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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 25 Nov 2009 09:43:12 -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/2009/Nov/25/t125916746898bc0jj5fqcvckm.htm/, Retrieved Wed, 05 Nov 2025 10:04:59 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=59454, Retrieved Wed, 05 Nov 2025 10:04:59 +0000

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User-defined keywords

Estimated Impact

426

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

-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [(Partial) Autocorrelation Function] [Identifying Integ...] [2009-11-22 12:26:39] [b98453cac15ba1066b407e146608df68]
-   PD          [(Partial) Autocorrelation Function] [ACF2] [2009-11-25 16:43:12] [2ecea65fec1cd5f6b1ab182881aa2a91] [Current]
-   P             [(Partial) Autocorrelation Function] [ACF (2)] [2009-12-17 14:49:32] [3b0db66ac8145b1be856a517e2900332] 
-   P             [(Partial) Autocorrelation Function] [ACF (3)] [2009-12-17 14:53:39] [3b0db66ac8145b1be856a517e2900332] 

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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=59454&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=59454&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59454&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	-0.213336	-1.6525	0.051829
2	-0.091258	-0.7069	0.241189
3	0.005843	0.0453	0.482025
4	-0.010794	-0.0836	0.466823
5	-0.057166	-0.4428	0.329749
6	0.076063	0.5892	0.278976
7	0.018986	0.1471	0.441787
8	0.069551	0.5387	0.29603
9	-0.04893	-0.379	0.35301
10	0.005501	0.0426	0.483077
11	0.100966	0.7821	0.218621
12	-0.058995	-0.457	0.32467
13	0.038998	0.3021	0.381819
14	-0.176717	-1.3688	0.088075
15	0.019551	0.1514	0.440068
16	0.208683	1.6164	0.055622
17	-0.130434	-1.0103	0.158195

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.213336 & -1.6525 & 0.051829 \tabularnewline
2 & -0.091258 & -0.7069 & 0.241189 \tabularnewline
3 & 0.005843 & 0.0453 & 0.482025 \tabularnewline
4 & -0.010794 & -0.0836 & 0.466823 \tabularnewline
5 & -0.057166 & -0.4428 & 0.329749 \tabularnewline
6 & 0.076063 & 0.5892 & 0.278976 \tabularnewline
7 & 0.018986 & 0.1471 & 0.441787 \tabularnewline
8 & 0.069551 & 0.5387 & 0.29603 \tabularnewline
9 & -0.04893 & -0.379 & 0.35301 \tabularnewline
10 & 0.005501 & 0.0426 & 0.483077 \tabularnewline
11 & 0.100966 & 0.7821 & 0.218621 \tabularnewline
12 & -0.058995 & -0.457 & 0.32467 \tabularnewline
13 & 0.038998 & 0.3021 & 0.381819 \tabularnewline
14 & -0.176717 & -1.3688 & 0.088075 \tabularnewline
15 & 0.019551 & 0.1514 & 0.440068 \tabularnewline
16 & 0.208683 & 1.6164 & 0.055622 \tabularnewline
17 & -0.130434 & -1.0103 & 0.158195 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59454&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]-0.213336[/C][C]-1.6525[/C][C]0.051829[/C][/ROW]
[ROW][C]2[/C][C]-0.091258[/C][C]-0.7069[/C][C]0.241189[/C][/ROW]
[ROW][C]3[/C][C]0.005843[/C][C]0.0453[/C][C]0.482025[/C][/ROW]
[ROW][C]4[/C][C]-0.010794[/C][C]-0.0836[/C][C]0.466823[/C][/ROW]
[ROW][C]5[/C][C]-0.057166[/C][C]-0.4428[/C][C]0.329749[/C][/ROW]
[ROW][C]6[/C][C]0.076063[/C][C]0.5892[/C][C]0.278976[/C][/ROW]
[ROW][C]7[/C][C]0.018986[/C][C]0.1471[/C][C]0.441787[/C][/ROW]
[ROW][C]8[/C][C]0.069551[/C][C]0.5387[/C][C]0.29603[/C][/ROW]
[ROW][C]9[/C][C]-0.04893[/C][C]-0.379[/C][C]0.35301[/C][/ROW]
[ROW][C]10[/C][C]0.005501[/C][C]0.0426[/C][C]0.483077[/C][/ROW]
[ROW][C]11[/C][C]0.100966[/C][C]0.7821[/C][C]0.218621[/C][/ROW]
[ROW][C]12[/C][C]-0.058995[/C][C]-0.457[/C][C]0.32467[/C][/ROW]
[ROW][C]13[/C][C]0.038998[/C][C]0.3021[/C][C]0.381819[/C][/ROW]
[ROW][C]14[/C][C]-0.176717[/C][C]-1.3688[/C][C]0.088075[/C][/ROW]
[ROW][C]15[/C][C]0.019551[/C][C]0.1514[/C][C]0.440068[/C][/ROW]
[ROW][C]16[/C][C]0.208683[/C][C]1.6164[/C][C]0.055622[/C][/ROW]
[ROW][C]17[/C][C]-0.130434[/C][C]-1.0103[/C][C]0.158195[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59454&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59454&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	-0.213336	-1.6525	0.051829
2	-0.091258	-0.7069	0.241189
3	0.005843	0.0453	0.482025
4	-0.010794	-0.0836	0.466823
5	-0.057166	-0.4428	0.329749
6	0.076063	0.5892	0.278976
7	0.018986	0.1471	0.441787
8	0.069551	0.5387	0.29603
9	-0.04893	-0.379	0.35301
10	0.005501	0.0426	0.483077
11	0.100966	0.7821	0.218621
12	-0.058995	-0.457	0.32467
13	0.038998	0.3021	0.381819
14	-0.176717	-1.3688	0.088075
15	0.019551	0.1514	0.440068
16	0.208683	1.6164	0.055622
17	-0.130434	-1.0103	0.158195

