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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 21 Dec 2016 10:37:20 +0000

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/2016/Dec/21/t1482316658vjtenbqqdg311pb.htm/, Retrieved Tue, 07 May 2024 02:10:51 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 07 May 2024 02:10:51 +0200

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

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	'Sir Maurice George Kendall' @ kendall.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.396084	-3.8605	0.000103
2	-0.165339	-1.6115	0.055191
3	0.105296	1.0263	0.153679
4	0.04249	0.4141	0.339851
5	-0.123682	-1.2055	0.115501
6	0.074986	0.7309	0.233327
7	0.057752	0.5629	0.287415
8	-0.132342	-1.2899	0.100107
9	-0.114419	-1.1152	0.133785
10	0.261266	2.5465	0.006244
11	0.023927	0.2332	0.40805
12	-0.248018	-2.4174	0.00877
13	0.112602	1.0975	0.137597
14	0.051886	0.5057	0.307113
15	-0.140298	-1.3675	0.087355
16	0.119027	1.1601	0.124451
17	0.028563	0.2784	0.390657
18	-0.066577	-0.6489	0.258979
19	-0.05115	-0.4985	0.309625
20	0.13863	1.3512	0.089921

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.396084 & -3.8605 & 0.000103 \tabularnewline
2 & -0.165339 & -1.6115 & 0.055191 \tabularnewline
3 & 0.105296 & 1.0263 & 0.153679 \tabularnewline
4 & 0.04249 & 0.4141 & 0.339851 \tabularnewline
5 & -0.123682 & -1.2055 & 0.115501 \tabularnewline
6 & 0.074986 & 0.7309 & 0.233327 \tabularnewline
7 & 0.057752 & 0.5629 & 0.287415 \tabularnewline
8 & -0.132342 & -1.2899 & 0.100107 \tabularnewline
9 & -0.114419 & -1.1152 & 0.133785 \tabularnewline
10 & 0.261266 & 2.5465 & 0.006244 \tabularnewline
11 & 0.023927 & 0.2332 & 0.40805 \tabularnewline
12 & -0.248018 & -2.4174 & 0.00877 \tabularnewline
13 & 0.112602 & 1.0975 & 0.137597 \tabularnewline
14 & 0.051886 & 0.5057 & 0.307113 \tabularnewline
15 & -0.140298 & -1.3675 & 0.087355 \tabularnewline
16 & 0.119027 & 1.1601 & 0.124451 \tabularnewline
17 & 0.028563 & 0.2784 & 0.390657 \tabularnewline
