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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 16 Jul 2008 03:25:44 -0600

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/2008/Jul/16/t1216200380vquh1g1wpet6h4g.htm/, Retrieved Tue, 22 Sep 2026 22:01:01 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13844, Retrieved Tue, 22 Sep 2026 22:01:01 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

668

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

-       [(Partial) Autocorrelation Function] [non-seasonal tren...] [2008-07-16 09:25:44] [d41d8cd98f00b204e9800998ecf8427e] [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	'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=13844&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=13844&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13844&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.166964	-4.5173	4e-06
2	-0.195012	-5.2762	0
3	-0.168444	-4.5573	3e-06
4	0.005484	0.1484	0.441045
5	0.06049	1.6366	0.051072
6	0.002962	0.0801	0.468072
7	-0.020879	-0.5649	0.286162
8	-0.0309	-0.836	0.201713
9	-0.03085	-0.8347	0.202092
10	0.046645	1.262	0.103675
11	-0.003933	-0.1064	0.457642
12	0.02911	0.7876	0.2156
13	-0.001614	-0.0437	0.482592
14	-0.033075	-0.8949	0.185576
15	-0.021018	-0.5687	0.28488
16	0.062585	1.6933	0.045415
17	-0.007453	-0.2016	0.420124
18	-0.001539	-0.0416	0.483396
19	-0.042904	-1.1608	0.123052
20	0.039246	1.0618	0.144336
21	-0.012643	-0.3421	0.366201
22	0.006642	0.1797	0.428718
23	-0.009994	-0.2704	0.393467
24	0.021902	0.5926	0.276825
25	-0.016508	-0.4466	0.327637
26	-0.03415	-0.924	0.177908
27	0.017629	0.477	0.316765
28	-0.02315	-0.6263	0.265641