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.213336	-1.6525	0.051829
2	-0.143292	-1.1099	0.135728
3	-0.050257	-0.3893	0.349221
4	-0.036721	-0.2844	0.388526
5	-0.077546	-0.6007	0.275162
6	0.041468	0.3212	0.374584
7	0.033689	0.261	0.397509
8	0.102261	0.7921	0.215709
9	0.000703	0.0054	0.497837
10	0.017084	0.1323	0.447583
11	0.121967	0.9447	0.174288
12	-0.00126	-0.0098	0.496123
13	0.05981	0.4633	0.322416
14	-0.191443	-1.4829	0.071666
15	-0.065246	-0.5054	0.307568
16	0.178657	1.3839	0.085762
17	-0.079861	-0.6186	0.26926

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.213336 & -1.6525 & 0.051829 \tabularnewline
2 & -0.143292 & -1.1099 & 0.135728 \tabularnewline
3 & -0.050257 & -0.3893 & 0.349221 \tabularnewline
4 & -0.036721 & -0.2844 & 0.388526 \tabularnewline
5 & -0.077546 & -0.6007 & 0.275162 \tabularnewline
6 & 0.041468 & 0.3212 & 0.374584 \tabularnewline
7 & 0.033689 & 0.261 & 0.397509 \tabularnewline
8 & 0.102261 & 0.7921 & 0.215709 \tabularnewline
9 & 0.000703 & 0.0054 & 0.497837 \tabularnewline
10 & 0.017084 & 0.1323 & 0.447583 \tabularnewline
11 & 0.121967 & 0.9447 & 0.174288 \tabularnewline
12 & -0.00126 & -0.0098 & 0.496123 \tabularnewline
13 & 0.05981 & 0.4633 & 0.322416 \tabularnewline
14 & -0.191443 & -1.4829 & 0.071666 \tabularnewline
15 & -0.065246 & -0.5054 & 0.307568 \tabularnewline
16 & 0.178657 & 1.3839 & 0.085762 \tabularnewline
17 & -0.079861 & -0.6186 & 0.26926 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59454&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]-0.213336[/C][C]-1.6525[/C][C]0.051829[/C][/ROW]
[ROW][C]2[/C][C]-0.143292[/C][C]-1.1099[/C][C]0.135728[/C][/ROW]
[ROW][C]3[/C][C]-0.050257[/C][C]-0.3893[/C][C]0.349221[/C][/ROW]
[ROW][C]4[/C][C]-0.036721[/C][C]-0.2844[/C][C]0.388526[/C][/ROW]
[ROW][C]5[/C][C]-0.077546[/C][C]-0.6007[/C][C]0.275162[/C][/ROW]
[ROW][C]6[/C][C]0.041468[/C][C]0.3212[/C][C]0.374584[/C][/ROW]
[ROW][C]7[/C][C]0.033689[/C][C]0.261[/C][C]0.397509[/C][/ROW]
[ROW][C]8[/C][C]0.102261[/C][C]0.7921[/C][C]0.215709[/C][/ROW]
[ROW][C]9[/C][C]0.000703[/C][C]0.0054[/C][C]0.497837[/C][/ROW]
[ROW][C]10[/C][C]0.017084[/C][C]0.1323[/C][C]0.447583[/C][/ROW]
[ROW][C]11[/C][C]0.121967[/C][C]0.9447[/C][C]0.174288[/C][/ROW]
[ROW][C]12[/C][C]-0.00126[/C][C]-0.0098[/C][C]0.496123[/C][/ROW]
[ROW][C]13[/C][C]0.05981[/C][C]0.4633[/C][C]0.322416[/C][/ROW]
[ROW][C]14[/C][C]-0.191443[/C][C]-1.4829[/C][C]0.071666[/C][/ROW]
[ROW][C]15[/C][C]-0.065246[/C][C]-0.5054[/C][C]0.307568[/C][/ROW]
[ROW][C]16[/C][C]0.178657[/C][C]1.3839[/C][C]0.085762[/C][/ROW]
[ROW][C]17[/C][C]-0.079861[/C][C]-0.6186[/C][C]0.26926[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59454&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59454&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	-0.213336	-1.6525	0.051829
2	-0.143292	-1.1099	0.135728
3	-0.050257	-0.3893	0.349221
4	-0.036721	-0.2844	0.388526
5	-0.077546	-0.6007	0.275162
6	0.041468	0.3212	0.374584
7	0.033689	0.261	0.397509
8	0.102261	0.7921	0.215709
9	0.000703	0.0054	0.497837
10	0.017084	0.1323	0.447583
11	0.121967	0.9447	0.174288
12	-0.00126	-0.0098	0.496123
13	0.05981	0.4633	0.322416
14	-0.191443	-1.4829	0.071666
15	-0.065246	-0.5054	0.307568
16	0.178657	1.3839	0.085762
17	-0.079861	-0.6186	0.26926

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 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code