][/ROW]
[ROW][C]2[/C][C]-0.246204[/C][C]-3.4819[/C][C]0.000306[/C][/ROW]
[ROW][C]3[/C][C]-0.269573[/C][C]-3.8123[/C][C]9.2e-05[/C][/ROW]
[ROW][C]4[/C][C]-0.222724[/C][C]-3.1498[/C][C]0.000942[/C][/ROW]
[ROW][C]5[/C][C]-0.002781[/C][C]-0.0393[/C][C]0.484332[/C][/ROW]
[ROW][C]6[/C][C]-0.108525[/C][C]-1.5348[/C][C]0.06321[/C][/ROW]
[ROW][C]7[/C][C]-0.064284[/C][C]-0.9091[/C][C]0.182192[/C][/ROW]
[ROW][C]8[/C][C]-0.025761[/C][C]-0.3643[/C][C]0.358003[/C][/ROW]
[ROW][C]9[/C][C]-0.12915[/C][C]-1.8265[/C][C]0.034636[/C][/ROW]
[ROW][C]10[/C][C]-0.121006[/C][C]-1.7113[/C][C]0.044289[/C][/ROW]
[ROW][C]11[/C][C]-0.083935[/C][C]-1.187[/C][C]0.118314[/C][/ROW]
[ROW][C]12[/C][C]-0.13677[/C][C]-1.9342[/C][C]0.027249[/C][/ROW]
[ROW][C]13[/C][C]-0.05284[/C][C]-0.7473[/C][C]0.227891[/C][/ROW]
[ROW][C]14[/C][C]-0.05152[/C][C]-0.7286[/C][C]0.233548[/C][/ROW]
[ROW][C]15[/C][C]-0.041472[/C][C]-0.5865[/C][C]0.279101[/C][/ROW]
[ROW][C]16[/C][C]0.090911[/C][C]1.2857[/C][C]0.100022[/C][/ROW]
[ROW][C]17[/C][C]0.06476[/C][C]0.9158[/C][C]0.180426[/C][/ROW]
[ROW][C]18[/C][C]-0.015706[/C][C]-0.2221[/C][C]0.412224[/C][/ROW]
[ROW][C]19[/C][C]0.016165[/C][C]0.2286[/C][C]0.409702[/C][/ROW]
[ROW][C]20[/C][C]-0.005033[/C][C]-0.0712[/C][C]0.471664[/C][/ROW]
[ROW][C]21[/C][C]-0.071835[/C][C]-1.0159[/C][C]0.155452[/C][/ROW]
[ROW][C]22[/C][C]-0.017327[/C][C]-0.245[/C][C]0.403339[/C][/ROW]
[ROW][C]23[/C][C]-0.030982[/C][C]-0.4382[/C][C]0.330875[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=98569&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=98569&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	-0.159445	-2.2549	0.012612
2	-0.246204	-3.4819	0.000306
3	-0.269573	-3.8123	9.2e-05
4	-0.222724	-3.1498	0.000942
5	-0.002781	-0.0393	0.484332
6	-0.108525	-1.5348	0.06321
7	-0.064284	-0.9091	0.182192
8	-0.025761	-0.3643	0.358003
9	-0.12915	-1.8265	0.034636
10	-0.121006	-1.7113	0.044289
11	-0.083935	-1.187	0.118314
12	-0.13677	-1.9342	0.027249
13	-0.05284	-0.7473	0.227891
14	-0.05152	-0.7286	0.233548
15	-0.041472	-0.5865	0.279101
16	0.090911	1.2857	0.100022
17	0.06476	0.9158	0.180426
18	-0.015706	-0.2221	0.412224
19	0.016165	0.2286	0.409702
20	-0.005033	-0.0712	0.471664
21	-0.071835	-1.0159	0.155452
22	-0.017327	-0.245	0.403339
23	-0.030982	-0.4382	0.330875

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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