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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 20 Jan 2015 08:51:45 +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/2015/Jan/20/t1421744734f1639p39zf4adqq.htm/, Retrieved Wed, 15 May 2024 21:37:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=274868, Retrieved Wed, 15 May 2024 21:37:47 +0000

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-       [(Partial) Autocorrelation Function] [] [2015-01-20 08:51:45] [d41d8cd98f00b204e9800998ecf8427e] [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=274868&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=274868&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=274868&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	0.736681	8.4638	0
2	0.438743	5.0408	1e-06
3	0.017856	0.2052	0.418884
4	-0.423749	-4.8685	2e-06
5	-0.711565	-8.1753	0
6	-0.813339	-9.3446	0
7	-0.717381	-8.2421	0
8	-0.400271	-4.5988	5e-06
9	0.028606	0.3287	0.371467
10	0.417361	4.7951	2e-06
11	0.691807	7.9483	0
12	0.890752	10.234	0
13	0.660649	7.5903	0
14	0.401145	4.6088	5e-06
15	0.004708	0.0541	0.478474
16	-0.39157	-4.4988	7e-06
17	-0.648096	-7.4461	0
18	-0.753031	-8.6517	0
19	-0.65648	-7.5424	0
20	-0.367455	-4.2217	2.2e-05
21	0.007468	0.0858	0.46588

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.736681 & 8.4638 & 0 \tabularnewline
2 & 0.438743 & 5.0408 & 1e-06 \tabularnewline
3 & 0.017856 & 0.2052 & 0.418884 \tabularnewline
4 & -0.423749 & -4.8685 & 2e-06 \tabularnewline
5 & -0.711565 & -8.1753 & 0 \tabularnewline
6 & -0.813339 & -9.3446 & 0 \tabularnewline
7 & -0.717381 & -8.2421 & 0 \tabularnewline
8 & -0.400271 & -4.5988 & 5e-06 \tabularnewline
9 & 0.028606 & 0.3287 & 0.371467 \tabularnewline
10 & 0.417361 & 4.7951 & 2e-06 \tabularnewline
11 & 0.691807 & 7.9483 & 0 \tabularnewline
12 & 0.890752 & 10.234 & 0 \tabularnewline
13 & 0.660649 & 7.5903 & 0 \tabularnewline
14 & 0.401145 & 4.6088 & 5e-06 \tabularnewline
15 & 0.004708 & 0.0541 & 0.478474 \tabularnewline
16 & -0.39157 & -4.4988 & 7e-06 \tabularnewline
17 & -0.648096 & -7.4461 & 0 \tabularnewline
18 & -0.753031 & -8.6517 & 0 \tabularnewline
19 & -0.65648 & -7.5424 & 0 \tabularnewline
20 & -0.367455 & -4.2217 & 2.2e-05 \tabularnewline
21 & 0.007468 & 0.0858 & 0.46588 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=274868&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]0.736681[/C][C]8.4638[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.438743[/C][C]5.0408[/C][C]1e-06[/C][/ROW]
[ROW][C]3[/C][C]0.017856[/C][C]0.2052[/C][C]0.418884[/C][/ROW]
[ROW][C]4[/C][C]-0.423749[/C][C]-4.8685[/C][C]2e-06[/C][/ROW]
[ROW][C]5[/C][C]-0.711565[/C][C]-8.1753[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]-0.813339[/C][C]-9.3446[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]-0.717381[/C][C]-8.2421[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]-0.400271[/C][C]-4.5988[/C][C]5e-06[/C][/ROW]
[ROW][C]9[/C][C]0.028606[/C][C]0.3287[/C][C]0.371467[/C][/ROW]
[ROW][C]10[/C][C]0.417361[/C][C]4.7951[/C][C]2e-06[/C][/ROW]
[ROW][C]11[/C][C]0.691807[/C][C]7.9483[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.890752[/C][C]10.234[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.660649[/C][C]7.5903[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.401145[/C][C]4.6088[/C][C]5e-06[/C][/ROW]
[ROW][C]15[/C][C]0.004708[/C][C]0.0541[/C][C]0.478474[/C][/ROW]
[ROW][C]16[/C][C]-0.39157[/C][C]-4.4988[/C][C]7e-06[/C][/ROW]
[ROW][C]17[/C][C]-0.648096[/C][C]-7.4461[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]-0.753031[/C][C]-8.6517[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]-0.65648[/C][C]-7.5424[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]-0.367455[/C][C]-4.2217[/C][C]2.2e-05[/C][/ROW]
[ROW][C]21[/C][C]0.007468[/C][C]0.0858[/C][C]0.46588[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=274868&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=274868&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	0.736681	8.4638	0
2	0.438743	5.0408	1e-06
3	0.017856	0.2052	0.418884
4	-0.423749	-4.8685	2e-06
5	-0.711565	-8.1753	0
6	-0.813339	-9.3446	0
7	-0.717381	-8.2421	0
8	-0.400271	-4.5988	5e-06
9	0.028606	0.3287	0.371467
10	0.417361	4.7951	2e-06
11	0.691807	7.9483	0
12	0.890752	10.234	0
13	0.660649	7.5903	0
14	0.401145	4.6088	5e-06
15	0.004708	0.0541	0.478474
16	-0.39157	-4.4988	7e-06
17	-0.648096	-7.4461	0
18	-0.753031	-8.6517	0
19	-0.65648	-7.5424	0
20	-0.367455	-4.2217	2.2e-05
21	0.007468	0.0858	0.46588

