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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 26 Nov 2007 11:12:16 -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/Nov/26/t1196100172nlu4e2n2f96sk3p.htm/, Retrieved Tue, 10 Feb 2026 08:10:04 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6605, Retrieved Tue, 10 Feb 2026 08:10:04 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

471

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

-       [(Partial) Autocorrelation Function] [autocorr. frank] [2007-11-26 18:12:16] [6bdd947de0ee04552c8f0fc807f31807] [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	1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6605&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]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=6605&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6605&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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	7.746	0
1	0.271197	2.1007	0.01994
2	0.059359	0.4598	0.323663
3	0.404667	3.1345	0.001332
4	-0.002013	-0.0156	0.506194
5	0.077887	0.6033	0.274289
6	0.438339	3.3954	0.00061
7	0.01554	0.1204	0.452296
8	0.013367	0.1035	0.458941
9	0.282042	2.1847	0.016415
10	-0.131983	-1.0223	0.844636
11	0.148045	1.1467	0.128019
12	0.605382	4.6893	8e-06
13	0.022459	0.174	0.431239
14	0.001091	0.0085	0.496641
15	0.201538	1.5611	0.061879
16	-0.176652	-1.3683	0.911847

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.746 & 0 \tabularnewline
1 & 0.271197 & 2.1007 & 0.01994 \tabularnewline
2 & 0.059359 & 0.4598 & 0.323663 \tabularnewline
3 & 0.404667 & 3.1345 & 0.001332 \tabularnewline
4 & -0.002013 & -0.0156 & 0.506194 \tabularnewline
5 & 0.077887 & 0.6033 & 0.274289 \tabularnewline
6 & 0.438339 & 3.3954 & 0.00061 \tabularnewline
7 & 0.01554 & 0.1204 & 0.452296 \tabularnewline
8 & 0.013367 & 0.1035 & 0.458941 \tabularnewline
9 & 0.282042 & 2.1847 & 0.016415 \tabularnewline
10 & -0.131983 & -1.0223 & 0.844636 \tabularnewline
11 & 0.148045 & 1.1467 & 0.128019 \tabularnewline
12 & 0.605382 & 4.6893 & 8e-06 \tabularnewline
13 & 0.022459 & 0.174 & 0.431239 \tabularnewline
14 & 0.001091 & 0.0085 & 0.496641 \tabularnewline
15 & 0.201538 & 1.5611 & 0.061879 \tabularnewline
16 & -0.176652 & -1.3683 & 0.911847 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6605&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]7.746[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.271197[/C][C]2.1007[/C][C]0.01994[/C][/ROW]
[ROW][C]2[/C][C]0.059359[/C][C]0.4598[/C][C]0.323663[/C][/ROW]
[ROW][C]3[/C][C]0.404667[/C][C]3.1345[/C][C]0.001332[/C][/ROW]
[ROW][C]4[/C][C]-0.002013[/C][C]-0.0156[/C][C]0.506194[/C][/ROW]
[ROW][C]5[/C][C]0.077887[/C][C]0.6033[/C][C]0.274289[/C][/ROW]
[ROW][C]6[/C][C]0.438339[/C][C]3.3954[/C][C]0.00061[/C][/ROW]
[ROW][C]7[/C][C]0.01554[/C][C]0.1204[/C][C]0.452296[/C][/ROW]
[ROW][C]8[/C][C]0.013367[/C][C]0.1035[/C][C]0.458941[/C][/ROW]
[ROW][C]9[/C][C]0.282042[/C][C]2.1847[/C][C]0.016415[/C][/ROW]
[ROW][C]10[/C][C]-0.131983[/C][C]-1.0223[/C][C]0.844636[/C][/ROW]
[ROW][C]11[/C][C]0.148045[/C][C]1.1467[/C][C]0.128019[/C][/ROW]
[ROW][C]12[/C][C]0.605382[/C][C]4.6893[/C][C]8e-06[/C][/ROW]
[ROW][C]13[/C][C]0.022459[/C][C]0.174[/C][C]0.431239[/C][/ROW]
[ROW][C]14[/C][C]0.001091[/C][C]0.0085[/C][C]0.496641[/C][/ROW]
[ROW][C]15[/C][C]0.201538[/C][C]1.5611[/C][C]0.061879[/C][/ROW]
[ROW][C]16[/C][C]-0.176652[/C][C]-1.3683[/C][C]0.911847[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6605&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6605&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	7.746	0
1	0.271197	2.1007	0.01994
2	0.059359	0.4598	0.323663
3	0.404667	3.1345	0.001332
4	-0.002013	-0.0156	0.506194
5	0.077887	0.6033	0.274289
6	0.438339	3.3954	0.00061
7	0.01554	0.1204	0.452296
8	0.013367	0.1035	0.458941
9	0.282042	2.1847	0.016415
10	-0.131983	-1.0223	0.844636
11	0.148045	1.1467	0.128019
12	0.605382	4.6893	8e-06
13	0.022459	0.174	0.431239
14	0.001091	0.0085	0.496641
15	0.201538	1.5611	0.061879
16	-0.176652	-1.3683	0.911847

