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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 23 Dec 2008 07:27:57 -0700

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/Dec/23/t1230042587hahbrqj9il7si7z.htm/, Retrieved Tue, 10 Feb 2026 13:25:53 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36303, Retrieved Tue, 10 Feb 2026 13:25:53 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

480

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 13:13:15] [74be16979710d4c4e7c6647856088456]
-    D    [Standard Deviation-Mean Plot] [SMP eigen tijdreeks] [2008-12-15 19:50:53] [74be16979710d4c4e7c6647856088456]
- RMPD        [(Partial) Autocorrelation Function] [paper] [2008-12-23 14:27:57] [5bd06487453d0eec7a1bf04bf9f25085] [Current]
-   P           [(Partial) Autocorrelation Function] [paper] [2008-12-23 14:38:06] [5262baed313b307078ce11eb68e9efe6] 
-   P             [(Partial) Autocorrelation Function] [Paper] [2008-12-23 15:13:44] [5262baed313b307078ce11eb68e9efe6] 
-   P               [(Partial) Autocorrelation Function] [paper] [2008-12-23 15:16:02] [5262baed313b307078ce11eb68e9efe6] 
- RMP           [Spectral Analysis] [paper] [2008-12-23 14:54:12] [5262baed313b307078ce11eb68e9efe6] 
-   P           [(Partial) Autocorrelation Function] [Paper] [2008-12-23 15:11:14] [5262baed313b307078ce11eb68e9efe6] 

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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=36303&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=36303&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36303&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	-0.015239	-0.147	0.441742
2	-0.031778	-0.3065	0.379973
3	0.012054	0.1162	0.453856
4	0.095248	0.9185	0.180356
5	0.072615	0.7003	0.242752
6	0.081545	0.7864	0.216819
7	0.022897	0.2208	0.412861
8	0.096131	0.9271	0.178148
9	0.124994	1.2054	0.115554
10	-0.039893	-0.3847	0.350663
11	-0.012359	-0.1192	0.452693
12	-0.233959	-2.2562	0.0132
13	0.001924	0.0186	0.492619
14	0.260658	2.5137	0.006833
15	-0.006068	-0.0585	0.47673
16	-0.042649	-0.4113	0.340902
17	-0.066922	-0.6454	0.260137
18	0.053223	0.5133	0.304492
19	0.064283	0.6199	0.268412
20	0.013807	0.1332	0.44718

