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Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 16 Dec 2010 20:25:22 +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/16/t1292531032e9uf6xypocjnfi6.htm/, Retrieved Fri, 03 May 2024 12:12:24 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111262, Retrieved Fri, 03 May 2024 12:12:24 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

149

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      [(Partial) Autocorrelation Function] [Workshop 6] [2010-12-16 20:25:22] [f149abcac50db27facd6576b094a0cd9] [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	3 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111262&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111262&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111262&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	3 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.339641	-3.3104	0.000659
2	-0.224508	-2.1882	0.015552
3	0.093507	0.9114	0.182197
4	0.140126	1.3658	0.087616
5	-0.191564	-1.8671	0.032483
6	-0.027925	-0.2722	0.393038
7	0.09889	0.9639	0.168781
8	0.022235	0.2167	0.414444
9	-0.081154	-0.791	0.215459
10	0.059105	0.5761	0.282959
11	0.196452	1.9148	0.029265
12	-0.306458	-2.987	0.001792
13	-0.080167	-0.7814	0.218264
14	0.155303	1.5137	0.06671
15	0.105926	1.0324	0.152244
16	-0.236498	-2.3051	0.011669
17	0.124075	1.2093	0.114769
18	0.037832	0.3687	0.356571
19	0.089505	0.8724	0.1926
20	-0.181859	-1.7725	0.039755

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.339641 & -3.3104 & 0.000659 \tabularnewline
2 & -0.224508 & -2.1882 & 0.015552 \tabularnewline
3 & 0.093507 & 0.9114 & 0.182197 \tabularnewline
4 & 0.140126 & 1.3658 & 0.087616 \tabularnewline
5 & -0.191564 & -1.8671 & 0.032483 \tabularnewline
6 & -0.027925 & -0.2722 & 0.393038 \tabularnewline
7 & 0.09889 & 0.9639 & 0.168781 \tabularnewline
8 & 0.022235 & 0.2167 & 0.414444 \tabularnewline
9 & -0.081154 & -0.791 & 0.215459 \tabularnewline
10 & 0.059105 & 0.5761 & 0.282959 \tabularnewline
11 & 0.196452 & 1.9148 & 0.029265 \tabularnewline
12 & -0.306458 & -2.987 & 0.001792 \tabularnewline
13 & -0.080167 & -0.7814 & 0.218264 \tabularnewline
14 & 0.155303 & 1.5137 & 0.06671 \tabularnewline
15 & 0.105926 & 1.0324 & 0.152244 \tabularnewline
16 & -0.236498 & -2.3051 & 0.011669 \tabularnewline
