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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 19 Oct 2014 17:23:39 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Oct/19/t1413735899rc30p05z7fa8mmm.htm/, Retrieved Sat, 11 May 2024 11:50:12 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=243698, Retrieved Sat, 11 May 2024 11:50:12 +0000

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-       [(Partial) Autocorrelation Function] [] [2014-10-19 16:23:39] [517bf63cbd197750110a40d4d2cd39d6] [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=243698&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=243698&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243698&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	-0.001138	-0.0095	0.496243
2	0.037937	0.3151	0.376806
3	0.041706	0.3464	0.365036
4	-0.072986	-0.6063	0.273162
5	-0.039698	-0.3298	0.371291
6	-0.22499	-1.8689	0.03294
7	-0.058192	-0.4834	0.31518
8	-0.114161	-0.9483	0.173146
9	0.021958	0.1824	0.427903
10	0.030132	0.2503	0.401551
11	-0.158024	-1.3126	0.096825
12	0.552372	4.5883	1e-05
13	-0.179036	-1.4872	0.07076
14	-0.035782	-0.2972	0.383593
15	-0.029944	-0.2487	0.402154
16	-0.088227	-0.7329	0.23306
17	-0.072457	-0.6019	0.274616
18	-0.172607	-1.4338	0.078075

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.001138 & -0.0095 & 0.496243 \tabularnewline
2 & 0.037937 & 0.3151 & 0.376806 \tabularnewline
3 & 0.041706 & 0.3464 & 0.365036 \tabularnewline
4 & -0.072986 & -0.6063 & 0.273162 \tabularnewline
5 & -0.039698 & -0.3298 & 0.371291 \tabularnewline
6 & -0.22499 & -1.8689 & 0.03294 \tabularnewline
7 & -0.058192 & -0.4834 & 0.31518 \tabularnewline
8 & -0.114161 & -0.9483 & 0.173146 \tabularnewline
9 & 0.021958 & 0.1824 & 0.427903 \tabularnewline
10 & 0.030132 & 0.2503 & 0.401551 \tabularnewline
11 & -0.158024 & -1.3126 & 0.096825 \tabularnewline
12 & 0.552372 & 4.5883 & 1e-05 \tabularnewline
13 & -0.179036 & -1.4872 & 0.07076 \tabularnewline
14 & -0.035782 & -0.2972 & 0.383593 \tabularnewline
15 & -0.029944 & -0.2487 & 0.402154 \tabularnewline
16 & -0.088227 & -0.7329 & 0.23306 \tabularnewline
17 & -0.072457 & -0.6019 & 0.274616 \tabularnewline
18 & -0.172607 & -1.4338 & 0.078075 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243698&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]-0.001138[/C][C]-0.0095[/C][C]0.496243[/C][/ROW]
[ROW][C]2[/C][C]0.037937[/C][C]0.3151[/C][C]0.376806[/C][/ROW]
[ROW][C]3[/C][C]0.041706[/C][C]0.3464[/C][C]0.365036[/C][/ROW]
[ROW][C]4[/C][C]-0.072986[/C][C]-0.6063[/C][C]0.273162[/C][/ROW]
[ROW][C]5[/C][C]-0.039698[/C][C]-0.3298[/C][C]0.371291[/C][/ROW]
[ROW][C]6[/C][C]-0.22499[/C][C]-1.8689[/C][C]0.03294[/C][/ROW]
[ROW][C]7[/C][C]-0.058192[/C][C]-0.4834[/C][C]0.31518[/C][/ROW]
[ROW][C]8[/C][C]-0.114161[/C][C]-0.9483[/C][C]0.173146[/C][/ROW]
[ROW][C]9[/C][C]0.021958[/C][C]0.1824[/C][C]0.427903[/C][/ROW]
[ROW][C]10[/C][C]0.030132[/C][C]0.2503[/C][C]0.401551[/C][/ROW]
[ROW][C]11[/C][C]-0.158024[/C][C]-1.3126[/C][C]0.096825[/C][/ROW]
[ROW][C]12[/C][C]0.552372[/C][C]4.5883[/C][C]1e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.179036[/C][C]-1.4872[/C][C]0.07076[/C][/ROW]
[ROW][C]14[/C][C]-0.035782[/C][C]-0.2972[/C][C]0.383593[/C][/ROW]
[ROW][C]15[/C][C]-0.029944[/C][C]-0.2487[/C][C]0.402154[/C][/ROW]
[ROW][C]16[/C][C]-0.088227[/C][C]-0.7329[/C][C]0.23306[/C][/ROW]
[ROW][C]17[/C][C]-0.072457[/C][C]-0.6019[/C][C]0.274616[/C][/ROW]
[ROW][C]18[/C][C]-0.172607[/C][C]-1.4338[/C][C]0.078075[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243698&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243698&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	-0.001138	-0.0095	0.496243
2	0.037937	0.3151	0.376806
3	0.041706	0.3464	0.365036
4	-0.072986	-0.6063	0.273162
5	-0.039698	-0.3298	0.371291
6	-0.22499	-1.8689	0.03294
7	-0.058192	-0.4834	0.31518
8	-0.114161	-0.9483	0.173146
9	0.021958	0.1824	0.427903
10	0.030132	0.2503	0.401551
11	-0.158024	-1.3126	0.096825
12	0.552372	4.5883	1e-05
13	-0.179036	-1.4872	0.07076
14	-0.035782	-0.2972	0.383593
15	-0.029944	-0.2487	0.402154
16	-0.088227	-0.7329	0.23306
17	-0.072457	-0.6019	0.274616
18	-0.172607	-1.4338	0.078075

