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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 06 Dec 2011 12:06:04 -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/06/t1323191352jwhbuf1waodfgt4.htm/, Retrieved Mon, 29 Apr 2024 03:34:17 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=151743, Retrieved Mon, 29 Apr 2024 03:34:17 +0000

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-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [Unemployment] [2010-11-29 09:05:21] [b98453cac15ba1066b407e146608df68]
- R PD      [(Partial) Autocorrelation Function] [] [2011-12-06 17:06:04] [8a4496bd93dae12a8bdfa51e6ea7daab] [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	'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151743&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151743&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151743&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.665978	-4.5169	2.2e-05
2	0.234251	1.5888	0.059482
3	-0.081335	-0.5516	0.291932
4	0.050805	0.3446	0.365992
5	-0.015595	-0.1058	0.458112
6	-0.03046	-0.2066	0.418621
7	0.00256	0.0174	0.493112
8	0.069417	0.4708	0.320001
9	-0.051192	-0.3472	0.365012
10	-0.144577	-0.9806	0.165967
11	0.427953	2.9025	0.002833
12	-0.443988	-3.0113	0.002108
13	0.16377	1.1107	0.136226
14	0.041675	0.2827	0.389356
15	-0.086173	-0.5845	0.280886
16	0.125561	0.8516	0.199426
17	-0.190712	-1.2935	0.101153
18	0.171633	1.1641	0.125198

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.665978 & -4.5169 & 2.2e-05 \tabularnewline
2 & 0.234251 & 1.5888 & 0.059482 \tabularnewline
3 & -0.081335 & -0.5516 & 0.291932 \tabularnewline
4 & 0.050805 & 0.3446 & 0.365992 \tabularnewline
5 & -0.015595 & -0.1058 & 0.458112 \tabularnewline
6 & -0.03046 & -0.2066 & 0.418621 \tabularnewline
7 & 0.00256 & 0.0174 & 0.493112 \tabularnewline
8 & 0.069417 & 0.4708 & 0.320001 \tabularnewline
9 & -0.051192 & -0.3472 & 0.365012 \tabularnewline
10 & -0.144577 & -0.9806 & 0.165967 \tabularnewline
11 & 0.427953 & 2.9025 & 0.002833 \tabularnewline
12 & -0.443988 & -3.0113 & 0.002108 \tabularnewline
13 & 0.16377 & 1.1107 & 0.136226 \tabularnewline
14 & 0.041675 & 0.2827 & 0.389356 \tabularnewline
15 & -0.086173 & -0.5845 & 0.280886 \tabularnewline
16 & 0.125561 & 0.8516 & 0.199426 \tabularnewline
17 & -0.190712 & -1.2935 & 0.101153 \tabularnewline
18 & 0.171633 & 1.1641 & 0.125198 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151743&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]-0.665978[/C][C]-4.5169[/C][C]2.2e-05[/C][/ROW]
[ROW][C]2[/C][C]0.234251[/C][C]1.5888[/C][C]0.059482[/C][/ROW]
[ROW][C]3[/C][C]-0.081335[/C][C]-0.5516[/C][C]0.291932[/C][/ROW]
[ROW][C]4[/C][C]0.050805[/C][C]0.3446[/C][C]0.365992[/C][/ROW]
[ROW][C]5[/C][C]-0.015595[/C][C]-0.1058[/C][C]0.458112[/C][/ROW]
[ROW][C]6[/C][C]-0.03046[/C][C]-0.2066[/C][C]0.418621[/C][/ROW]
[ROW][C]7[/C][C]0.00256[/C][C]0.0174[/C][C]0.493112[/C][/ROW]
[ROW][C]8[/C][C]0.069417[/C][C]0.4708[/C][C]0.320001[/C][/ROW]
[ROW][C]9[/C][C]-0.051192[/C][C]-0.3472[/C][C]0.365012[/C][/ROW]
[ROW][C]10[/C][C]-0.144577[/C][C]-0.9806[/C][C]0.165967[/C][/ROW]
[ROW][C]11[/C][C]0.427953[/C][C]2.9025[/C][C]0.002833[/C][/ROW]
[ROW][C]12[/C][C]-0.443988[/C][C]-3.0113[/C][C]0.002108[/C][/ROW]
[ROW][C]13[/C][C]0.16377[/C][C]1.1107[/C][C]0.136226[/C][/ROW]
[ROW][C]14[/C][C]0.041675[/C][C]0.2827[/C][C]0.389356[/C][/ROW]
[ROW][C]15[/C][C]-0.086173[/C][C]-0.5845[/C][C]0.280886[/C][/ROW]
[ROW][C]16[/C][C]0.125561[/C][C]0.8516[/C][C]0.199426[/C][/ROW]
[ROW][C]17[/C][C]-0.190712[/C][C]-1.2935[/C][C]0.101153[/C][/ROW]
[ROW][C]18[/C][C]0.171633[/C][C]1.1641[/C][C]0.125198[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151743&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151743&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	-0.665978	-4.5169	2.2e-05
2	0.234251	1.5888	0.059482
3	-0.081335	-0.5516	0.291932
4	0.050805	0.3446	0.365992
5	-0.015595	-0.1058	0.458112
6	-0.03046	-0.2066	0.418621
7	0.00256	0.0174	0.493112
8	0.069417	0.4708	0.320001
9	-0.051192	-0.3472	0.365012
10	-0.144577	-0.9806	0.165967
11	0.427953	2.9025	0.002833
12	-0.443988	-3.0113	0.002108
13	0.16377	1.1107	0.136226
14	0.041675	0.2827	0.389356
15	-0.086173	-0.5845	0.280886
16	0.125561	0.8516	0.199426
17	-0.190712	-1.2935	0.101153
18	0.171633	1.1641	0.125198

