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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 16 Jul 2008 03:23:32 -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/t1216200263vfu8od4cl2cvonu.htm/, Retrieved Sat, 01 Aug 2026 11:20:05 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13843, Retrieved Sat, 01 Aug 2026 11:20:05 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

618

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

-       [(Partial) Autocorrelation Function] [non-seasonal trend] [2008-07-16 09:23:32] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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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	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13843&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13843&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13843&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	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.798921	21.63	0
2	0.663924	17.9751	0
3	0.60475	16.373	0
4	0.61293	16.5944	0
5	0.619238	16.7652	0
6	0.602046	16.2998	0
7	0.583869	15.8077	0
8	0.574086	15.5428	0
9	0.576135	15.5983	0
10	0.591318	16.0093	0
11	0.587916	15.9172	0
12	0.586742	15.8854	0
13	0.573702	15.5324	0
14	0.562521	15.2297	0
15	0.563396	15.2534	0
16	0.572575	15.5019	0
17	0.557483	15.0933	0
18	0.546236	14.7888	0
19	0.535933	14.5098	0
20	0.542343	14.6834	0
21	0.533984	14.4571	0
22	0.530032	14.3501	0
23	0.525293	14.2218	0
24	0.523764	14.1804	0
25	0.510161	13.8121	0
26	0.502828	13.6136	0
27	0.510179	13.8126	0
28	0.510544	13.8225	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.798921 & 21.63 & 0 \tabularnewline
2 & 0.663924 & 17.9751 & 0 \tabularnewline
3 & 0.60475 & 16.373 & 0 \tabularnewline
4 & 0.61293 & 16.5944 & 0 \tabularnewline
5 & 0.619238 & 16.7652 & 0 \tabularnewline
6 & 0.602046 & 16.2998 & 0 \tabularnewline
7 & 0.583869 & 15.8077 & 0 \tabularnewline
8 & 0.574086 & 15.5428 & 0 \tabularnewline
9 & 0.576135 & 15.5983 & 0 \tabularnewline
10 & 0.591318 & 16.0093 & 0 \tabularnewline
11 & 0.587916 & 15.9172 & 0 \tabularnewline
12 & 0.586742 & 15.8854 & 0 \tabularnewline
13 & 0.573702 & 15.5324 & 0 \tabularnewline
14 & 0.562521 & 15.2297 & 0 \tabularnewline
15 & 0.563396 & 15.2534 & 0 \tabularnewline
16 & 0.572575 & 15.5019 & 0 \tabularnewline
17 & 0.557483 & 15.0933 & 0 \tabularnewline
18 & 0.546236 & 14.7888 & 0 \tabularnewline
19 & 0.535933 & 14.5098 & 0 \tabularnewline
20 & 0.542343 & 14.6834 & 0 \tabularnewline
21 & 0.533984 & 14.4571 & 0 \tabularnewline
22 & 0.530032 & 14.3501 & 0 \tabularnewline
23 & 0.525293 & 14.2218 & 0 \tabularnewline
24 & 0.523764 & 14.1804 & 0 \tabularnewline
25 & 0.510161 & 13.8121 & 0 \tabularnewline
26 & 0.502828 & 13.6136 & 0 \tabularnewline
27 & 0.510179 & 13.8126 & 0 \tabularnewline
