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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

Fri, 17 Dec 2010 20:26:36 +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/2010/Dec/17/t1292617488s7nlxzzl81n763q.htm/, Retrieved Fri, 03 May 2024 15:20:37 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111712, Retrieved Fri, 03 May 2024 15:20:37 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

159

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

-     [Univariate Data Series] [Bouwvergunningen] [2009-11-02 16:57:06] [11ac052cc87d77b9933b02bea117068e]
-   P   [Univariate Data Series] [Bouwvergunningen ...] [2009-11-11 14:29:30] [11ac052cc87d77b9933b02bea117068e]
- RMPD    [Variance Reduction Matrix] [Workshop 6] [2010-12-16 20:00:53] [29e492448d11757ae0fad5ef6e7f8e86]
- RMPD        [(Partial) Autocorrelation Function] [] [2010-12-17 20:26:36] [0956ee981dded61b2e7128dae94e5715] [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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111712&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]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=111712&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111712&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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.974859	7.9796	0
2	0.936935	7.6691	0
3	0.899764	7.3649	0
4	0.856557	7.0112	0
5	0.797706	6.5295	0
6	0.730512	5.9795	0
7	0.659883	5.4014	0
8	0.593384	4.8571	4e-06
9	0.522334	4.2755	3.1e-05
10	0.448463	3.6708	0.00024
11	0.37884	3.1009	0.001411
12	0.308445	2.5247	0.006976
13	0.235466	1.9274	0.029087
14	0.161895	1.3252	0.094809
15	0.087333	0.7148	0.238593
16	0.01367	0.1119	0.455622
17	-0.061804	-0.5059	0.307298
18	-0.135795	-1.1115	0.135156

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.974859 & 7.9796 & 0 \tabularnewline
2 & 0.936935 & 7.6691 & 0 \tabularnewline
3 & 0.899764 & 7.3649 & 0 \tabularnewline
4 & 0.856557 & 7.0112 & 0 \tabularnewline
5 & 0.797706 & 6.5295 & 0 \tabularnewline
6 & 0.730512 & 5.9795 & 0 \tabularnewline
7 & 0.659883 & 5.4014 & 0 \tabularnewline
8 & 0.593384 & 4.8571 & 4e-06 \tabularnewline
9 & 0.522334 & 4.2755 & 3.1e-05 \tabularnewline
10 & 0.448463 & 3.6708 & 0.00024 \tabularnewline
11 & 0.37884 & 3.1009 & 0.001411 \tabularnewline
12 & 0.308445 & 2.5247 & 0.006976 \tabularnewline
13 & 0.235466 & 1.9274 & 0.029087 \tabularnewline
14 & 0.161895 & 1.3252 & 0.094809 \tabularnewline
15 & 0.087333 & 0.7148 & 0.238593 \tabularnewline
16 & 0.01367 & 0.1119 & 0.455622 \tabularnewline
17 & -0.061804 & -0.5059 & 0.307298 \tabularnewline
18 & -0.135795 & -1.1115 & 0.135156 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111712&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]0.974859[/C][C]7.9796[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.936935[/C][C]7.6691[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.899764[/C][C]7.3649[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.856557[/C][C]7.0112[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.797706[/C][C]6.5295[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.730512[/C][C]5.9795[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.659883[/C][C]5.4014[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.593384[/C][C]4.8571[/C][C]4e-06[/C][/ROW]
[ROW][C]9[/C][C]0.522334[/C][C]4.2755[/C][C]3.1e-05[/C][/ROW]
[ROW][C]10[/C][C]0.448463[/C][C]3.6708[/C][C]0.00024[/C][/ROW]
[ROW][C]11[/C][C]0.37884[/C][C]3.1009[/C][C]0.001411[/C][/ROW]
[ROW][C]12[/C][C]0.308445[/C][C]2.5247[/C][C]0.006976[/C][/ROW]
[ROW][C]13[/C][C]0.235466[/C][C]1.9274[/C][C]0.029087[/C][/ROW]
[ROW][C]14[/C][C]0.161895[/C][C]1.3252[/C][C]0.094809[/C][/ROW]
[ROW][C]15[/C][C]0.087333[/C][C]0.7148[/C][C]0.238593[/C][/ROW]
[ROW][C]16[/C][C]0.01367[/C][C]0.1119[/C][C]0.455622[/C][/ROW]
[ROW][C]17[/C][C]-0.061804[/C][C]-0.5059[/C][C]0.307298[/C][/ROW]
[ROW][C]18[/C][C]-0.135795[/C][C]-1.1115[/C][C]0.135156[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111712&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111712&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	0.974859	7.9796	0
2	0.936935	7.6691	0
3	0.899764	7.3649	0
4	0.856557	7.0112	0
5	0.797706	6.5295	0
6	0.730512	5.9795	0
7	0.659883	5.4014	0
8	0.593384	4.8571	4e-06
9	0.522334	4.2755	3.1e-05
10	0.448463	3.6708	0.00024
11	0.37884	3.1009	0.001411
12	0.308445	2.5247	0.006976
13	0.235466	1.9274	0.029087
14	0.161895	1.3252	0.094809
15	0.087333	0.7148	0.238593
16	0.01367	0.1119	0.455622
17	-0.061804	-0.5059	0.307298
18	-0.135795	-1.1115	0.135156