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.271197	2.1007	0.01994
1	-0.015315	-0.1186	0.547017
2	0.423733	3.2822	0.00086
3	-0.293638	-2.2745	0.986738
4	0.284227	2.2016	0.015775
5	0.19139	1.4825	0.07172
6	-0.126839	-0.9825	0.835097
7	0.036309	0.2812	0.389745
8	0.037186	0.288	0.387152
9	-0.179219	-1.3882	0.914899
10	0.381316	2.9537	0.00224
11	0.340893	2.6405	0.005268
12	-0.235032	-1.8205	0.963168
13	-0.099659	-0.772	0.778415
14	-0.177591	-1.3756	0.912972
15	0.032239	0.2497	0.401827
16	-0.014792	-0.1146	0.545418

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.271197 & 2.1007 & 0.01994 \tabularnewline
1 & -0.015315 & -0.1186 & 0.547017 \tabularnewline
2 & 0.423733 & 3.2822 & 0.00086 \tabularnewline
3 & -0.293638 & -2.2745 & 0.986738 \tabularnewline
4 & 0.284227 & 2.2016 & 0.015775 \tabularnewline
5 & 0.19139 & 1.4825 & 0.07172 \tabularnewline
6 & -0.126839 & -0.9825 & 0.835097 \tabularnewline
7 & 0.036309 & 0.2812 & 0.389745 \tabularnewline
8 & 0.037186 & 0.288 & 0.387152 \tabularnewline
9 & -0.179219 & -1.3882 & 0.914899 \tabularnewline
10 & 0.381316 & 2.9537 & 0.00224 \tabularnewline
11 & 0.340893 & 2.6405 & 0.005268 \tabularnewline
12 & -0.235032 & -1.8205 & 0.963168 \tabularnewline
13 & -0.099659 & -0.772 & 0.778415 \tabularnewline
14 & -0.177591 & -1.3756 & 0.912972 \tabularnewline
15 & 0.032239 & 0.2497 & 0.401827 \tabularnewline
16 & -0.014792 & -0.1146 & 0.545418 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6605&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]0.271197[/C][C]2.1007[/C][C]0.01994[/C][/ROW]
[ROW][C]1[/C][C]-0.015315[/C][C]-0.1186[/C][C]0.547017[/C][/ROW]
[ROW][C]2[/C][C]0.423733[/C][C]3.2822[/C][C]0.00086[/C][/ROW]
[ROW][C]3[/C][C]-0.293638[/C][C]-2.2745[/C][C]0.986738[/C][/ROW]
[ROW][C]4[/C][C]0.284227[/C][C]2.2016[/C][C]0.015775[/C][/ROW]
[ROW][C]5[/C][C]0.19139[/C][C]1.4825[/C][C]0.07172[/C][/ROW]
[ROW][C]6[/C][C]-0.126839[/C][C]-0.9825[/C][C]0.835097[/C][/ROW]
[ROW][C]7[/C][C]0.036309[/C][C]0.2812[/C][C]0.389745[/C][/ROW]
[ROW][C]8[/C][C]0.037186[/C][C]0.288[/C][C]0.387152[/C][/ROW]
[ROW][C]9[/C][C]-0.179219[/C][C]-1.3882[/C][C]0.914899[/C][/ROW]
[ROW][C]10[/C][C]0.381316[/C][C]2.9537[/C][C]0.00224[/C][/ROW]
[ROW][C]11[/C][C]0.340893[/C][C]2.6405[/C][C]0.005268[/C][/ROW]
[ROW][C]12[/C][C]-0.235032[/C][C]-1.8205[/C][C]0.963168[/C][/ROW]
[ROW][C]13[/C][C]-0.099659[/C][C]-0.772[/C][C]0.778415[/C][/ROW]
[ROW][C]14[/C][C]-0.177591[/C][C]-1.3756[/C][C]0.912972[/C][/ROW]
[ROW][C]15[/C][C]0.032239[/C][C]0.2497[/C][C]0.401827[/C][/ROW]
[ROW][C]16[/C][C]-0.014792[/C][C]-0.1146[/C][C]0.545418[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6605&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6605&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	0.271197	2.1007	0.01994
1	-0.015315	-0.1186	0.547017
2	0.423733	3.2822	0.00086
3	-0.293638	-2.2745	0.986738
4	0.284227	2.2016	0.015775
5	0.19139	1.4825	0.07172
6	-0.126839	-0.9825	0.835097
7	0.036309	0.2812	0.389745
8	0.037186	0.288	0.387152
9	-0.179219	-1.3882	0.914899
10	0.381316	2.9537	0.00224
11	0.340893	2.6405	0.005268
12	-0.235032	-1.8205	0.963168
13	-0.099659	-0.772	0.778415
14	-0.177591	-1.3756	0.912972
15	0.032239	0.2497	0.401827
16	-0.014792	-0.1146	0.545418

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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