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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 23 Oct 2015 21:05:03 +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/2015/Oct/23/t14456307499ghbbamzcmdc882.htm/, Retrieved Tue, 14 May 2024 17:09:09 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=282973, Retrieved Tue, 14 May 2024 17:09:09 +0000

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-       [(Partial) Autocorrelation Function] [] [2015-10-23 20:05:03] [06d8efd1cada8e807c830d2ff46bf732] [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	'George Udny Yule' @ yule.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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282973&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282973&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282973&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	'George Udny Yule' @ yule.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.871358	7.9861	0
2	0.842034	7.7174	0
3	0.827727	7.5862	0
4	0.782924	7.1756	0
5	0.756015	6.929	0
6	0.727857	6.6709	0
7	0.650164	5.9589	0
8	0.620894	5.6906	0
9	0.572365	5.2458	1e-06
10	0.501923	4.6002	7e-06
11	0.490331	4.494	1.1e-05
12	0.49749	4.5596	9e-06
13	0.378208	3.4663	0.000417
14	0.357273	3.2745	0.000769
15	0.300806	2.7569	0.003578
16	0.26968	2.4717	0.007734
17	0.24871	2.2795	0.012587
18	0.208925	1.9148	0.029459
19	0.171714	1.5738	0.059648

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.871358 & 7.9861 & 0 \tabularnewline
2 & 0.842034 & 7.7174 & 0 \tabularnewline
3 & 0.827727 & 7.5862 & 0 \tabularnewline
4 & 0.782924 & 7.1756 & 0 \tabularnewline
5 & 0.756015 & 6.929 & 0 \tabularnewline
6 & 0.727857 & 6.6709 & 0 \tabularnewline
7 & 0.650164 & 5.9589 & 0 \tabularnewline
8 & 0.620894 & 5.6906 & 0 \tabularnewline
9 & 0.572365 & 5.2458 & 1e-06 \tabularnewline
10 & 0.501923 & 4.6002 & 7e-06 \tabularnewline
11 & 0.490331 & 4.494 & 1.1e-05 \tabularnewline
12 & 0.49749 & 4.5596 & 9e-06 \tabularnewline
13 & 0.378208 & 3.4663 & 0.000417 \tabularnewline
14 & 0.357273 & 3.2745 & 0.000769 \tabularnewline
15 & 0.300806 & 2.7569 & 0.003578 \tabularnewline
16 & 0.26968 & 2.4717 & 0.007734 \tabularnewline
17 & 0.24871 & 2.2795 & 0.012587 \tabularnewline
18 & 0.208925 & 1.9148 & 0.029459 \tabularnewline
19 & 0.171714 & 1.5738 & 0.059648 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282973&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]0.871358[/C][C]7.9861[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.842034[/C][C]7.7174[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.827727[/C][C]7.5862[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.782924[/C][C]7.1756[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.756015[/C][C]6.929[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.727857[/C][C]6.6709[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.650164[/C][C]5.9589[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.620894[/C][C]5.6906[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.572365[/C][C]5.2458[/C][C]1e-06[/C][/ROW]
[ROW][C]10[/C][C]0.501923[/C][C]4.6002[/C][C]7e-06[/C][/ROW]
[ROW][C]11[/C][C]0.490331[/C][C]4.494[/C][C]1.1e-05[/C][/ROW]
[ROW][C]12[/C][C]0.49749[/C][C]4.5596[/C][C]9e-06[/C][/ROW]
[ROW][C]13[/C][C]0.378208[/C][C]3.4663[/C][C]0.000417[/C][/ROW]
[ROW][C]14[/C][C]0.357273[/C][C]3.2745[/C][C]0.000769[/C][/ROW]
[ROW][C]15[/C][C]0.300806[/C][C]2.7569[/C][C]0.003578[/C][/ROW]
[ROW][C]16[/C][C]0.26968[/C][C]2.4717[/C][C]0.007734[/C][/ROW]
[ROW][C]17[/C][C]0.24871[/C][C]2.2795[/C][C]0.012587[/C][/ROW]
[ROW][C]18[/C][C]0.208925[/C][C]1.9148[/C][C]0.029459[/C][/ROW]
[ROW][C]19[/C][C]0.171714[/C][C]1.5738[/C][C]0.059648[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282973&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282973&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	0.871358	7.9861	0
2	0.842034	7.7174	0
3	0.827727	7.5862	0
4	0.782924	7.1756	0
5	0.756015	6.929	0
6	0.727857	6.6709	0
7	0.650164	5.9589	0
8	0.620894	5.6906	0
9	0.572365	5.2458	1e-06
10	0.501923	4.6002	7e-06
11	0.490331	4.494	1.1e-05
12	0.49749	4.5596	9e-06
13	0.378208	3.4663	0.000417
14	0.357273	3.2745	0.000769
15	0.300806	2.7569	0.003578
16	0.26968	2.4717	0.007734
17	0.24871	2.2795	0.012587
18	0.208925	1.9148	0.029459
19	0.171714	1.5738	0.059648

