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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 13 Dec 2007 04:03:25 -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/2007/Dec/13/t1197542970m0s2vcd1siajq4k.htm/, Retrieved Sun, 15 Feb 2026 04:34:59 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3431, Retrieved Sun, 15 Feb 2026 04:34:59 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

ACF van de consumptiegoederen

Estimated Impact

439

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

-     [(Partial) Autocorrelation Function] [Workshop 7 Q2] [2007-11-24 11:48:54] [daf9ae308ba7132eac41ee1ef73b223d]
-    D    [(Partial) Autocorrelation Function] [ACF van de consum...] [2007-12-13 11:03:25] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3431&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3431&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3431&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 compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	8.9443	0
1	0.388778	3.4773	0.000411
2	0.232595	2.0804	0.020345
3	0.503996	4.5079	1.1e-05
4	0.185138	1.6559	0.050827
5	0.288076	2.5766	0.005907
6	0.546138	4.8848	3e-06
7	0.188591	1.6868	0.047768
8	0.175746	1.5719	0.059958
9	0.408862	3.657	0.000228
10	0.087575	0.7833	0.217884
11	0.27066	2.4209	0.008874
12	0.614346	5.4949	0
13	0.157217	1.4062	0.08177
14	0.138825	1.2417	0.10899
15	0.275902	2.4677	0.007865
16	-0.006471	-0.0579	0.523004
17	0.154216	1.3794	0.085815
18	0.277923	2.4858	0.007504

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.9443 & 0 \tabularnewline
1 & 0.388778 & 3.4773 & 0.000411 \tabularnewline
2 & 0.232595 & 2.0804 & 0.020345 \tabularnewline
3 & 0.503996 & 4.5079 & 1.1e-05 \tabularnewline
4 & 0.185138 & 1.6559 & 0.050827 \tabularnewline
5 & 0.288076 & 2.5766 & 0.005907 \tabularnewline
6 & 0.546138 & 4.8848 & 3e-06 \tabularnewline
7 & 0.188591 & 1.6868 & 0.047768 \tabularnewline
8 & 0.175746 & 1.5719 & 0.059958 \tabularnewline
9 & 0.408862 & 3.657 & 0.000228 \tabularnewline
10 & 0.087575 & 0.7833 & 0.217884 \tabularnewline
11 & 0.27066 & 2.4209 & 0.008874 \tabularnewline
12 & 0.614346 & 5.4949 & 0 \tabularnewline
13 & 0.157217 & 1.4062 & 0.08177 \tabularnewline
14 & 0.138825 & 1.2417 & 0.10899 \tabularnewline
15 & 0.275902 & 2.4677 & 0.007865 \tabularnewline
16 & -0.006471 & -0.0579 & 0.523004 \tabularnewline
17 & 0.154216 & 1.3794 & 0.085815 \tabularnewline
18 & 0.277923 & 2.4858 & 0.007504 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3431&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]0[/C][C]1[/C][C]8.9443[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.388778[/C][C]3.4773[/C][C]0.000411[/C][/ROW]
[ROW][C]2[/C][C]0.232595[/C][C]2.0804[/C][C]0.020345[/C][/ROW]
[ROW][C]3[/C][C]0.503996[/C][C]4.5079[/C][C]1.1e-05[/C][/ROW]
[ROW][C]4[/C][C]0.185138[/C][C]1.6559[/C][C]0.050827[/C][/ROW]
[ROW][C]5[/C][C]0.288076[/C][C]2.5766[/C][C]0.005907[/C][/ROW]
[ROW][C]6[/C][C]0.546138[/C][C]4.8848[/C][C]3e-06[/C][/ROW]
[ROW][C]7[/C][C]0.188591[/C][C]1.6868[/C][C]0.047768[/C][/ROW]
[ROW][C]8[/C][C]0.175746[/C][C]1.5719[/C][C]0.059958[/C][/ROW]
[ROW][C]9[/C][C]0.408862[/C][C]3.657[/C][C]0.000228[/C][/ROW]
[ROW][C]10[/C][C]0.087575[/C][C]0.7833[/C][C]0.217884[/C][/ROW]
[ROW][C]11[/C][C]0.27066[/C][C]2.4209[/C][C]0.008874[/C][/ROW]
[ROW][C]12[/C][C]0.614346[/C][C]5.4949[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.157217[/C][C]1.4062[/C][C]0.08177[/C][/ROW]
[ROW][C]14[/C][C]0.138825[/C][C]1.2417[/C][C]0.10899[/C][/ROW]
[ROW][C]15[/C][C]0.275902[/C][C]2.4677[/C][C]0.007865[/C][/ROW]
[ROW][C]16[/C][C]-0.006471[/C][C]-0.0579[/C][C]0.523004[/C][/ROW]
[ROW][C]17[/C][C]0.154216[/C][C]1.3794[/C][C]0.085815[/C][/ROW]
[ROW][C]18[/C][C]0.277923[/C][C]2.4858[/C][C]0.007504[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3431&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3431&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
0	1	8.9443	0
1	0.388778	3.4773	0.000411
2	0.232595	2.0804	0.020345
3	0.503996	4.5079	1.1e-05
4	0.185138	1.6559	0.050827
5	0.288076	2.5766	0.005907
6	0.546138	4.8848	3e-06
7	0.188591	1.6868	0.047768
8	0.175746	1.5719	0.059958
9	0.408862	3.657	0.000228
10	0.087575	0.7833	0.217884
11	0.27066	2.4209	0.008874
12	0.614346	5.4949	0
13	0.157217	1.4062	0.08177
14	0.138825	1.2417	0.10899
15	0.275902	2.4677	0.007865
16	-0.006471	-0.0579	0.523004
17	0.154216	1.3794	0.085815
18	0.277923	2.4858	0.007504

