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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

Sat, 13 Dec 2008 05:23:36 -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/13/t12291710745s8zkrwswcmz6v6.htm/, Retrieved Mon, 25 May 2026 15:19:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=33010, Retrieved Mon, 25 May 2026 15:19:42 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

jenske_cole@hotmail.com

Estimated Impact

520

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

F     [Bivariate Kernel Density Estimation] [Various EDA Topic...] [2008-11-12 13:37:39] [8094ad203a218aaca2d1cea2c78c2d6e]
F    D  [Bivariate Kernel Density Estimation] [opdracht3 blok8 q...] [2008-11-12 17:51:49] [975daa21de49eaf4d491226310243f5a]
- RMPD      [(Partial) Autocorrelation Function] [paper autocorrela...] [2008-12-13 12:23:36] [120dfa2440e51a0cfc0f5296bc5d7460] [Current]
-             [(Partial) Autocorrelation Function] [paper autocorrela...] [2008-12-13 12:59:53] [975daa21de49eaf4d491226310243f5a] 
- RM            [ARIMA Backward Selection] [paper backward goe] [2008-12-13 13:24:53] [975daa21de49eaf4d491226310243f5a] 
-   P             [ARIMA Backward Selection] [paper backward......] [2008-12-17 14:15:55] [975daa21de49eaf4d491226310243f5a] 
-   P           [(Partial) Autocorrelation Function] [paper autocorrela...] [2008-12-17 14:11:49] [975daa21de49eaf4d491226310243f5a] 

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Dataseries X:

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Histogram

Boxplots

7.6
7.4
7.3
7.1
6.9
6.8
7.5
7.6
7.8
8
8.1
8.2
8.3
8.2
8
7.9
7.6
7.6
8.2
8.3
8.4
8.4
8.4
8.6
8.9
8.8
8.3
7.5
7.2
7.5
8.8
9.3
9.3
8.7
8.2
8.3
8.5
8.6
8.6
8.2
8.1
8
8.6
8.7
8.8
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8.1
8.2
8.1
8.1
7.9
7.9
7.9
8
8
7.9
8
7.7
7.2
7.5
7.3
7
7
7
7.2
7.3
7.1
6.8
6.6
6.2
6.2
6.8
6.9
6.8
6.7

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	'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 & 2 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=33010&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33010&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33010&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	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.47613	3.955	9.1e-05
2	-0.104949	-0.8718	0.193177
3	-0.566696	-4.7073	6e-06
4	-0.612886	-5.091	1e-06
5	-0.213626	-1.7745	0.040195
6	0.182787	1.5183	0.066748
7	0.340769	2.8306	0.00304
8	0.294526	2.4465	0.008488
9	0.088341	0.7338	0.232775
10	-0.078747	-0.6541	0.257605
11	-0.155541	-1.292	0.10033
12	-0.223281	-1.8547	0.033955
13	-0.051923	-0.4313	0.333795
14	0.076369	0.6344	0.26397
15	0.147405	1.2244	0.112475
16	0.100284	0.833	0.203854
17	-0.066954	-0.5562	0.289949
18	-0.103569	-0.8603	0.196299
19	-0.084725	-0.7038	0.241971