28 & 0.510544 & 13.8225 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13843&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]0.798921[/C][C]21.63[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.663924[/C][C]17.9751[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.60475[/C][C]16.373[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.61293[/C][C]16.5944[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.619238[/C][C]16.7652[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.602046[/C][C]16.2998[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.583869[/C][C]15.8077[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.574086[/C][C]15.5428[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.576135[/C][C]15.5983[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.591318[/C][C]16.0093[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.587916[/C][C]15.9172[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.586742[/C][C]15.8854[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.573702[/C][C]15.5324[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.562521[/C][C]15.2297[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.563396[/C][C]15.2534[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.572575[/C][C]15.5019[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.557483[/C][C]15.0933[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.546236[/C][C]14.7888[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.535933[/C][C]14.5098[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.542343[/C][C]14.6834[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.533984[/C][C]14.4571[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]0.530032[/C][C]14.3501[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]0.525293[/C][C]14.2218[/C][C]0[/C][/ROW]
[ROW][C]24[/C][C]0.523764[/C][C]14.1804[/C][C]0[/C][/ROW]
[ROW][C]25[/C][C]0.510161[/C][C]13.8121[/C][C]0[/C][/ROW]
[ROW][C]26[/C][C]0.502828[/C][C]13.6136[/C][C]0[/C][/ROW]
[ROW][C]27[/C][C]0.510179[/C][C]13.8126[/C][C]0[/C][/ROW]
[ROW][C]28[/C][C]0.510544[/C][C]13.8225[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13843&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13843&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	0.798921	21.63	0
2	0.663924	17.9751	0
3	0.60475	16.373	0
4	0.61293	16.5944	0
5	0.619238	16.7652	0
6	0.602046	16.2998	0
7	0.583869	15.8077	0
8	0.574086	15.5428	0
9	0.576135	15.5983	0
10	0.591318	16.0093	0
11	0.587916	15.9172	0
12	0.586742	15.8854	0
13	0.573702	15.5324	0
14	0.562521	15.2297	0
15	0.563396	15.2534	0
16	0.572575	15.5019	0
17	0.557483	15.0933	0
18	0.546236	14.7888	0
19	0.535933	14.5098	0
20	0.542343	14.6834	0
21	0.533984	14.4571	0
22	0.530032	14.3501	0
23	0.525293	14.2218	0
24	0.523764	14.1804	0
25	0.510161	13.8121	0
26	0.502828	13.6136	0
27	0.510179	13.8126	0
28	0.510544	13.8225	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.798921	21.63	0
2	0.070906	1.9197	0.027641
3	0.15362	4.1591	1.8e-05
4	0.21777	5.8959	0
5	0.12436	3.3669	4e-04
6	0.065077	1.7619	0.039252
7	0.07724	2.0912	0.018428
8	0.069604	1.8845	0.02995
9	0.077104	2.0875	0.018593
10	0.107222	2.9029	0.001904
11	0.043164	1.1686	0.121469
12	0.07487	2.027	0.02151
13	0.02529	0.6847	0.246874
14	0.025115	0.68	0.248372
15	0.052347	1.4173	0.078417
16	0.060888	1.6485	0.049842
17	-0.017024	-0.4609	0.322499
18	0.028921	0.783	0.21694
19	0.009242	0.2502	0.401243
20	0.040567	1.0983	0.136214
21	-0.013075	-0.354	0.361726
22	0.022644	0.6131	0.270015
23	0.014143	0.3829	0.350946
24	0.016894	0.4574	0.323764
25	-0.024713	-0.6691	0.251829
26	0.005778	0.1564	0.437863
27	0.041834	1.1326	0.128875
28	-0.001852	-0.0501	0.480016