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.974859	7.9796	0
2	-0.270186	-2.2116	0.015206
3	0.065085	0.5327	0.297987
4	-0.178761	-1.4632	0.074041
5	-0.292323	-2.3928	0.009766
6	-0.090981	-0.7447	0.229524
7	-0.106817	-0.8743	0.192531
8	0.123542	1.0112	0.157772
9	-0.121385	-0.9936	0.162002
10	0.020903	0.1711	0.432332
11	0.061307	0.5018	0.308719
12	-0.182646	-1.495	0.069802
13	-0.036815	-0.3013	0.382041
14	-0.115913	-0.9488	0.173069
15	-0.11541	-0.9447	0.174111
16	-0.036617	-0.2997	0.382659
17	-0.147073	-1.2038	0.116442
18	0.060669	0.4966	0.31055

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.974859 & 7.9796 & 0 \tabularnewline
2 & -0.270186 & -2.2116 & 0.015206 \tabularnewline
3 & 0.065085 & 0.5327 & 0.297987 \tabularnewline
4 & -0.178761 & -1.4632 & 0.074041 \tabularnewline
5 & -0.292323 & -2.3928 & 0.009766 \tabularnewline
6 & -0.090981 & -0.7447 & 0.229524 \tabularnewline
7 & -0.106817 & -0.8743 & 0.192531 \tabularnewline
8 & 0.123542 & 1.0112 & 0.157772 \tabularnewline
9 & -0.121385 & -0.9936 & 0.162002 \tabularnewline
10 & 0.020903 & 0.1711 & 0.432332 \tabularnewline
11 & 0.061307 & 0.5018 & 0.308719 \tabularnewline
12 & -0.182646 & -1.495 & 0.069802 \tabularnewline
13 & -0.036815 & -0.3013 & 0.382041 \tabularnewline
14 & -0.115913 & -0.9488 & 0.173069 \tabularnewline
15 & -0.11541 & -0.9447 & 0.174111 \tabularnewline
16 & -0.036617 & -0.2997 & 0.382659 \tabularnewline
17 & -0.147073 & -1.2038 & 0.116442 \tabularnewline
18 & 0.060669 & 0.4966 & 0.31055 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111712&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]0.974859[/C][C]7.9796[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.270186[/C][C]-2.2116[/C][C]0.015206[/C][/ROW]
[ROW][C]3[/C][C]0.065085[/C][C]0.5327[/C][C]0.297987[/C][/ROW]
[ROW][C]4[/C][C]-0.178761[/C][C]-1.4632[/C][C]0.074041[/C][/ROW]
[ROW][C]5[/C][C]-0.292323[/C][C]-2.3928[/C][C]0.009766[/C][/ROW]
[ROW][C]6[/C][C]-0.090981[/C][C]-0.7447[/C][C]0.229524[/C][/ROW]
[ROW][C]7[/C][C]-0.106817[/C][C]-0.8743[/C][C]0.192531[/C][/ROW]
[ROW][C]8[/C][C]0.123542[/C][C]1.0112[/C][C]0.157772[/C][/ROW]
[ROW][C]9[/C][C]-0.121385[/C][C]-0.9936[/C][C]0.162002[/C][/ROW]
[ROW][C]10[/C][C]0.020903[/C][C]0.1711[/C][C]0.432332[/C][/ROW]
[ROW][C]11[/C][C]0.061307[/C][C]0.5018[/C][C]0.308719[/C][/ROW]
[ROW][C]12[/C][C]-0.182646[/C][C]-1.495[/C][C]0.069802[/C][/ROW]
[ROW][C]13[/C][C]-0.036815[/C][C]-0.3013[/C][C]0.382041[/C][/ROW]
[ROW][C]14[/C][C]-0.115913[/C][C]-0.9488[/C][C]0.173069[/C][/ROW]
[ROW][C]15[/C][C]-0.11541[/C][C]-0.9447[/C][C]0.174111[/C][/ROW]
[ROW][C]16[/C][C]-0.036617[/C][C]-0.2997[/C][C]0.382659[/C][/ROW]
[ROW][C]17[/C][C]-0.147073[/C][C]-1.2038[/C][C]0.116442[/C][/ROW]
[ROW][C]18[/C][C]0.060669[/C][C]0.4966[/C][C]0.31055[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111712&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111712&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	0.974859	7.9796	0
2	-0.270186	-2.2116	0.015206
3	0.065085	0.5327	0.297987
4	-0.178761	-1.4632	0.074041
5	-0.292323	-2.3928	0.009766
6	-0.090981	-0.7447	0.229524
7	-0.106817	-0.8743	0.192531
8	0.123542	1.0112	0.157772
9	-0.121385	-0.9936	0.162002
10	0.020903	0.1711	0.432332
11	0.061307	0.5018	0.308719
12	-0.182646	-1.495	0.069802
13	-0.036815	-0.3013	0.382041
14	-0.115913	-0.9488	0.173069
15	-0.11541	-0.9447	0.174111
16	-0.036617	-0.2997	0.382659
17	-0.147073	-1.2038	0.116442
18	0.060669	0.4966	0.31055

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; 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