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.015239 & -0.147 & 0.441742 \tabularnewline
2 & -0.031778 & -0.3065 & 0.379973 \tabularnewline
3 & 0.012054 & 0.1162 & 0.453856 \tabularnewline
4 & 0.095248 & 0.9185 & 0.180356 \tabularnewline
5 & 0.072615 & 0.7003 & 0.242752 \tabularnewline
6 & 0.081545 & 0.7864 & 0.216819 \tabularnewline
7 & 0.022897 & 0.2208 & 0.412861 \tabularnewline
8 & 0.096131 & 0.9271 & 0.178148 \tabularnewline
9 & 0.124994 & 1.2054 & 0.115554 \tabularnewline
10 & -0.039893 & -0.3847 & 0.350663 \tabularnewline
11 & -0.012359 & -0.1192 & 0.452693 \tabularnewline
12 & -0.233959 & -2.2562 & 0.0132 \tabularnewline
13 & 0.001924 & 0.0186 & 0.492619 \tabularnewline
14 & 0.260658 & 2.5137 & 0.006833 \tabularnewline
15 & -0.006068 & -0.0585 & 0.47673 \tabularnewline
16 & -0.042649 & -0.4113 & 0.340902 \tabularnewline
17 & -0.066922 & -0.6454 & 0.260137 \tabularnewline
18 & 0.053223 & 0.5133 & 0.304492 \tabularnewline
19 & 0.064283 & 0.6199 & 0.268412 \tabularnewline
20 & 0.013807 & 0.1332 & 0.44718 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36303&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]-0.015239[/C][C]-0.147[/C][C]0.441742[/C][/ROW]
[ROW][C]2[/C][C]-0.031778[/C][C]-0.3065[/C][C]0.379973[/C][/ROW]
[ROW][C]3[/C][C]0.012054[/C][C]0.1162[/C][C]0.453856[/C][/ROW]
[ROW][C]4[/C][C]0.095248[/C][C]0.9185[/C][C]0.180356[/C][/ROW]
[ROW][C]5[/C][C]0.072615[/C][C]0.7003[/C][C]0.242752[/C][/ROW]
[ROW][C]6[/C][C]0.081545[/C][C]0.7864[/C][C]0.216819[/C][/ROW]
[ROW][C]7[/C][C]0.022897[/C][C]0.2208[/C][C]0.412861[/C][/ROW]
[ROW][C]8[/C][C]0.096131[/C][C]0.9271[/C][C]0.178148[/C][/ROW]
[ROW][C]9[/C][C]0.124994[/C][C]1.2054[/C][C]0.115554[/C][/ROW]
[ROW][C]10[/C][C]-0.039893[/C][C]-0.3847[/C][C]0.350663[/C][/ROW]
[ROW][C]11[/C][C]-0.012359[/C][C]-0.1192[/C][C]0.452693[/C][/ROW]
[ROW][C]12[/C][C]-0.233959[/C][C]-2.2562[/C][C]0.0132[/C][/ROW]
[ROW][C]13[/C][C]0.001924[/C][C]0.0186[/C][C]0.492619[/C][/ROW]
[ROW][C]14[/C][C]0.260658[/C][C]2.5137[/C][C]0.006833[/C][/ROW]
[ROW][C]15[/C][C]-0.006068[/C][C]-0.0585[/C][C]0.47673[/C][/ROW]
[ROW][C]16[/C][C]-0.042649[/C][C]-0.4113[/C][C]0.340902[/C][/ROW]
[ROW][C]17[/C][C]-0.066922[/C][C]-0.6454[/C][C]0.260137[/C][/ROW]
[ROW][C]18[/C][C]0.053223[/C][C]0.5133[/C][C]0.304492[/C][/ROW]
[ROW][C]19[/C][C]0.064283[/C][C]0.6199[/C][C]0.268412[/C][/ROW]
[ROW][C]20[/C][C]0.013807[/C][C]0.1332[/C][C]0.44718[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36303&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36303&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	-0.015239	-0.147	0.441742
2	-0.031778	-0.3065	0.379973
3	0.012054	0.1162	0.453856
4	0.095248	0.9185	0.180356
5	0.072615	0.7003	0.242752
6	0.081545	0.7864	0.216819
7	0.022897	0.2208	0.412861
8	0.096131	0.9271	0.178148
9	0.124994	1.2054	0.115554
10	-0.039893	-0.3847	0.350663
11	-0.012359	-0.1192	0.452693
12	-0.233959	-2.2562	0.0132
13	0.001924	0.0186	0.492619
14	0.260658	2.5137	0.006833
15	-0.006068	-0.0585	0.47673
16	-0.042649	-0.4113	0.340902
17	-0.066922	-0.6454	0.260137
18	0.053223	0.5133	0.304492
19	0.064283	0.6199	0.268412
20	0.013807	0.1332	0.44718

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.015239	-0.147	0.441742
2	-0.032017	-0.3088	0.379096
3	0.01108	0.1069	0.457569
4	0.094721	0.9135	0.181682
5	0.077166	0.7442	0.229327
6	0.091642	0.8838	0.189552
7	0.030407	0.2932	0.384999
8	0.094971	0.9159	0.181052
9	0.120864	1.1656	0.123384
10	-0.046883	-0.4521	0.326118
11	-0.025387	-0.2448	0.403565
12	-0.283938	-2.7382	0.003702
13	-0.073994	-0.7136	0.238639
14	0.23185	2.2359	0.013876
15	0.008766	0.0845	0.466406
16	0.023108	0.2228	0.412073
17	-0.062952	-0.6071	0.272635
18	0.051049	0.4923	0.311834
19	0.098675	0.9516	0.171888
20	0.046018	0.4438	0.329116