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.388778	3.4773	0.000411
1	0.095949	0.8582	0.196674
2	0.4577	4.0938	5e-05
3	-0.199615	-1.7854	0.961008
4	0.329501	2.9471	0.002101
5	0.233198	2.0858	0.020093
6	-0.103326	-0.9242	0.820912
7	-0.03042	-0.2721	0.606872
8	0.137808	1.2326	0.110669
9	-0.171229	-1.5315	0.935207
10	0.278174	2.4881	0.007461
11	0.32129	2.8737	0.002597
12	-0.186636	-1.6693	0.950519
13	-0.112266	-1.0041	0.84083
14	-0.180929	-1.6183	0.94523
15	-0.029889	-0.2673	0.60505
16	-0.066925	-0.5986	0.724432
17	-0.119425	-1.0682	0.855672
18	-2.3e-05	-2e-04	0.500081

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.388778 & 3.4773 & 0.000411 \tabularnewline
1 & 0.095949 & 0.8582 & 0.196674 \tabularnewline
2 & 0.4577 & 4.0938 & 5e-05 \tabularnewline
3 & -0.199615 & -1.7854 & 0.961008 \tabularnewline
4 & 0.329501 & 2.9471 & 0.002101 \tabularnewline
5 & 0.233198 & 2.0858 & 0.020093 \tabularnewline
6 & -0.103326 & -0.9242 & 0.820912 \tabularnewline
7 & -0.03042 & -0.2721 & 0.606872 \tabularnewline
8 & 0.137808 & 1.2326 & 0.110669 \tabularnewline
9 & -0.171229 & -1.5315 & 0.935207 \tabularnewline
10 & 0.278174 & 2.4881 & 0.007461 \tabularnewline
11 & 0.32129 & 2.8737 & 0.002597 \tabularnewline
12 & -0.186636 & -1.6693 & 0.950519 \tabularnewline
13 & -0.112266 & -1.0041 & 0.84083 \tabularnewline
14 & -0.180929 & -1.6183 & 0.94523 \tabularnewline
15 & -0.029889 & -0.2673 & 0.60505 \tabularnewline
16 & -0.066925 & -0.5986 & 0.724432 \tabularnewline
17 & -0.119425 & -1.0682 & 0.855672 \tabularnewline
18 & -2.3e-05 & -2e-04 & 0.500081 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3431&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]0[/C][C]0.388778[/C][C]3.4773[/C][C]0.000411[/C][/ROW]
[ROW][C]1[/C][C]0.095949[/C][C]0.8582[/C][C]0.196674[/C][/ROW]
[ROW][C]2[/C][C]0.4577[/C][C]4.0938[/C][C]5e-05[/C][/ROW]
[ROW][C]3[/C][C]-0.199615[/C][C]-1.7854[/C][C]0.961008[/C][/ROW]
[ROW][C]4[/C][C]0.329501[/C][C]2.9471[/C][C]0.002101[/C][/ROW]
[ROW][C]5[/C][C]0.233198[/C][C]2.0858[/C][C]0.020093[/C][/ROW]
[ROW][C]6[/C][C]-0.103326[/C][C]-0.9242[/C][C]0.820912[/C][/ROW]
[ROW][C]7[/C][C]-0.03042[/C][C]-0.2721[/C][C]0.606872[/C][/ROW]
[ROW][C]8[/C][C]0.137808[/C][C]1.2326[/C][C]0.110669[/C][/ROW]
[ROW][C]9[/C][C]-0.171229[/C][C]-1.5315[/C][C]0.935207[/C][/ROW]
[ROW][C]10[/C][C]0.278174[/C][C]2.4881[/C][C]0.007461[/C][/ROW]
[ROW][C]11[/C][C]0.32129[/C][C]2.8737[/C][C]0.002597[/C][/ROW]
[ROW][C]12[/C][C]-0.186636[/C][C]-1.6693[/C][C]0.950519[/C][/ROW]
[ROW][C]13[/C][C]-0.112266[/C][C]-1.0041[/C][C]0.84083[/C][/ROW]
[ROW][C]14[/C][C]-0.180929[/C][C]-1.6183[/C][C]0.94523[/C][/ROW]
[ROW][C]15[/C][C]-0.029889[/C][C]-0.2673[/C][C]0.60505[/C][/ROW]
[ROW][C]16[/C][C]-0.066925[/C][C]-0.5986[/C][C]0.724432[/C][/ROW]
[ROW][C]17[/C][C]-0.119425[/C][C]-1.0682[/C][C]0.855672[/C][/ROW]
[ROW][C]18[/C][C]-2.3e-05[/C][C]-2e-04[/C][C]0.500081[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3431&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3431&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
0	0.388778	3.4773	0.000411
1	0.095949	0.8582	0.196674
2	0.4577	4.0938	5e-05
3	-0.199615	-1.7854	0.961008
4	0.329501	2.9471	0.002101
5	0.233198	2.0858	0.020093
6	-0.103326	-0.9242	0.820912
7	-0.03042	-0.2721	0.606872
8	0.137808	1.2326	0.110669
9	-0.171229	-1.5315	0.935207
10	0.278174	2.4881	0.007461
11	0.32129	2.8737	0.002597
12	-0.186636	-1.6693	0.950519
13	-0.112266	-1.0041	0.84083
14	-0.180929	-1.6183	0.94523
15	-0.029889	-0.2673	0.60505
16	-0.066925	-0.5986	0.724432
17	-0.119425	-1.0682	0.855672
18	-2.3e-05	-2e-04	0.500081

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 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; 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 1:par1) {
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(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-1,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(mytstat,lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

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Input Parameters & R Code