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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

Mon, 19 Dec 2011 19:09:45 -0500

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/2011/Dec/19/t1324339812vptf4w9rpdw9d4h.htm/, Retrieved Wed, 15 May 2024 18:59:14 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=157748, Retrieved Wed, 15 May 2024 18:59:14 +0000

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-     [(Partial) Autocorrelation Function] [paper] [2011-12-20 00:02:17] [43239ed98a62e091c70785d80176537f]
- R P     [(Partial) Autocorrelation Function] [paper] [2011-12-20 00:09:45] [6e647d331a8f33aa61a2d78ef323178e] [Current]

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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' @ jenkins.wessa.net

\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' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157748&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157748&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157748&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' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.291002	-2.2728	0.013287
2	0.218171	1.704	0.046738
3	0.075947	0.5932	0.277631
4	-0.083729	-0.6539	0.257802
5	0.022596	0.1765	0.430251
6	-0.075011	-0.5859	0.280068
7	0.031198	0.2437	0.404154
8	-0.151709	-1.1849	0.120329
9	-0.064104	-0.5007	0.309203
10	-0.100204	-0.7826	0.21844
11	-0.068611	-0.5359	0.296999
12	0.073809	0.5765	0.283211
13	-0.099433	-0.7766	0.220198
14	0.028168	0.22	0.413304
15	0.011828	0.0924	0.463349
16	-0.114213	-0.892	0.187941
17	0.109296	0.8536	0.198325
18	-0.125779	-0.9824	0.164899

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.291002 & -2.2728 & 0.013287 \tabularnewline
2 & 0.218171 & 1.704 & 0.046738 \tabularnewline
3 & 0.075947 & 0.5932 & 0.277631 \tabularnewline
4 & -0.083729 & -0.6539 & 0.257802 \tabularnewline
5 & 0.022596 & 0.1765 & 0.430251 \tabularnewline
6 & -0.075011 & -0.5859 & 0.280068 \tabularnewline
7 & 0.031198 & 0.2437 & 0.404154 \tabularnewline
8 & -0.151709 & -1.1849 & 0.120329 \tabularnewline
9 & -0.064104 & -0.5007 & 0.309203 \tabularnewline
10 & -0.100204 & -0.7826 & 0.21844 \tabularnewline
11 & -0.068611 & -0.5359 & 0.296999 \tabularnewline
12 & 0.073809 & 0.5765 & 0.283211 \tabularnewline
13 & -0.099433 & -0.7766 & 0.220198 \tabularnewline
14 & 0.028168 & 0.22 & 0.413304 \tabularnewline
15 & 0.011828 & 0.0924 & 0.463349 \tabularnewline
16 & -0.114213 & -0.892 & 0.187941 \tabularnewline
17 & 0.109296 & 0.8536 & 0.198325 \tabularnewline
18 & -0.125779 & -0.9824 & 0.164899 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157748&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]-0.291002[/C][C]-2.2728[/C][C]0.013287[/C][/ROW]
[ROW][C]2[/C][C]0.218171[/C][C]1.704[/C][C]0.046738[/C][/ROW]
[ROW][C]3[/C][C]0.075947[/C][C]0.5932[/C][C]0.277631[/C][/ROW]
[ROW][C]4[/C][C]-0.083729[/C][C]-0.6539[/C][C]0.257802[/C][/ROW]
[ROW][C]5[/C][C]0.022596[/C][C]0.1765[/C][C]0.430251[/C][/ROW]
[ROW][C]6[/C][C]-0.075011[/C][C]-0.5859[/C][C]0.280068[/C][/ROW]
[ROW][C]7[/C][C]0.031198[/C][C]0.2437[/C][C]0.404154[/C][/ROW]
[ROW][C]8[/C][C]-0.151709[/C][C]-1.1849[/C][C]0.120329[/C][/ROW]
[ROW][C]9[/C][C]-0.064104[/C][C]-0.5007[/C][C]0.309203[/C][/ROW]
[ROW][C]10[/C][C]-0.100204[/C][C]-0.7826[/C][C]0.21844[/C][/ROW]
[ROW][C]11[/C][C]-0.068611[/C][C]-0.5359[/C][C]0.296999[/C][/ROW]
[ROW][C]12[/C][C]0.073809[/C][C]0.5765[/C][C]0.283211[/C][/ROW]
[ROW][C]13[/C][C]-0.099433[/C][C]-0.7766[/C][C]0.220198[/C][/ROW]
[ROW][C]14[/C][C]0.028168[/C][C]0.22[/C][C]0.413304[/C][/ROW]
[ROW][C]15[/C][C]0.011828[/C][C]0.0924[/C][C]0.463349[/C][/ROW]
[ROW][C]16[/C][C]-0.114213[/C][C]-0.892[/C][C]0.187941[/C][/ROW]
[ROW][C]17[/C][C]0.109296[/C][C]0.8536[/C][C]0.198325[/C][/ROW]
[ROW][C]18[/C][C]-0.125779[/C][C]-0.9824[/C][C]0.164899[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157748&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157748&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	-0.291002	-2.2728	0.013287
2	0.218171	1.704	0.046738
3	0.075947	0.5932	0.277631
4	-0.083729	-0.6539	0.257802
5	0.022596	0.1765	0.430251
6	-0.075011	-0.5859	0.280068
7	0.031198	0.2437	0.404154
8	-0.151709	-1.1849	0.120329
9	-0.064104	-0.5007	0.309203
10	-0.100204	-0.7826	0.21844
11	-0.068611	-0.5359	0.296999
12	0.073809	0.5765	0.283211
13	-0.099433	-0.7766	0.220198
14	0.028168	0.22	0.413304
15	0.011828	0.0924	0.463349
16	-0.114213	-0.892	0.187941
17	0.109296	0.8536	0.198325
18	-0.125779	-0.9824	0.164899