17 & 0.124075 & 1.2093 & 0.114769 \tabularnewline
18 & 0.037832 & 0.3687 & 0.356571 \tabularnewline
19 & 0.089505 & 0.8724 & 0.1926 \tabularnewline
20 & -0.181859 & -1.7725 & 0.039755 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111262&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]-0.339641[/C][C]-3.3104[/C][C]0.000659[/C][/ROW]
[ROW][C]2[/C][C]-0.224508[/C][C]-2.1882[/C][C]0.015552[/C][/ROW]
[ROW][C]3[/C][C]0.093507[/C][C]0.9114[/C][C]0.182197[/C][/ROW]
[ROW][C]4[/C][C]0.140126[/C][C]1.3658[/C][C]0.087616[/C][/ROW]
[ROW][C]5[/C][C]-0.191564[/C][C]-1.8671[/C][C]0.032483[/C][/ROW]
[ROW][C]6[/C][C]-0.027925[/C][C]-0.2722[/C][C]0.393038[/C][/ROW]
[ROW][C]7[/C][C]0.09889[/C][C]0.9639[/C][C]0.168781[/C][/ROW]
[ROW][C]8[/C][C]0.022235[/C][C]0.2167[/C][C]0.414444[/C][/ROW]
[ROW][C]9[/C][C]-0.081154[/C][C]-0.791[/C][C]0.215459[/C][/ROW]
[ROW][C]10[/C][C]0.059105[/C][C]0.5761[/C][C]0.282959[/C][/ROW]
[ROW][C]11[/C][C]0.196452[/C][C]1.9148[/C][C]0.029265[/C][/ROW]
[ROW][C]12[/C][C]-0.306458[/C][C]-2.987[/C][C]0.001792[/C][/ROW]
[ROW][C]13[/C][C]-0.080167[/C][C]-0.7814[/C][C]0.218264[/C][/ROW]
[ROW][C]14[/C][C]0.155303[/C][C]1.5137[/C][C]0.06671[/C][/ROW]
[ROW][C]15[/C][C]0.105926[/C][C]1.0324[/C][C]0.152244[/C][/ROW]
[ROW][C]16[/C][C]-0.236498[/C][C]-2.3051[/C][C]0.011669[/C][/ROW]
[ROW][C]17[/C][C]0.124075[/C][C]1.2093[/C][C]0.114769[/C][/ROW]
[ROW][C]18[/C][C]0.037832[/C][C]0.3687[/C][C]0.356571[/C][/ROW]
[ROW][C]19[/C][C]0.089505[/C][C]0.8724[/C][C]0.1926[/C][/ROW]
[ROW][C]20[/C][C]-0.181859[/C][C]-1.7725[/C][C]0.039755[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111262&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111262&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	-0.339641	-3.3104	0.000659
2	-0.224508	-2.1882	0.015552
3	0.093507	0.9114	0.182197
4	0.140126	1.3658	0.087616
5	-0.191564	-1.8671	0.032483
6	-0.027925	-0.2722	0.393038
7	0.09889	0.9639	0.168781
8	0.022235	0.2167	0.414444
9	-0.081154	-0.791	0.215459
10	0.059105	0.5761	0.282959
11	0.196452	1.9148	0.029265
12	-0.306458	-2.987	0.001792
13	-0.080167	-0.7814	0.218264
14	0.155303	1.5137	0.06671
15	0.105926	1.0324	0.152244
16	-0.236498	-2.3051	0.011669
17	0.124075	1.2093	0.114769
18	0.037832	0.3687	0.356571
19	0.089505	0.8724	0.1926
20	-0.181859	-1.7725	0.039755