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.166964 & -4.5173 & 4e-06 \tabularnewline
2 & -0.195012 & -5.2762 & 0 \tabularnewline
3 & -0.168444 & -4.5573 & 3e-06 \tabularnewline
4 & 0.005484 & 0.1484 & 0.441045 \tabularnewline
5 & 0.06049 & 1.6366 & 0.051072 \tabularnewline
6 & 0.002962 & 0.0801 & 0.468072 \tabularnewline
7 & -0.020879 & -0.5649 & 0.286162 \tabularnewline
8 & -0.0309 & -0.836 & 0.201713 \tabularnewline
9 & -0.03085 & -0.8347 & 0.202092 \tabularnewline
10 & 0.046645 & 1.262 & 0.103675 \tabularnewline
11 & -0.003933 & -0.1064 & 0.457642 \tabularnewline
12 & 0.02911 & 0.7876 & 0.2156 \tabularnewline
13 & -0.001614 & -0.0437 & 0.482592 \tabularnewline
14 & -0.033075 & -0.8949 & 0.185576 \tabularnewline
15 & -0.021018 & -0.5687 & 0.28488 \tabularnewline
16 & 0.062585 & 1.6933 & 0.045415 \tabularnewline
17 & -0.007453 & -0.2016 & 0.420124 \tabularnewline
18 & -0.001539 & -0.0416 & 0.483396 \tabularnewline
19 & -0.042904 & -1.1608 & 0.123052 \tabularnewline
20 & 0.039246 & 1.0618 & 0.144336 \tabularnewline
21 & -0.012643 & -0.3421 & 0.366201 \tabularnewline
22 & 0.006642 & 0.1797 & 0.428718 \tabularnewline
23 & -0.009994 & -0.2704 & 0.393467 \tabularnewline
24 & 0.021902 & 0.5926 & 0.276825 \tabularnewline
25 & -0.016508 & -0.4466 & 0.327637 \tabularnewline
26 & -0.03415 & -0.924 & 0.177908 \tabularnewline
27 & 0.017629 & 0.477 & 0.316765 \tabularnewline
28 & -0.02315 & -0.6263 & 0.265641 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13844&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]-0.166964[/C][C]-4.5173[/C][C]4e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.195012[/C][C]-5.2762[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]-0.168444[/C][C]-4.5573[/C][C]3e-06[/C][/ROW]
[ROW][C]4[/C][C]0.005484[/C][C]0.1484[/C][C]0.441045[/C][/ROW]
[ROW][C]5[/C][C]0.06049[/C][C]1.6366[/C][C]0.051072[/C][/ROW]
[ROW][C]6[/C][C]0.002962[/C][C]0.0801[/C][C]0.468072[/C][/ROW]
[ROW][C]7[/C][C]-0.020879[/C][C]-0.5649[/C][C]0.286162[/C][/ROW]
[ROW][C]8[/C][C]-0.0309[/C][C]-0.836[/C][C]0.201713[/C][/ROW]
[ROW][C]9[/C][C]-0.03085[/C][C]-0.8347[/C][C]0.202092[/C][/ROW]
[ROW][C]10[/C][C]0.046645[/C][C]1.262[/C][C]0.103675[/C][/ROW]
[ROW][C]11[/C][C]-0.003933[/C][C]-0.1064[/C][C]0.457642[/C][/ROW]
[ROW][C]12[/C][C]0.02911[/C][C]0.7876[/C][C]0.2156[/C][/ROW]
[ROW][C]13[/C][C]-0.001614[/C][C]-0.0437[/C][C]0.482592[/C][/ROW]
[ROW][C]14[/C][C]-0.033075[/C][C]-0.8949[/C][C]0.185576[/C][/ROW]
[ROW][C]15[/C][C]-0.021018[/C][C]-0.5687[/C][C]0.28488[/C][/ROW]
[ROW][C]16[/C][C]0.062585[/C][C]1.6933[/C][C]0.045415[/C][/ROW]
[ROW][C]17[/C][C]-0.007453[/C][C]-0.2016[/C][C]0.420124[/C][/ROW]
[ROW][C]18[/C][C]-0.001539[/C][C]-0.0416[/C][C]0.483396[/C][/ROW]
[ROW][C]19[/C][C]-0.042904[/C][C]-1.1608[/C][C]0.123052[/C][/ROW]
[ROW][C]20[/C][C]0.039246[/C][C]1.0618[/C][C]0.144336[/C][/ROW]
[ROW][C]21[/C][C]-0.012643[/C][C]-0.3421[/C][C]0.366201[/C][/ROW]
[ROW][C]22[/C][C]0.006642[/C][C]0.1797[/C][C]0.428718[/C][/ROW]
[ROW][C]23[/C][C]-0.009994[/C][C]-0.2704[/C][C]0.393467[/C][/ROW]
[ROW][C]24[/C][C]0.021902[/C][C]0.5926[/C][C]0.276825[/C][/ROW]
[ROW][C]25[/C][C]-0.016508[/C][C]-0.4466[/C][C]0.327637[/C][/ROW]
[ROW][C]26[/C][C]-0.03415[/C][C]-0.924[/C][C]0.177908[/C][/ROW]
[ROW][C]27[/C][C]0.017629[/C][C]0.477[/C][C]0.316765[/C][/ROW]
[ROW][C]28[/C][C]-0.02315[/C][C]-0.6263[/C][C]0.265641[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13844&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13844&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	-0.166964	-4.5173	4e-06
2	-0.195012	-5.2762	0
3	-0.168444	-4.5573	3e-06
4	0.005484	0.1484	0.441045
5	0.06049	1.6366	0.051072
6	0.002962	0.0801	0.468072
7	-0.020879	-0.5649	0.286162
8	-0.0309	-0.836	0.201713
9	-0.03085	-0.8347	0.202092
10	0.046645	1.262	0.103675
11	-0.003933	-0.1064	0.457642
12	0.02911	0.7876	0.2156
13	-0.001614	-0.0437	0.482592
14	-0.033075	-0.8949	0.185576
15	-0.021018	-0.5687	0.28488
16	0.062585	1.6933	0.045415
17	-0.007453	-0.2016	0.420124
18	-0.001539	-0.0416	0.483396
19	-0.042904	-1.1608	0.123052
20	0.039246	1.0618	0.144336
21	-0.012643	-0.3421	0.366201
22	0.006642	0.1797	0.428718
23	-0.009994	-0.2704	0.393467
24	0.021902	0.5926	0.276825
25	-0.016508	-0.4466	0.327637
26	-0.03415	-0.924	0.177908
27	0.017629	0.477	0.316765
28	-0.02315	-0.6263	0.265641