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.47613 & 3.955 & 9.1e-05 \tabularnewline
2 & -0.104949 & -0.8718 & 0.193177 \tabularnewline
3 & -0.566696 & -4.7073 & 6e-06 \tabularnewline
4 & -0.612886 & -5.091 & 1e-06 \tabularnewline
5 & -0.213626 & -1.7745 & 0.040195 \tabularnewline
6 & 0.182787 & 1.5183 & 0.066748 \tabularnewline
7 & 0.340769 & 2.8306 & 0.00304 \tabularnewline
8 & 0.294526 & 2.4465 & 0.008488 \tabularnewline
9 & 0.088341 & 0.7338 & 0.232775 \tabularnewline
10 & -0.078747 & -0.6541 & 0.257605 \tabularnewline
11 & -0.155541 & -1.292 & 0.10033 \tabularnewline
12 & -0.223281 & -1.8547 & 0.033955 \tabularnewline
13 & -0.051923 & -0.4313 & 0.333795 \tabularnewline
14 & 0.076369 & 0.6344 & 0.26397 \tabularnewline
15 & 0.147405 & 1.2244 & 0.112475 \tabularnewline
16 & 0.100284 & 0.833 & 0.203854 \tabularnewline
17 & -0.066954 & -0.5562 & 0.289949 \tabularnewline
18 & -0.103569 & -0.8603 & 0.196299 \tabularnewline
19 & -0.084725 & -0.7038 & 0.241971 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33010&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]0.47613[/C][C]3.955[/C][C]9.1e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.104949[/C][C]-0.8718[/C][C]0.193177[/C][/ROW]
[ROW][C]3[/C][C]-0.566696[/C][C]-4.7073[/C][C]6e-06[/C][/ROW]
[ROW][C]4[/C][C]-0.612886[/C][C]-5.091[/C][C]1e-06[/C][/ROW]
[ROW][C]5[/C][C]-0.213626[/C][C]-1.7745[/C][C]0.040195[/C][/ROW]
[ROW][C]6[/C][C]0.182787[/C][C]1.5183[/C][C]0.066748[/C][/ROW]
[ROW][C]7[/C][C]0.340769[/C][C]2.8306[/C][C]0.00304[/C][/ROW]
[ROW][C]8[/C][C]0.294526[/C][C]2.4465[/C][C]0.008488[/C][/ROW]
[ROW][C]9[/C][C]0.088341[/C][C]0.7338[/C][C]0.232775[/C][/ROW]
[ROW][C]10[/C][C]-0.078747[/C][C]-0.6541[/C][C]0.257605[/C][/ROW]
[ROW][C]11[/C][C]-0.155541[/C][C]-1.292[/C][C]0.10033[/C][/ROW]
[ROW][C]12[/C][C]-0.223281[/C][C]-1.8547[/C][C]0.033955[/C][/ROW]
[ROW][C]13[/C][C]-0.051923[/C][C]-0.4313[/C][C]0.333795[/C][/ROW]
[ROW][C]14[/C][C]0.076369[/C][C]0.6344[/C][C]0.26397[/C][/ROW]
[ROW][C]15[/C][C]0.147405[/C][C]1.2244[/C][C]0.112475[/C][/ROW]
[ROW][C]16[/C][C]0.100284[/C][C]0.833[/C][C]0.203854[/C][/ROW]
[ROW][C]17[/C][C]-0.066954[/C][C]-0.5562[/C][C]0.289949[/C][/ROW]
[ROW][C]18[/C][C]-0.103569[/C][C]-0.8603[/C][C]0.196299[/C][/ROW]
[ROW][C]19[/C][C]-0.084725[/C][C]-0.7038[/C][C]0.241971[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33010&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33010&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	0.47613	3.955	9.1e-05
2	-0.104949	-0.8718	0.193177
3	-0.566696	-4.7073	6e-06
4	-0.612886	-5.091	1e-06
5	-0.213626	-1.7745	0.040195
6	0.182787	1.5183	0.066748
7	0.340769	2.8306	0.00304
8	0.294526	2.4465	0.008488
9	0.088341	0.7338	0.232775
10	-0.078747	-0.6541	0.257605
11	-0.155541	-1.292	0.10033
12	-0.223281	-1.8547	0.033955
13	-0.051923	-0.4313	0.333795
14	0.076369	0.6344	0.26397
15	0.147405	1.2244	0.112475
16	0.100284	0.833	0.203854
17	-0.066954	-0.5562	0.289949
18	-0.103569	-0.8603	0.196299
19	-0.084725	-0.7038	0.241971

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.47613	3.955	9.1e-05
2	-0.428875	-3.5625	0.000336
3	-0.461277	-3.8317	0.000139
4	-0.265509	-2.2055	0.015377
5	0.034581	0.2872	0.387392
6	-0.112974	-0.9384	0.175647
7	-0.199673	-1.6586	0.050867
8	0.007363	0.0612	0.475705
9	0.04156	0.3452	0.365489
10	0.027519	0.2286	0.409931
11	-0.013743	-0.1142	0.454722
12	-0.166558	-1.3835	0.08548
13	0.195325	1.6225	0.054629
14	0.04639	0.3853	0.350584
15	-0.052396	-0.4352	0.332376
16	-0.094127	-0.7819	0.21848
17	-0.063453	-0.5271	0.299913
18	0.109288	0.9078	0.183568
19	-0.0927	-0.77	0.221956