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.339641	-3.3104	0.000659
2	-0.384182	-3.7445	0.000155
3	-0.189004	-1.8422	0.034284
4	0.028168	0.2745	0.392129
5	-0.141359	-1.3778	0.085752
6	-0.13858	-1.3507	0.089998
7	-0.081851	-0.7978	0.213493
8	-0.023048	-0.2246	0.411371
9	-0.038778	-0.378	0.35315
10	0.021228	0.2069	0.418263
11	0.263503	2.5683	0.005889
12	-0.107888	-1.0516	0.147835
13	-0.210495	-2.0516	0.021478
14	-0.168906	-1.6463	0.051504
15	0.024905	0.2427	0.404362
16	-0.088684	-0.8644	0.194776
17	0.014968	0.1459	0.442159
18	-0.092141	-0.8981	0.185707
19	0.127616	1.2438	0.108308
20	-0.02033	-0.1982	0.421675

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.339641 & -3.3104 & 0.000659 \tabularnewline
2 & -0.384182 & -3.7445 & 0.000155 \tabularnewline
3 & -0.189004 & -1.8422 & 0.034284 \tabularnewline
4 & 0.028168 & 0.2745 & 0.392129 \tabularnewline
5 & -0.141359 & -1.3778 & 0.085752 \tabularnewline
6 & -0.13858 & -1.3507 & 0.089998 \tabularnewline
7 & -0.081851 & -0.7978 & 0.213493 \tabularnewline
8 & -0.023048 & -0.2246 & 0.411371 \tabularnewline
9 & -0.038778 & -0.378 & 0.35315 \tabularnewline
10 & 0.021228 & 0.2069 & 0.418263 \tabularnewline
11 & 0.263503 & 2.5683 & 0.005889 \tabularnewline
12 & -0.107888 & -1.0516 & 0.147835 \tabularnewline
13 & -0.210495 & -2.0516 & 0.021478 \tabularnewline
14 & -0.168906 & -1.6463 & 0.051504 \tabularnewline
15 & 0.024905 & 0.2427 & 0.404362 \tabularnewline
16 & -0.088684 & -0.8644 & 0.194776 \tabularnewline
17 & 0.014968 & 0.1459 & 0.442159 \tabularnewline
18 & -0.092141 & -0.8981 & 0.185707 \tabularnewline
19 & 0.127616 & 1.2438 & 0.108308 \tabularnewline
20 & -0.02033 & -0.1982 & 0.421675 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111262&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]-0.339641[/C][C]-3.3104[/C][C]0.000659[/C][/ROW]
[ROW][C]2[/C][C]-0.384182[/C][C]-3.7445[/C][C]0.000155[/C][/ROW]
[ROW][C]3[/C][C]-0.189004[/C][C]-1.8422[/C][C]0.034284[/C][/ROW]
[ROW][C]4[/C][C]0.028168[/C][C]0.2745[/C][C]0.392129[/C][/ROW]
[ROW][C]5[/C][C]-0.141359[/C][C]-1.3778[/C][C]0.085752[/C][/ROW]
[ROW][C]6[/C][C]-0.13858[/C][C]-1.3507[/C][C]0.089998[/C][/ROW]
[ROW][C]7[/C][C]-0.081851[/C][C]-0.7978[/C][C]0.213493[/C][/ROW]
[ROW][C]8[/C][C]-0.023048[/C][C]-0.2246[/C][C]0.411371[/C][/ROW]
[ROW][C]9[/C][C]-0.038778[/C][C]-0.378[/C][C]0.35315[/C][/ROW]
[ROW][C]10[/C][C]0.021228[/C][C]0.2069[/C][C]0.418263[/C][/ROW]
[ROW][C]11[/C][C]0.263503[/C][C]2.5683[/C][C]0.005889[/C][/ROW]
[ROW][C]12[/C][C]-0.107888[/C][C]-1.0516[/C][C]0.147835[/C][/ROW]
[ROW][C]13[/C][C]-0.210495[/C][C]-2.0516[/C][C]0.021478[/C][/ROW]
[ROW][C]14[/C][C]-0.168906[/C][C]-1.6463[/C][C]0.051504[/C][/ROW]
[ROW][C]15[/C][C]0.024905[/C][C]0.2427[/C][C]0.404362[/C][/ROW]
[ROW][C]16[/C][C]-0.088684[/C][C]-0.8644[/C][C]0.194776[/C][/ROW]
[ROW][C]17[/C][C]0.014968[/C][C]0.1459[/C][C]0.442159[/C][/ROW]
[ROW][C]18[/C][C]-0.092141[/C][C]-0.8981[/C][C]0.185707[/C][/ROW]
[ROW][C]19[/C][C]0.127616[/C][C]1.2438[/C][C]0.108308[/C][/ROW]
[ROW][C]20[/C][C]-0.02033[/C][C]-0.1982[/C][C]0.421675[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111262&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111262&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	-0.339641	-3.3104	0.000659
2	-0.384182	-3.7445	0.000155
3	-0.189004	-1.8422	0.034284
4	0.028168	0.2745	0.392129
5	-0.141359	-1.3778	0.085752
6	-0.13858	-1.3507	0.089998
7	-0.081851	-0.7978	0.213493
8	-0.023048	-0.2246	0.411371
9	-0.038778	-0.378	0.35315
10	0.021228	0.2069	0.418263
11	0.263503	2.5683	0.005889
12	-0.107888	-1.0516	0.147835
13	-0.210495	-2.0516	0.021478
14	-0.168906	-1.6463	0.051504
15	0.024905	0.2427	0.404362
16	-0.088684	-0.8644	0.194776
17	0.014968	0.1459	0.442159
18	-0.092141	-0.8981	0.185707
19	0.127616	1.2438	0.108308
20	-0.02033	-0.1982	0.421675

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):

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code