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.665978	-4.5169	2.2e-05
2	-0.376074	-2.5507	0.007072
3	-0.245131	-1.6626	0.051601
4	-0.119725	-0.812	0.210483
5	-0.026196	-0.1777	0.429881
6	-0.059367	-0.4026	0.344536
7	-0.121381	-0.8232	0.207307
8	0.011067	0.0751	0.470247
9	0.077853	0.528	0.300011
10	-0.290394	-1.9695	0.027465
11	0.32072	2.1752	0.017395
12	0.170592	1.157	0.126621
13	-0.203569	-1.3807	0.087026
14	0.019114	0.1296	0.448709
15	-0.061242	-0.4154	0.339903
16	0.057718	0.3915	0.348632
17	-0.044565	-0.3023	0.381911
18	-0.013302	-0.0902	0.464253

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.665978 & -4.5169 & 2.2e-05 \tabularnewline
2 & -0.376074 & -2.5507 & 0.007072 \tabularnewline
3 & -0.245131 & -1.6626 & 0.051601 \tabularnewline
4 & -0.119725 & -0.812 & 0.210483 \tabularnewline
5 & -0.026196 & -0.1777 & 0.429881 \tabularnewline
6 & -0.059367 & -0.4026 & 0.344536 \tabularnewline
7 & -0.121381 & -0.8232 & 0.207307 \tabularnewline
8 & 0.011067 & 0.0751 & 0.470247 \tabularnewline
9 & 0.077853 & 0.528 & 0.300011 \tabularnewline
10 & -0.290394 & -1.9695 & 0.027465 \tabularnewline
11 & 0.32072 & 2.1752 & 0.017395 \tabularnewline
12 & 0.170592 & 1.157 & 0.126621 \tabularnewline
13 & -0.203569 & -1.3807 & 0.087026 \tabularnewline
14 & 0.019114 & 0.1296 & 0.448709 \tabularnewline
15 & -0.061242 & -0.4154 & 0.339903 \tabularnewline
16 & 0.057718 & 0.3915 & 0.348632 \tabularnewline
17 & -0.044565 & -0.3023 & 0.381911 \tabularnewline
18 & -0.013302 & -0.0902 & 0.464253 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151743&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]-0.665978[/C][C]-4.5169[/C][C]2.2e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.376074[/C][C]-2.5507[/C][C]0.007072[/C][/ROW]
[ROW][C]3[/C][C]-0.245131[/C][C]-1.6626[/C][C]0.051601[/C][/ROW]
[ROW][C]4[/C][C]-0.119725[/C][C]-0.812[/C][C]0.210483[/C][/ROW]
[ROW][C]5[/C][C]-0.026196[/C][C]-0.1777[/C][C]0.429881[/C][/ROW]
[ROW][C]6[/C][C]-0.059367[/C][C]-0.4026[/C][C]0.344536[/C][/ROW]
[ROW][C]7[/C][C]-0.121381[/C][C]-0.8232[/C][C]0.207307[/C][/ROW]
[ROW][C]8[/C][C]0.011067[/C][C]0.0751[/C][C]0.470247[/C][/ROW]
[ROW][C]9[/C][C]0.077853[/C][C]0.528[/C][C]0.300011[/C][/ROW]
[ROW][C]10[/C][C]-0.290394[/C][C]-1.9695[/C][C]0.027465[/C][/ROW]
[ROW][C]11[/C][C]0.32072[/C][C]2.1752[/C][C]0.017395[/C][/ROW]
[ROW][C]12[/C][C]0.170592[/C][C]1.157[/C][C]0.126621[/C][/ROW]
[ROW][C]13[/C][C]-0.203569[/C][C]-1.3807[/C][C]0.087026[/C][/ROW]
[ROW][C]14[/C][C]0.019114[/C][C]0.1296[/C][C]0.448709[/C][/ROW]
[ROW][C]15[/C][C]-0.061242[/C][C]-0.4154[/C][C]0.339903[/C][/ROW]
[ROW][C]16[/C][C]0.057718[/C][C]0.3915[/C][C]0.348632[/C][/ROW]
[ROW][C]17[/C][C]-0.044565[/C][C]-0.3023[/C][C]0.381911[/C][/ROW]
[ROW][C]18[/C][C]-0.013302[/C][C]-0.0902[/C][C]0.464253[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151743&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151743&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	-0.665978	-4.5169	2.2e-05
2	-0.376074	-2.5507	0.007072
3	-0.245131	-1.6626	0.051601
4	-0.119725	-0.812	0.210483
5	-0.026196	-0.1777	0.429881
6	-0.059367	-0.4026	0.344536
7	-0.121381	-0.8232	0.207307
8	0.011067	0.0751	0.470247
9	0.077853	0.528	0.300011
10	-0.290394	-1.9695	0.027465
11	0.32072	2.1752	0.017395
12	0.170592	1.157	0.126621
13	-0.203569	-1.3807	0.087026
14	0.019114	0.1296	0.448709
15	-0.061242	-0.4154	0.339903
16	0.057718	0.3915	0.348632
17	-0.044565	-0.3023	0.381911
18	-0.013302	-0.0902	0.464253

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 = 2 ; par4 = 2 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 2 ; par4 = 2 ; 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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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code