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.798921 & 21.63 & 0 \tabularnewline
2 & 0.070906 & 1.9197 & 0.027641 \tabularnewline
3 & 0.15362 & 4.1591 & 1.8e-05 \tabularnewline
4 & 0.21777 & 5.8959 & 0 \tabularnewline
5 & 0.12436 & 3.3669 & 4e-04 \tabularnewline
6 & 0.065077 & 1.7619 & 0.039252 \tabularnewline
7 & 0.07724 & 2.0912 & 0.018428 \tabularnewline
8 & 0.069604 & 1.8845 & 0.02995 \tabularnewline
9 & 0.077104 & 2.0875 & 0.018593 \tabularnewline
10 & 0.107222 & 2.9029 & 0.001904 \tabularnewline
11 & 0.043164 & 1.1686 & 0.121469 \tabularnewline
12 & 0.07487 & 2.027 & 0.02151 \tabularnewline
13 & 0.02529 & 0.6847 & 0.246874 \tabularnewline
14 & 0.025115 & 0.68 & 0.248372 \tabularnewline
15 & 0.052347 & 1.4173 & 0.078417 \tabularnewline
16 & 0.060888 & 1.6485 & 0.049842 \tabularnewline
17 & -0.017024 & -0.4609 & 0.322499 \tabularnewline
18 & 0.028921 & 0.783 & 0.21694 \tabularnewline
19 & 0.009242 & 0.2502 & 0.401243 \tabularnewline
20 & 0.040567 & 1.0983 & 0.136214 \tabularnewline
21 & -0.013075 & -0.354 & 0.361726 \tabularnewline
22 & 0.022644 & 0.6131 & 0.270015 \tabularnewline
23 & 0.014143 & 0.3829 & 0.350946 \tabularnewline
24 & 0.016894 & 0.4574 & 0.323764 \tabularnewline
25 & -0.024713 & -0.6691 & 0.251829 \tabularnewline
26 & 0.005778 & 0.1564 & 0.437863 \tabularnewline
27 & 0.041834 & 1.1326 & 0.128875 \tabularnewline
28 & -0.001852 & -0.0501 & 0.480016 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13843&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]0.798921[/C][C]21.63[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.070906[/C][C]1.9197[/C][C]0.027641[/C][/ROW]
[ROW][C]3[/C][C]0.15362[/C][C]4.1591[/C][C]1.8e-05[/C][/ROW]
[ROW][C]4[/C][C]0.21777[/C][C]5.8959[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.12436[/C][C]3.3669[/C][C]4e-04[/C][/ROW]
[ROW][C]6[/C][C]0.065077[/C][C]1.7619[/C][C]0.039252[/C][/ROW]
[ROW][C]7[/C][C]0.07724[/C][C]2.0912[/C][C]0.018428[/C][/ROW]
[ROW][C]8[/C][C]0.069604[/C][C]1.8845[/C][C]0.02995[/C][/ROW]
[ROW][C]9[/C][C]0.077104[/C][C]2.0875[/C][C]0.018593[/C][/ROW]
[ROW][C]10[/C][C]0.107222[/C][C]2.9029[/C][C]0.001904[/C][/ROW]
[ROW][C]11[/C][C]0.043164[/C][C]1.1686[/C][C]0.121469[/C][/ROW]
[ROW][C]12[/C][C]0.07487[/C][C]2.027[/C][C]0.02151[/C][/ROW]
[ROW][C]13[/C][C]0.02529[/C][C]0.6847[/C][C]0.246874[/C][/ROW]
[ROW][C]14[/C][C]0.025115[/C][C]0.68[/C][C]0.248372[/C][/ROW]
[ROW][C]15[/C][C]0.052347[/C][C]1.4173[/C][C]0.078417[/C][/ROW]
[ROW][C]16[/C][C]0.060888[/C][C]1.6485[/C][C]0.049842[/C][/ROW]
[ROW][C]17[/C][C]-0.017024[/C][C]-0.4609[/C][C]0.322499[/C][/ROW]
[ROW][C]18[/C][C]0.028921[/C][C]0.783[/C][C]0.21694[/C][/ROW]
[ROW][C]19[/C][C]0.009242[/C][C]0.2502[/C][C]0.401243[/C][/ROW]
[ROW][C]20[/C][C]0.040567[/C][C]1.0983[/C][C]0.136214[/C][/ROW]
[ROW][C]21[/C][C]-0.013075[/C][C]-0.354[/C][C]0.361726[/C][/ROW]
[ROW][C]22[/C][C]0.022644[/C][C]0.6131[/C][C]0.270015[/C][/ROW]
[ROW][C]23[/C][C]0.014143[/C][C]0.3829[/C][C]0.350946[/C][/ROW]
[ROW][C]24[/C][C]0.016894[/C][C]0.4574[/C][C]0.323764[/C][/ROW]
[ROW][C]25[/C][C]-0.024713[/C][C]-0.6691[/C][C]0.251829[/C][/ROW]
[ROW][C]26[/C][C]0.005778[/C][C]0.1564[/C][C]0.437863[/C][/ROW]
[ROW][C]27[/C][C]0.041834[/C][C]1.1326[/C][C]0.128875[/C][/ROW]
[ROW][C]28[/C][C]-0.001852[/C][C]-0.0501[/C][C]0.480016[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13843&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13843&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	0.798921	21.63	0
2	0.070906	1.9197	0.027641
3	0.15362	4.1591	1.8e-05
4	0.21777	5.8959	0
5	0.12436	3.3669	4e-04
6	0.065077	1.7619	0.039252
7	0.07724	2.0912	0.018428
8	0.069604	1.8845	0.02995
9	0.077104	2.0875	0.018593
10	0.107222	2.9029	0.001904
11	0.043164	1.1686	0.121469
12	0.07487	2.027	0.02151
13	0.02529	0.6847	0.246874
14	0.025115	0.68	0.248372
15	0.052347	1.4173	0.078417
16	0.060888	1.6485	0.049842
17	-0.017024	-0.4609	0.322499
18	0.028921	0.783	0.21694
19	0.009242	0.2502	0.401243
20	0.040567	1.0983	0.136214
21	-0.013075	-0.354	0.361726
22	0.022644	0.6131	0.270015
23	0.014143	0.3829	0.350946
24	0.016894	0.4574	0.323764
25	-0.024713	-0.6691	0.251829
26	0.005778	0.1564	0.437863
27	0.041834	1.1326	0.128875
28	-0.001852	-0.0501	0.480016

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 = 1 ;

Parameters (R input):

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