18 & -0.066577 & -0.6489 & 0.258979 \tabularnewline
19 & -0.05115 & -0.4985 & 0.309625 \tabularnewline
20 & 0.13863 & 1.3512 & 0.089921 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]-0.396084[/C][C]-3.8605[/C][C]0.000103[/C][/ROW]
[ROW][C]2[/C][C]-0.165339[/C][C]-1.6115[/C][C]0.055191[/C][/ROW]
[ROW][C]3[/C][C]0.105296[/C][C]1.0263[/C][C]0.153679[/C][/ROW]
[ROW][C]4[/C][C]0.04249[/C][C]0.4141[/C][C]0.339851[/C][/ROW]
[ROW][C]5[/C][C]-0.123682[/C][C]-1.2055[/C][C]0.115501[/C][/ROW]
[ROW][C]6[/C][C]0.074986[/C][C]0.7309[/C][C]0.233327[/C][/ROW]
[ROW][C]7[/C][C]0.057752[/C][C]0.5629[/C][C]0.287415[/C][/ROW]
[ROW][C]8[/C][C]-0.132342[/C][C]-1.2899[/C][C]0.100107[/C][/ROW]
[ROW][C]9[/C][C]-0.114419[/C][C]-1.1152[/C][C]0.133785[/C][/ROW]
[ROW][C]10[/C][C]0.261266[/C][C]2.5465[/C][C]0.006244[/C][/ROW]
[ROW][C]11[/C][C]0.023927[/C][C]0.2332[/C][C]0.40805[/C][/ROW]
[ROW][C]12[/C][C]-0.248018[/C][C]-2.4174[/C][C]0.00877[/C][/ROW]
[ROW][C]13[/C][C]0.112602[/C][C]1.0975[/C][C]0.137597[/C][/ROW]
[ROW][C]14[/C][C]0.051886[/C][C]0.5057[/C][C]0.307113[/C][/ROW]
[ROW][C]15[/C][C]-0.140298[/C][C]-1.3675[/C][C]0.087355[/C][/ROW]
[ROW][C]16[/C][C]0.119027[/C][C]1.1601[/C][C]0.124451[/C][/ROW]
[ROW][C]17[/C][C]0.028563[/C][C]0.2784[/C][C]0.390657[/C][/ROW]
[ROW][C]18[/C][C]-0.066577[/C][C]-0.6489[/C][C]0.258979[/C][/ROW]
[ROW][C]19[/C][C]-0.05115[/C][C]-0.4985[/C][C]0.309625[/C][/ROW]
[ROW][C]20[/C][C]0.13863[/C][C]1.3512[/C][C]0.089921[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	-0.396084	-3.8605	0.000103
2	-0.165339	-1.6115	0.055191
3	0.105296	1.0263	0.153679
4	0.04249	0.4141	0.339851
5	-0.123682	-1.2055	0.115501
6	0.074986	0.7309	0.233327
7	0.057752	0.5629	0.287415
8	-0.132342	-1.2899	0.100107
9	-0.114419	-1.1152	0.133785
10	0.261266	2.5465	0.006244
11	0.023927	0.2332	0.40805
12	-0.248018	-2.4174	0.00877
13	0.112602	1.0975	0.137597
14	0.051886	0.5057	0.307113
15	-0.140298	-1.3675	0.087355
16	0.119027	1.1601	0.124451
17	0.028563	0.2784	0.390657
18	-0.066577	-0.6489	0.258979
19	-0.05115	-0.4985	0.309625
20	0.13863	1.3512	0.089921