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.001138	-0.0095	0.496243
2	0.037936	0.3151	0.37681
3	0.041851	0.3476	0.364586
4	-0.074506	-0.6189	0.269014
5	-0.043412	-0.3606	0.359747
6	-0.223391	-1.8556	0.033889
7	-0.055284	-0.4592	0.323759
8	-0.109538	-0.9099	0.183023
9	0.037082	0.308	0.379496
10	0.008302	0.069	0.472609
11	-0.186749	-1.5513	0.062708
12	0.527551	4.3822	2.1e-05
13	-0.355938	-2.9566	0.002127
14	-0.004606	-0.0383	0.484794
15	-0.118367	-0.9832	0.164466
16	-0.028651	-0.238	0.406297
17	-0.134863	-1.1203	0.133245
18	0.015815	0.1314	0.447932

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.001138 & -0.0095 & 0.496243 \tabularnewline
2 & 0.037936 & 0.3151 & 0.37681 \tabularnewline
3 & 0.041851 & 0.3476 & 0.364586 \tabularnewline
4 & -0.074506 & -0.6189 & 0.269014 \tabularnewline
5 & -0.043412 & -0.3606 & 0.359747 \tabularnewline
6 & -0.223391 & -1.8556 & 0.033889 \tabularnewline
7 & -0.055284 & -0.4592 & 0.323759 \tabularnewline
8 & -0.109538 & -0.9099 & 0.183023 \tabularnewline
9 & 0.037082 & 0.308 & 0.379496 \tabularnewline
10 & 0.008302 & 0.069 & 0.472609 \tabularnewline
11 & -0.186749 & -1.5513 & 0.062708 \tabularnewline
12 & 0.527551 & 4.3822 & 2.1e-05 \tabularnewline
13 & -0.355938 & -2.9566 & 0.002127 \tabularnewline
14 & -0.004606 & -0.0383 & 0.484794 \tabularnewline
15 & -0.118367 & -0.9832 & 0.164466 \tabularnewline
16 & -0.028651 & -0.238 & 0.406297 \tabularnewline
17 & -0.134863 & -1.1203 & 0.133245 \tabularnewline
18 & 0.015815 & 0.1314 & 0.447932 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243698&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]-0.001138[/C][C]-0.0095[/C][C]0.496243[/C][/ROW]
[ROW][C]2[/C][C]0.037936[/C][C]0.3151[/C][C]0.37681[/C][/ROW]
[ROW][C]3[/C][C]0.041851[/C][C]0.3476[/C][C]0.364586[/C][/ROW]
[ROW][C]4[/C][C]-0.074506[/C][C]-0.6189[/C][C]0.269014[/C][/ROW]
[ROW][C]5[/C][C]-0.043412[/C][C]-0.3606[/C][C]0.359747[/C][/ROW]
[ROW][C]6[/C][C]-0.223391[/C][C]-1.8556[/C][C]0.033889[/C][/ROW]
[ROW][C]7[/C][C]-0.055284[/C][C]-0.4592[/C][C]0.323759[/C][/ROW]
[ROW][C]8[/C][C]-0.109538[/C][C]-0.9099[/C][C]0.183023[/C][/ROW]
[ROW][C]9[/C][C]0.037082[/C][C]0.308[/C][C]0.379496[/C][/ROW]
[ROW][C]10[/C][C]0.008302[/C][C]0.069[/C][C]0.472609[/C][/ROW]
[ROW][C]11[/C][C]-0.186749[/C][C]-1.5513[/C][C]0.062708[/C][/ROW]
[ROW][C]12[/C][C]0.527551[/C][C]4.3822[/C][C]2.1e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.355938[/C][C]-2.9566[/C][C]0.002127[/C][/ROW]
[ROW][C]14[/C][C]-0.004606[/C][C]-0.0383[/C][C]0.484794[/C][/ROW]
[ROW][C]15[/C][C]-0.118367[/C][C]-0.9832[/C][C]0.164466[/C][/ROW]
[ROW][C]16[/C][C]-0.028651[/C][C]-0.238[/C][C]0.406297[/C][/ROW]
[ROW][C]17[/C][C]-0.134863[/C][C]-1.1203[/C][C]0.133245[/C][/ROW]
[ROW][C]18[/C][C]0.015815[/C][C]0.1314[/C][C]0.447932[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243698&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243698&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	-0.001138	-0.0095	0.496243
2	0.037936	0.3151	0.37681
3	0.041851	0.3476	0.364586
4	-0.074506	-0.6189	0.269014
5	-0.043412	-0.3606	0.359747
6	-0.223391	-1.8556	0.033889
7	-0.055284	-0.4592	0.323759
8	-0.109538	-0.9099	0.183023
9	0.037082	0.308	0.379496
10	0.008302	0.069	0.472609
11	-0.186749	-1.5513	0.062708
12	0.527551	4.3822	2.1e-05
13	-0.355938	-2.9566	0.002127
14	-0.004606	-0.0383	0.484794
15	-0.118367	-0.9832	0.164466
16	-0.028651	-0.238	0.406297
17	-0.134863	-1.1203	0.133245
18	0.015815	0.1314	0.447932

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 = 0 ; par4 = 0 ; par5 = 6 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 6 ; 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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code