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.871358	7.9861	0
2	0.34382	3.1512	0.001127
3	0.219939	2.0158	0.02351
4	-0.014929	-0.1368	0.445748
5	0.016733	0.1534	0.439241
6	-0.001472	-0.0135	0.494635
7	-0.236451	-2.1671	0.016529
8	-0.015837	-0.1451	0.442472
9	-0.070499	-0.6461	0.259978
10	-0.132478	-1.2142	0.114041
11	0.130069	1.1921	0.118289
12	0.298237	2.7334	0.003821
13	-0.401296	-3.6779	0.000207
14	-0.00963	-0.0883	0.464941
15	-0.099386	-0.9109	0.18248
16	0.118921	1.0899	0.139432
17	-0.028282	-0.2592	0.398054
18	0.030829	0.2826	0.389106
19	0.125069	1.1463	0.127468

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.871358 & 7.9861 & 0 \tabularnewline
2 & 0.34382 & 3.1512 & 0.001127 \tabularnewline
3 & 0.219939 & 2.0158 & 0.02351 \tabularnewline
4 & -0.014929 & -0.1368 & 0.445748 \tabularnewline
5 & 0.016733 & 0.1534 & 0.439241 \tabularnewline
6 & -0.001472 & -0.0135 & 0.494635 \tabularnewline
7 & -0.236451 & -2.1671 & 0.016529 \tabularnewline
8 & -0.015837 & -0.1451 & 0.442472 \tabularnewline
9 & -0.070499 & -0.6461 & 0.259978 \tabularnewline
10 & -0.132478 & -1.2142 & 0.114041 \tabularnewline
11 & 0.130069 & 1.1921 & 0.118289 \tabularnewline
12 & 0.298237 & 2.7334 & 0.003821 \tabularnewline
13 & -0.401296 & -3.6779 & 0.000207 \tabularnewline
14 & -0.00963 & -0.0883 & 0.464941 \tabularnewline
15 & -0.099386 & -0.9109 & 0.18248 \tabularnewline
16 & 0.118921 & 1.0899 & 0.139432 \tabularnewline
17 & -0.028282 & -0.2592 & 0.398054 \tabularnewline
18 & 0.030829 & 0.2826 & 0.389106 \tabularnewline
19 & 0.125069 & 1.1463 & 0.127468 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282973&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]0.871358[/C][C]7.9861[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.34382[/C][C]3.1512[/C][C]0.001127[/C][/ROW]
[ROW][C]3[/C][C]0.219939[/C][C]2.0158[/C][C]0.02351[/C][/ROW]
[ROW][C]4[/C][C]-0.014929[/C][C]-0.1368[/C][C]0.445748[/C][/ROW]
[ROW][C]5[/C][C]0.016733[/C][C]0.1534[/C][C]0.439241[/C][/ROW]
[ROW][C]6[/C][C]-0.001472[/C][C]-0.0135[/C][C]0.494635[/C][/ROW]
[ROW][C]7[/C][C]-0.236451[/C][C]-2.1671[/C][C]0.016529[/C][/ROW]
[ROW][C]8[/C][C]-0.015837[/C][C]-0.1451[/C][C]0.442472[/C][/ROW]
[ROW][C]9[/C][C]-0.070499[/C][C]-0.6461[/C][C]0.259978[/C][/ROW]
[ROW][C]10[/C][C]-0.132478[/C][C]-1.2142[/C][C]0.114041[/C][/ROW]
[ROW][C]11[/C][C]0.130069[/C][C]1.1921[/C][C]0.118289[/C][/ROW]
[ROW][C]12[/C][C]0.298237[/C][C]2.7334[/C][C]0.003821[/C][/ROW]
[ROW][C]13[/C][C]-0.401296[/C][C]-3.6779[/C][C]0.000207[/C][/ROW]
[ROW][C]14[/C][C]-0.00963[/C][C]-0.0883[/C][C]0.464941[/C][/ROW]
[ROW][C]15[/C][C]-0.099386[/C][C]-0.9109[/C][C]0.18248[/C][/ROW]
[ROW][C]16[/C][C]0.118921[/C][C]1.0899[/C][C]0.139432[/C][/ROW]
[ROW][C]17[/C][C]-0.028282[/C][C]-0.2592[/C][C]0.398054[/C][/ROW]
[ROW][C]18[/C][C]0.030829[/C][C]0.2826[/C][C]0.389106[/C][/ROW]
[ROW][C]19[/C][C]0.125069[/C][C]1.1463[/C][C]0.127468[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282973&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282973&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	0.871358	7.9861	0
2	0.34382	3.1512	0.001127
3	0.219939	2.0158	0.02351
4	-0.014929	-0.1368	0.445748
5	0.016733	0.1534	0.439241
6	-0.001472	-0.0135	0.494635
7	-0.236451	-2.1671	0.016529
8	-0.015837	-0.1451	0.442472
9	-0.070499	-0.6461	0.259978
10	-0.132478	-1.2142	0.114041
11	0.130069	1.1921	0.118289
12	0.298237	2.7334	0.003821
13	-0.401296	-3.6779	0.000207
14	-0.00963	-0.0883	0.464941
15	-0.099386	-0.9109	0.18248
16	0.118921	1.0899	0.139432
17	-0.028282	-0.2592	0.398054
18	0.030829	0.2826	0.389106
19	0.125069	1.1463	0.127468

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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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code