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.396084	-3.8605	0.000103
2	-0.382179	-3.725	0.000166
3	-0.189723	-1.8492	0.03377
4	-0.068781	-0.6704	0.252116
5	-0.155983	-1.5203	0.065874
6	-0.055644	-0.5423	0.294425
7	0.026775	0.261	0.39734
8	-0.092453	-0.9011	0.184902
9	-0.287784	-2.805	0.003052
10	-0.024672	-0.2405	0.405239
11	0.127804	1.2457	0.107973
12	-0.100389	-0.9785	0.165162
13	-0.067961	-0.6624	0.254658
14	-0.053848	-0.5248	0.300455
15	-0.144209	-1.4056	0.081556
16	-0.020516	-0.2	0.420966
17	-0.046118	-0.4495	0.327046
18	-0.005385	-0.0525	0.479127
19	-0.012103	-0.118	0.453171
20	0.040318	0.393	0.347612

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.396084 & -3.8605 & 0.000103 \tabularnewline
2 & -0.382179 & -3.725 & 0.000166 \tabularnewline
3 & -0.189723 & -1.8492 & 0.03377 \tabularnewline
4 & -0.068781 & -0.6704 & 0.252116 \tabularnewline
5 & -0.155983 & -1.5203 & 0.065874 \tabularnewline
6 & -0.055644 & -0.5423 & 0.294425 \tabularnewline
7 & 0.026775 & 0.261 & 0.39734 \tabularnewline
8 & -0.092453 & -0.9011 & 0.184902 \tabularnewline
9 & -0.287784 & -2.805 & 0.003052 \tabularnewline
10 & -0.024672 & -0.2405 & 0.405239 \tabularnewline
11 & 0.127804 & 1.2457 & 0.107973 \tabularnewline
12 & -0.100389 & -0.9785 & 0.165162 \tabularnewline
13 & -0.067961 & -0.6624 & 0.254658 \tabularnewline
14 & -0.053848 & -0.5248 & 0.300455 \tabularnewline
15 & -0.144209 & -1.4056 & 0.081556 \tabularnewline
16 & -0.020516 & -0.2 & 0.420966 \tabularnewline
17 & -0.046118 & -0.4495 & 0.327046 \tabularnewline
18 & -0.005385 & -0.0525 & 0.479127 \tabularnewline
19 & -0.012103 & -0.118 & 0.453171 \tabularnewline
20 & 0.040318 & 0.393 & 0.347612 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]-0.396084[/C][C]-3.8605[/C][C]0.000103[/C][/ROW]
[ROW][C]2[/C][C]-0.382179[/C][C]-3.725[/C][C]0.000166[/C][/ROW]
[ROW][C]3[/C][C]-0.189723[/C][C]-1.8492[/C][C]0.03377[/C][/ROW]
[ROW][C]4[/C][C]-0.068781[/C][C]-0.6704[/C][C]0.252116[/C][/ROW]
[ROW][C]5[/C][C]-0.155983[/C][C]-1.5203[/C][C]0.065874[/C][/ROW]
[ROW][C]6[/C][C]-0.055644[/C][C]-0.5423[/C][C]0.294425[/C][/ROW]
[ROW][C]7[/C][C]0.026775[/C][C]0.261[/C][C]0.39734[/C][/ROW]
[ROW][C]8[/C][C]-0.092453[/C][C]-0.9011[/C][C]0.184902[/C][/ROW]
[ROW][C]9[/C][C]-0.287784[/C][C]-2.805[/C][C]0.003052[/C][/ROW]
[ROW][C]10[/C][C]-0.024672[/C][C]-0.2405[/C][C]0.405239[/C][/ROW]
[ROW][C]11[/C][C]0.127804[/C][C]1.2457[/C][C]0.107973[/C][/ROW]
[ROW][C]12[/C][C]-0.100389[/C][C]-0.9785[/C][C]0.165162[/C][/ROW]
[ROW][C]13[/C][C]-0.067961[/C][C]-0.6624[/C][C]0.254658[/C][/ROW]
[ROW][C]14[/C][C]-0.053848[/C][C]-0.5248[/C][C]0.300455[/C][/ROW]
[ROW][C]15[/C][C]-0.144209[/C][C]-1.4056[/C][C]0.081556[/C][/ROW]
[ROW][C]16[/C][C]-0.020516[/C][C]-0.2[/C][C]0.420966[/C][/ROW]
[ROW][C]17[/C][C]-0.046118[/C][C]-0.4495[/C][C]0.327046[/C][/ROW]
[ROW][C]18[/C][C]-0.005385[/C][C]-0.0525[/C][C]0.479127[/C][/ROW]
[ROW][C]19[/C][C]-0.012103[/C][C]-0.118[/C][C]0.453171[/C][/ROW]
[ROW][C]20[/C][C]0.040318[/C][C]0.393[/C][C]0.347612[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	-0.396084	-3.8605	0.000103
2	-0.382179	-3.725	0.000166
3	-0.189723	-1.8492	0.03377
4	-0.068781	-0.6704	0.252116
5	-0.155983	-1.5203	0.065874
6	-0.055644	-0.5423	0.294425
7	0.026775	0.261	0.39734
8	-0.092453	-0.9011	0.184902
9	-0.287784	-2.805	0.003052
10	-0.024672	-0.2405	0.405239
11	0.127804	1.2457	0.107973
12	-0.100389	-0.9785	0.165162
13	-0.067961	-0.6624	0.254658
14	-0.053848	-0.5248	0.300455
15	-0.144209	-1.4056	0.081556
16	-0.020516	-0.2	0.420966
17	-0.046118	-0.4495	0.327046
18	-0.005385	-0.0525	0.479127
19	-0.012103	-0.118	0.453171
20	0.040318	0.393	0.347612

Figure 1

PNG link

Postscript link

PDF link

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

R code (references can be found in the software module):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '1'
par2 <- '1'
par1 <- 'Default'
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)
x <- na.omit(x)
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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code