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.736681	8.4638	0
2	-0.227324	-2.6118	0.005026
3	-0.487388	-5.5997	0
4	-0.521603	-5.9928	0
5	-0.300683	-3.4546	0.000371
6	-0.15678	-1.8013	0.036972
7	-0.145943	-1.6768	0.047978
8	0.051291	0.5893	0.278339
9	0.22599	2.5964	0.005244
10	0.113791	1.3074	0.096682
11	-0.013896	-0.1596	0.436701
12	0.55778	6.4084	0
13	-0.393759	-4.5239	7e-06
14	0.088248	1.0139	0.156244
15	0.134244	1.5423	0.062692
16	0.19736	2.2675	0.012492
17	-0.048365	-0.5557	0.289689
18	-0.016672	-0.1916	0.424194
19	0.127896	1.4694	0.07205
20	-0.132929	-1.5272	0.064547
21	-0.128228	-1.4732	0.071535

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.736681 & 8.4638 & 0 \tabularnewline
2 & -0.227324 & -2.6118 & 0.005026 \tabularnewline
3 & -0.487388 & -5.5997 & 0 \tabularnewline
4 & -0.521603 & -5.9928 & 0 \tabularnewline
5 & -0.300683 & -3.4546 & 0.000371 \tabularnewline
6 & -0.15678 & -1.8013 & 0.036972 \tabularnewline
7 & -0.145943 & -1.6768 & 0.047978 \tabularnewline
8 & 0.051291 & 0.5893 & 0.278339 \tabularnewline
9 & 0.22599 & 2.5964 & 0.005244 \tabularnewline
10 & 0.113791 & 1.3074 & 0.096682 \tabularnewline
11 & -0.013896 & -0.1596 & 0.436701 \tabularnewline
12 & 0.55778 & 6.4084 & 0 \tabularnewline
13 & -0.393759 & -4.5239 & 7e-06 \tabularnewline
14 & 0.088248 & 1.0139 & 0.156244 \tabularnewline
15 & 0.134244 & 1.5423 & 0.062692 \tabularnewline
16 & 0.19736 & 2.2675 & 0.012492 \tabularnewline
17 & -0.048365 & -0.5557 & 0.289689 \tabularnewline
18 & -0.016672 & -0.1916 & 0.424194 \tabularnewline
19 & 0.127896 & 1.4694 & 0.07205 \tabularnewline
20 & -0.132929 & -1.5272 & 0.064547 \tabularnewline
21 & -0.128228 & -1.4732 & 0.071535 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=274868&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]0.736681[/C][C]8.4638[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.227324[/C][C]-2.6118[/C][C]0.005026[/C][/ROW]
[ROW][C]3[/C][C]-0.487388[/C][C]-5.5997[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]-0.521603[/C][C]-5.9928[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]-0.300683[/C][C]-3.4546[/C][C]0.000371[/C][/ROW]
[ROW][C]6[/C][C]-0.15678[/C][C]-1.8013[/C][C]0.036972[/C][/ROW]
[ROW][C]7[/C][C]-0.145943[/C][C]-1.6768[/C][C]0.047978[/C][/ROW]
[ROW][C]8[/C][C]0.051291[/C][C]0.5893[/C][C]0.278339[/C][/ROW]
[ROW][C]9[/C][C]0.22599[/C][C]2.5964[/C][C]0.005244[/C][/ROW]
[ROW][C]10[/C][C]0.113791[/C][C]1.3074[/C][C]0.096682[/C][/ROW]
[ROW][C]11[/C][C]-0.013896[/C][C]-0.1596[/C][C]0.436701[/C][/ROW]
[ROW][C]12[/C][C]0.55778[/C][C]6.4084[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.393759[/C][C]-4.5239[/C][C]7e-06[/C][/ROW]
[ROW][C]14[/C][C]0.088248[/C][C]1.0139[/C][C]0.156244[/C][/ROW]
[ROW][C]15[/C][C]0.134244[/C][C]1.5423[/C][C]0.062692[/C][/ROW]
[ROW][C]16[/C][C]0.19736[/C][C]2.2675[/C][C]0.012492[/C][/ROW]
[ROW][C]17[/C][C]-0.048365[/C][C]-0.5557[/C][C]0.289689[/C][/ROW]
[ROW][C]18[/C][C]-0.016672[/C][C]-0.1916[/C][C]0.424194[/C][/ROW]
[ROW][C]19[/C][C]0.127896[/C][C]1.4694[/C][C]0.07205[/C][/ROW]
[ROW][C]20[/C][C]-0.132929[/C][C]-1.5272[/C][C]0.064547[/C][/ROW]
[ROW][C]21[/C][C]-0.128228[/C][C]-1.4732[/C][C]0.071535[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=274868&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=274868&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	0.736681	8.4638	0
2	-0.227324	-2.6118	0.005026
3	-0.487388	-5.5997	0
4	-0.521603	-5.9928	0
5	-0.300683	-3.4546	0.000371
6	-0.15678	-1.8013	0.036972
7	-0.145943	-1.6768	0.047978
8	0.051291	0.5893	0.278339
9	0.22599	2.5964	0.005244
10	0.113791	1.3074	0.096682
11	-0.013896	-0.1596	0.436701
12	0.55778	6.4084	0
13	-0.393759	-4.5239	7e-06
14	0.088248	1.0139	0.156244
15	0.134244	1.5423	0.062692
16	0.19736	2.2675	0.012492
17	-0.048365	-0.5557	0.289689
18	-0.016672	-0.1916	0.424194
19	0.127896	1.4694	0.07205
20	-0.132929	-1.5272	0.064547
21	-0.128228	-1.4732	0.071535

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 = -0.1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = -0.1 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code