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.47613 & 3.955 & 9.1e-05 \tabularnewline
2 & -0.428875 & -3.5625 & 0.000336 \tabularnewline
3 & -0.461277 & -3.8317 & 0.000139 \tabularnewline
4 & -0.265509 & -2.2055 & 0.015377 \tabularnewline
5 & 0.034581 & 0.2872 & 0.387392 \tabularnewline
6 & -0.112974 & -0.9384 & 0.175647 \tabularnewline
7 & -0.199673 & -1.6586 & 0.050867 \tabularnewline
8 & 0.007363 & 0.0612 & 0.475705 \tabularnewline
9 & 0.04156 & 0.3452 & 0.365489 \tabularnewline
10 & 0.027519 & 0.2286 & 0.409931 \tabularnewline
11 & -0.013743 & -0.1142 & 0.454722 \tabularnewline
12 & -0.166558 & -1.3835 & 0.08548 \tabularnewline
13 & 0.195325 & 1.6225 & 0.054629 \tabularnewline
14 & 0.04639 & 0.3853 & 0.350584 \tabularnewline
15 & -0.052396 & -0.4352 & 0.332376 \tabularnewline
16 & -0.094127 & -0.7819 & 0.21848 \tabularnewline
17 & -0.063453 & -0.5271 & 0.299913 \tabularnewline
18 & 0.109288 & 0.9078 & 0.183568 \tabularnewline
19 & -0.0927 & -0.77 & 0.221956 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33010&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]0.47613[/C][C]3.955[/C][C]9.1e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.428875[/C][C]-3.5625[/C][C]0.000336[/C][/ROW]
[ROW][C]3[/C][C]-0.461277[/C][C]-3.8317[/C][C]0.000139[/C][/ROW]
[ROW][C]4[/C][C]-0.265509[/C][C]-2.2055[/C][C]0.015377[/C][/ROW]
[ROW][C]5[/C][C]0.034581[/C][C]0.2872[/C][C]0.387392[/C][/ROW]
[ROW][C]6[/C][C]-0.112974[/C][C]-0.9384[/C][C]0.175647[/C][/ROW]
[ROW][C]7[/C][C]-0.199673[/C][C]-1.6586[/C][C]0.050867[/C][/ROW]
[ROW][C]8[/C][C]0.007363[/C][C]0.0612[/C][C]0.475705[/C][/ROW]
[ROW][C]9[/C][C]0.04156[/C][C]0.3452[/C][C]0.365489[/C][/ROW]
[ROW][C]10[/C][C]0.027519[/C][C]0.2286[/C][C]0.409931[/C][/ROW]
[ROW][C]11[/C][C]-0.013743[/C][C]-0.1142[/C][C]0.454722[/C][/ROW]
[ROW][C]12[/C][C]-0.166558[/C][C]-1.3835[/C][C]0.08548[/C][/ROW]
[ROW][C]13[/C][C]0.195325[/C][C]1.6225[/C][C]0.054629[/C][/ROW]
[ROW][C]14[/C][C]0.04639[/C][C]0.3853[/C][C]0.350584[/C][/ROW]
[ROW][C]15[/C][C]-0.052396[/C][C]-0.4352[/C][C]0.332376[/C][/ROW]
[ROW][C]16[/C][C]-0.094127[/C][C]-0.7819[/C][C]0.21848[/C][/ROW]
[ROW][C]17[/C][C]-0.063453[/C][C]-0.5271[/C][C]0.299913[/C][/ROW]
[ROW][C]18[/C][C]0.109288[/C][C]0.9078[/C][C]0.183568[/C][/ROW]
[ROW][C]19[/C][C]-0.0927[/C][C]-0.77[/C][C]0.221956[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33010&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33010&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	0.47613	3.955	9.1e-05
2	-0.428875	-3.5625	0.000336
3	-0.461277	-3.8317	0.000139
4	-0.265509	-2.2055	0.015377
5	0.034581	0.2872	0.387392
6	-0.112974	-0.9384	0.175647
7	-0.199673	-1.6586	0.050867
8	0.007363	0.0612	0.475705
9	0.04156	0.3452	0.365489
10	0.027519	0.2286	0.409931
11	-0.013743	-0.1142	0.454722
12	-0.166558	-1.3835	0.08548
13	0.195325	1.6225	0.054629
14	0.04639	0.3853	0.350584
15	-0.052396	-0.4352	0.332376
16	-0.094127	-0.7819	0.21848
17	-0.063453	-0.5271	0.299913
18	0.109288	0.9078	0.183568
19	-0.0927	-0.77	0.221956

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 4 ;

Parameters (R input):

par1 = Default ; par2 = 2.0 ; 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