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.166964	-4.5173	4e-06
2	-0.229281	-6.2033	0
3	-0.26791	-7.2484	0
4	-0.163294	-4.418	6e-06
5	-0.097957	-2.6503	0.004108
6	-0.106003	-2.868	0.002125
7	-0.0949	-2.5676	0.00522
8	-0.101974	-2.759	0.002972
9	-0.128355	-3.4727	0.000273
10	-0.064801	-1.7532	0.039992
11	-0.094038	-2.5442	0.005578
12	-0.043969	-1.1896	0.117294
13	-0.038055	-1.0296	0.151773
14	-0.068853	-1.8629	0.031442
15	-0.076395	-2.0669	0.019548
16	0.004923	0.1332	0.447034
17	-0.038293	-1.036	0.150266
18	-0.015822	-0.4281	0.334363
19	-0.047268	-1.2788	0.100678
20	0.011957	0.3235	0.373207
21	-0.026041	-0.7045	0.240657
22	-0.00925	-0.2503	0.401231
23	-0.015859	-0.4291	0.333995
24	0.019114	0.5171	0.302604
25	-0.008649	-0.234	0.407529
26	-0.044633	-1.2076	0.1138
27	-0.005548	-0.1501	0.440366
28	-0.065228	-1.7648	0.03901