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.015239 & -0.147 & 0.441742 \tabularnewline
2 & -0.032017 & -0.3088 & 0.379096 \tabularnewline
3 & 0.01108 & 0.1069 & 0.457569 \tabularnewline
4 & 0.094721 & 0.9135 & 0.181682 \tabularnewline
5 & 0.077166 & 0.7442 & 0.229327 \tabularnewline
6 & 0.091642 & 0.8838 & 0.189552 \tabularnewline
7 & 0.030407 & 0.2932 & 0.384999 \tabularnewline
8 & 0.094971 & 0.9159 & 0.181052 \tabularnewline
9 & 0.120864 & 1.1656 & 0.123384 \tabularnewline
10 & -0.046883 & -0.4521 & 0.326118 \tabularnewline
11 & -0.025387 & -0.2448 & 0.403565 \tabularnewline
12 & -0.283938 & -2.7382 & 0.003702 \tabularnewline
13 & -0.073994 & -0.7136 & 0.238639 \tabularnewline
14 & 0.23185 & 2.2359 & 0.013876 \tabularnewline
15 & 0.008766 & 0.0845 & 0.466406 \tabularnewline
16 & 0.023108 & 0.2228 & 0.412073 \tabularnewline
17 & -0.062952 & -0.6071 & 0.272635 \tabularnewline
18 & 0.051049 & 0.4923 & 0.311834 \tabularnewline
19 & 0.098675 & 0.9516 & 0.171888 \tabularnewline
20 & 0.046018 & 0.4438 & 0.329116 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36303&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]-0.015239[/C][C]-0.147[/C][C]0.441742[/C][/ROW]
[ROW][C]2[/C][C]-0.032017[/C][C]-0.3088[/C][C]0.379096[/C][/ROW]
[ROW][C]3[/C][C]0.01108[/C][C]0.1069[/C][C]0.457569[/C][/ROW]
[ROW][C]4[/C][C]0.094721[/C][C]0.9135[/C][C]0.181682[/C][/ROW]
[ROW][C]5[/C][C]0.077166[/C][C]0.7442[/C][C]0.229327[/C][/ROW]
[ROW][C]6[/C][C]0.091642[/C][C]0.8838[/C][C]0.189552[/C][/ROW]
[ROW][C]7[/C][C]0.030407[/C][C]0.2932[/C][C]0.384999[/C][/ROW]
[ROW][C]8[/C][C]0.094971[/C][C]0.9159[/C][C]0.181052[/C][/ROW]
[ROW][C]9[/C][C]0.120864[/C][C]1.1656[/C][C]0.123384[/C][/ROW]
[ROW][C]10[/C][C]-0.046883[/C][C]-0.4521[/C][C]0.326118[/C][/ROW]
[ROW][C]11[/C][C]-0.025387[/C][C]-0.2448[/C][C]0.403565[/C][/ROW]
[ROW][C]12[/C][C]-0.283938[/C][C]-2.7382[/C][C]0.003702[/C][/ROW]
[ROW][C]13[/C][C]-0.073994[/C][C]-0.7136[/C][C]0.238639[/C][/ROW]
[ROW][C]14[/C][C]0.23185[/C][C]2.2359[/C][C]0.013876[/C][/ROW]
[ROW][C]15[/C][C]0.008766[/C][C]0.0845[/C][C]0.466406[/C][/ROW]
[ROW][C]16[/C][C]0.023108[/C][C]0.2228[/C][C]0.412073[/C][/ROW]
[ROW][C]17[/C][C]-0.062952[/C][C]-0.6071[/C][C]0.272635[/C][/ROW]
[ROW][C]18[/C][C]0.051049[/C][C]0.4923[/C][C]0.311834[/C][/ROW]
[ROW][C]19[/C][C]0.098675[/C][C]0.9516[/C][C]0.171888[/C][/ROW]
[ROW][C]20[/C][C]0.046018[/C][C]0.4438[/C][C]0.329116[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36303&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36303&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	-0.015239	-0.147	0.441742
2	-0.032017	-0.3088	0.379096
3	0.01108	0.1069	0.457569
4	0.094721	0.9135	0.181682
5	0.077166	0.7442	0.229327
6	0.091642	0.8838	0.189552
7	0.030407	0.2932	0.384999
8	0.094971	0.9159	0.181052
9	0.120864	1.1656	0.123384
10	-0.046883	-0.4521	0.326118
11	-0.025387	-0.2448	0.403565
12	-0.283938	-2.7382	0.003702
13	-0.073994	-0.7136	0.238639
14	0.23185	2.2359	0.013876
15	0.008766	0.0845	0.466406
16	0.023108	0.2228	0.412073
17	-0.062952	-0.6071	0.272635
18	0.051049	0.4923	0.311834
19	0.098675	0.9516	0.171888
20	0.046018	0.4438	0.329116

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 = 1 ; par5 = 12 ;

Parameters (R input):

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