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.291002	-2.2728	0.013287
2	0.145839	1.139	0.12957
3	0.192684	1.5049	0.068754
4	-0.056705	-0.4429	0.329709
5	-0.081783	-0.6387	0.262689
6	-0.084242	-0.658	0.256521
7	0.030704	0.2398	0.405643
8	-0.122059	-0.9533	0.172098
9	-0.159813	-1.2482	0.108368
10	-0.13786	-1.0767	0.142923
11	-0.056186	-0.4388	0.331169
12	0.111707	0.8725	0.19319
13	-0.030539	-0.2385	0.406141
14	-0.093508	-0.7303	0.233995
15	-0.024903	-0.1945	0.423217
16	-0.121584	-0.9496	0.173031
17	0.012078	0.0943	0.462579
18	-0.123855	-0.9673	0.168597

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.291002 & -2.2728 & 0.013287 \tabularnewline
2 & 0.145839 & 1.139 & 0.12957 \tabularnewline
3 & 0.192684 & 1.5049 & 0.068754 \tabularnewline
4 & -0.056705 & -0.4429 & 0.329709 \tabularnewline
5 & -0.081783 & -0.6387 & 0.262689 \tabularnewline
6 & -0.084242 & -0.658 & 0.256521 \tabularnewline
7 & 0.030704 & 0.2398 & 0.405643 \tabularnewline
8 & -0.122059 & -0.9533 & 0.172098 \tabularnewline
9 & -0.159813 & -1.2482 & 0.108368 \tabularnewline
10 & -0.13786 & -1.0767 & 0.142923 \tabularnewline
11 & -0.056186 & -0.4388 & 0.331169 \tabularnewline
12 & 0.111707 & 0.8725 & 0.19319 \tabularnewline
13 & -0.030539 & -0.2385 & 0.406141 \tabularnewline
14 & -0.093508 & -0.7303 & 0.233995 \tabularnewline
15 & -0.024903 & -0.1945 & 0.423217 \tabularnewline
16 & -0.121584 & -0.9496 & 0.173031 \tabularnewline
17 & 0.012078 & 0.0943 & 0.462579 \tabularnewline
18 & -0.123855 & -0.9673 & 0.168597 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157748&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]-0.291002[/C][C]-2.2728[/C][C]0.013287[/C][/ROW]
[ROW][C]2[/C][C]0.145839[/C][C]1.139[/C][C]0.12957[/C][/ROW]
[ROW][C]3[/C][C]0.192684[/C][C]1.5049[/C][C]0.068754[/C][/ROW]
[ROW][C]4[/C][C]-0.056705[/C][C]-0.4429[/C][C]0.329709[/C][/ROW]
[ROW][C]5[/C][C]-0.081783[/C][C]-0.6387[/C][C]0.262689[/C][/ROW]
[ROW][C]6[/C][C]-0.084242[/C][C]-0.658[/C][C]0.256521[/C][/ROW]
[ROW][C]7[/C][C]0.030704[/C][C]0.2398[/C][C]0.405643[/C][/ROW]
[ROW][C]8[/C][C]-0.122059[/C][C]-0.9533[/C][C]0.172098[/C][/ROW]
[ROW][C]9[/C][C]-0.159813[/C][C]-1.2482[/C][C]0.108368[/C][/ROW]
[ROW][C]10[/C][C]-0.13786[/C][C]-1.0767[/C][C]0.142923[/C][/ROW]
[ROW][C]11[/C][C]-0.056186[/C][C]-0.4388[/C][C]0.331169[/C][/ROW]
[ROW][C]12[/C][C]0.111707[/C][C]0.8725[/C][C]0.19319[/C][/ROW]
[ROW][C]13[/C][C]-0.030539[/C][C]-0.2385[/C][C]0.406141[/C][/ROW]
[ROW][C]14[/C][C]-0.093508[/C][C]-0.7303[/C][C]0.233995[/C][/ROW]
[ROW][C]15[/C][C]-0.024903[/C][C]-0.1945[/C][C]0.423217[/C][/ROW]
[ROW][C]16[/C][C]-0.121584[/C][C]-0.9496[/C][C]0.173031[/C][/ROW]
[ROW][C]17[/C][C]0.012078[/C][C]0.0943[/C][C]0.462579[/C][/ROW]
[ROW][C]18[/C][C]-0.123855[/C][C]-0.9673[/C][C]0.168597[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157748&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157748&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	-0.291002	-2.2728	0.013287
2	0.145839	1.139	0.12957
3	0.192684	1.5049	0.068754
4	-0.056705	-0.4429	0.329709
5	-0.081783	-0.6387	0.262689
6	-0.084242	-0.658	0.256521
7	0.030704	0.2398	0.405643
8	-0.122059	-0.9533	0.172098
9	-0.159813	-1.2482	0.108368
10	-0.13786	-1.0767	0.142923
11	-0.056186	-0.4388	0.331169
12	0.111707	0.8725	0.19319
13	-0.030539	-0.2385	0.406141
14	-0.093508	-0.7303	0.233995
15	-0.024903	-0.1945	0.423217
16	-0.121584	-0.9496	0.173031
17	0.012078	0.0943	0.462579
18	-0.123855	-0.9673	0.168597

Figure 1

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Postscript link

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Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 4 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 4 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

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 (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
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