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.166964 & -4.5173 & 4e-06 \tabularnewline
2 & -0.229281 & -6.2033 & 0 \tabularnewline
3 & -0.26791 & -7.2484 & 0 \tabularnewline
4 & -0.163294 & -4.418 & 6e-06 \tabularnewline
5 & -0.097957 & -2.6503 & 0.004108 \tabularnewline
6 & -0.106003 & -2.868 & 0.002125 \tabularnewline
7 & -0.0949 & -2.5676 & 0.00522 \tabularnewline
8 & -0.101974 & -2.759 & 0.002972 \tabularnewline
9 & -0.128355 & -3.4727 & 0.000273 \tabularnewline
10 & -0.064801 & -1.7532 & 0.039992 \tabularnewline
11 & -0.094038 & -2.5442 & 0.005578 \tabularnewline
12 & -0.043969 & -1.1896 & 0.117294 \tabularnewline
13 & -0.038055 & -1.0296 & 0.151773 \tabularnewline
14 & -0.068853 & -1.8629 & 0.031442 \tabularnewline
15 & -0.076395 & -2.0669 & 0.019548 \tabularnewline
16 & 0.004923 & 0.1332 & 0.447034 \tabularnewline
17 & -0.038293 & -1.036 & 0.150266 \tabularnewline
18 & -0.015822 & -0.4281 & 0.334363 \tabularnewline
19 & -0.047268 & -1.2788 & 0.100678 \tabularnewline
20 & 0.011957 & 0.3235 & 0.373207 \tabularnewline
21 & -0.026041 & -0.7045 & 0.240657 \tabularnewline
22 & -0.00925 & -0.2503 & 0.401231 \tabularnewline
23 & -0.015859 & -0.4291 & 0.333995 \tabularnewline
24 & 0.019114 & 0.5171 & 0.302604 \tabularnewline
25 & -0.008649 & -0.234 & 0.407529 \tabularnewline
26 & -0.044633 & -1.2076 & 0.1138 \tabularnewline
27 & -0.005548 & -0.1501 & 0.440366 \tabularnewline
28 & -0.065228 & -1.7648 & 0.03901 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13844&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]-0.166964[/C][C]-4.5173[/C][C]4e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.229281[/C][C]-6.2033[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]-0.26791[/C][C]-7.2484[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]-0.163294[/C][C]-4.418[/C][C]6e-06[/C][/ROW]
[ROW][C]5[/C][C]-0.097957[/C][C]-2.6503[/C][C]0.004108[/C][/ROW]
[ROW][C]6[/C][C]-0.106003[/C][C]-2.868[/C][C]0.002125[/C][/ROW]
[ROW][C]7[/C][C]-0.0949[/C][C]-2.5676[/C][C]0.00522[/C][/ROW]
[ROW][C]8[/C][C]-0.101974[/C][C]-2.759[/C][C]0.002972[/C][/ROW]
[ROW][C]9[/C][C]-0.128355[/C][C]-3.4727[/C][C]0.000273[/C][/ROW]
[ROW][C]10[/C][C]-0.064801[/C][C]-1.7532[/C][C]0.039992[/C][/ROW]
[ROW][C]11[/C][C]-0.094038[/C][C]-2.5442[/C][C]0.005578[/C][/ROW]
[ROW][C]12[/C][C]-0.043969[/C][C]-1.1896[/C][C]0.117294[/C][/ROW]
[ROW][C]13[/C][C]-0.038055[/C][C]-1.0296[/C][C]0.151773[/C][/ROW]
[ROW][C]14[/C][C]-0.068853[/C][C]-1.8629[/C][C]0.031442[/C][/ROW]
[ROW][C]15[/C][C]-0.076395[/C][C]-2.0669[/C][C]0.019548[/C][/ROW]
[ROW][C]16[/C][C]0.004923[/C][C]0.1332[/C][C]0.447034[/C][/ROW]
[ROW][C]17[/C][C]-0.038293[/C][C]-1.036[/C][C]0.150266[/C][/ROW]
[ROW][C]18[/C][C]-0.015822[/C][C]-0.4281[/C][C]0.334363[/C][/ROW]
[ROW][C]19[/C][C]-0.047268[/C][C]-1.2788[/C][C]0.100678[/C][/ROW]
[ROW][C]20[/C][C]0.011957[/C][C]0.3235[/C][C]0.373207[/C][/ROW]
[ROW][C]21[/C][C]-0.026041[/C][C]-0.7045[/C][C]0.240657[/C][/ROW]
[ROW][C]22[/C][C]-0.00925[/C][C]-0.2503[/C][C]0.401231[/C][/ROW]
[ROW][C]23[/C][C]-0.015859[/C][C]-0.4291[/C][C]0.333995[/C][/ROW]
[ROW][C]24[/C][C]0.019114[/C][C]0.5171[/C][C]0.302604[/C][/ROW]
[ROW][C]25[/C][C]-0.008649[/C][C]-0.234[/C][C]0.407529[/C][/ROW]
[ROW][C]26[/C][C]-0.044633[/C][C]-1.2076[/C][C]0.1138[/C][/ROW]
[ROW][C]27[/C][C]-0.005548[/C][C]-0.1501[/C][C]0.440366[/C][/ROW]
[ROW][C]28[/C][C]-0.065228[/C][C]-1.7648[/C][C]0.03901[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13844&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13844&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	-0.166964	-4.5173	4e-06
2	-0.229281	-6.2033	0
3	-0.26791	-7.2484	0
4	-0.163294	-4.418	6e-06
5	-0.097957	-2.6503	0.004108
6	-0.106003	-2.868	0.002125
7	-0.0949	-2.5676	0.00522
8	-0.101974	-2.759	0.002972
9	-0.128355	-3.4727	0.000273
10	-0.064801	-1.7532	0.039992
11	-0.094038	-2.5442	0.005578
12	-0.043969	-1.1896	0.117294
13	-0.038055	-1.0296	0.151773
14	-0.068853	-1.8629	0.031442
15	-0.076395	-2.0669	0.019548
16	0.004923	0.1332	0.447034
17	-0.038293	-1.036	0.150266
18	-0.015822	-0.4281	0.334363
19	-0.047268	-1.2788	0.100678
20	0.011957	0.3235	0.373207
21	-0.026041	-0.7045	0.240657
22	-0.00925	-0.2503	0.401231
23	-0.015859	-0.4291	0.333995
24	0.019114	0.5171	0.302604
25	-0.008649	-0.234	0.407529
26	-0.044633	-1.2076	0.1138
27	-0.005548	-0.1501	0.440366
28	-0.065228	-1.7648	0.03901

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 = 1 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 1 ;

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