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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 25 May 2016 21:47:22 +0100

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/2016/May/25/t1464209580xpnbp36svufeyis.htm/, Retrieved Mon, 29 Apr 2024 04:08:19 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=295590, Retrieved Mon, 29 Apr 2024 04:08:19 +0000

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Estimated Impact

147

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

-       [(Partial) Autocorrelation Function] [] [2016-05-25 20:47:22] [3d038f408b3fdbe799ace9817e748893] [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=295590&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=295590&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295590&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	0.456647	4.0588	5.8e-05
2	0.345376	3.0698	0.001468
3	0.356936	3.1725	0.001077
4	0.08237	0.7321	0.233131
5	0.010116	0.0899	0.464293
6	0.011561	0.1028	0.459209
7	-0.132948	-1.1817	0.120441
8	-0.169075	-1.5028	0.068442
9	-0.183526	-1.6312	0.053413
10	-0.187861	-1.6697	0.049464
11	-0.176301	-1.567	0.060557
12	-0.137283	-1.2202	0.113009
13	-0.222543	-1.978	0.025707
14	-0.138728	-1.233	0.110608
15	-0.156069	-1.3872	0.084645
16	-0.052023	-0.4624	0.322536
17	0.028902	0.2569	0.398968
18	0.007225	0.0642	0.474478
19	0.024566	0.2184	0.413859

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.456647 & 4.0588 & 5.8e-05 \tabularnewline
2 & 0.345376 & 3.0698 & 0.001468 \tabularnewline
3 & 0.356936 & 3.1725 & 0.001077 \tabularnewline
4 & 0.08237 & 0.7321 & 0.233131 \tabularnewline
5 & 0.010116 & 0.0899 & 0.464293 \tabularnewline
6 & 0.011561 & 0.1028 & 0.459209 \tabularnewline
7 & -0.132948 & -1.1817 & 0.120441 \tabularnewline
8 & -0.169075 & -1.5028 & 0.068442 \tabularnewline
9 & -0.183526 & -1.6312 & 0.053413 \tabularnewline
10 & -0.187861 & -1.6697 & 0.049464 \tabularnewline
11 & -0.176301 & -1.567 & 0.060557 \tabularnewline
12 & -0.137283 & -1.2202 & 0.113009 \tabularnewline
13 & -0.222543 & -1.978 & 0.025707 \tabularnewline
14 & -0.138728 & -1.233 & 0.110608 \tabularnewline
15 & -0.156069 & -1.3872 & 0.084645 \tabularnewline
16 & -0.052023 & -0.4624 & 0.322536 \tabularnewline
17 & 0.028902 & 0.2569 & 0.398968 \tabularnewline
18 & 0.007225 & 0.0642 & 0.474478 \tabularnewline
19 & 0.024566 & 0.2184 & 0.413859 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295590&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]0.456647[/C][C]4.0588[/C][C]5.8e-05[/C][/ROW]
[ROW][C]2[/C][C]0.345376[/C][C]3.0698[/C][C]0.001468[/C][/ROW]
[ROW][C]3[/C][C]0.356936[/C][C]3.1725[/C][C]0.001077[/C][/ROW]
[ROW][C]4[/C][C]0.08237[/C][C]0.7321[/C][C]0.233131[/C][/ROW]
[ROW][C]5[/C][C]0.010116[/C][C]0.0899[/C][C]0.464293[/C][/ROW]
[ROW][C]6[/C][C]0.011561[/C][C]0.1028[/C][C]0.459209[/C][/ROW]
[ROW][C]7[/C][C]-0.132948[/C][C]-1.1817[/C][C]0.120441[/C][/ROW]
[ROW][C]8[/C][C]-0.169075[/C][C]-1.5028[/C][C]0.068442[/C][/ROW]
[ROW][C]9[/C][C]-0.183526[/C][C]-1.6312[/C][C]0.053413[/C][/ROW]
[ROW][C]10[/C][C]-0.187861[/C][C]-1.6697[/C][C]0.049464[/C][/ROW]
[ROW][C]11[/C][C]-0.176301[/C][C]-1.567[/C][C]0.060557[/C][/ROW]
[ROW][C]12[/C][C]-0.137283[/C][C]-1.2202[/C][C]0.113009[/C][/ROW]
[ROW][C]13[/C][C]-0.222543[/C][C]-1.978[/C][C]0.025707[/C][/ROW]
[ROW][C]14[/C][C]-0.138728[/C][C]-1.233[/C][C]0.110608[/C][/ROW]
[ROW][C]15[/C][C]-0.156069[/C][C]-1.3872[/C][C]0.084645[/C][/ROW]
[ROW][C]16[/C][C]-0.052023[/C][C]-0.4624[/C][C]0.322536[/C][/ROW]
[ROW][C]17[/C][C]0.028902[/C][C]0.2569[/C][C]0.398968[/C][/ROW]
[ROW][C]18[/C][C]0.007225[/C][C]0.0642[/C][C]0.474478[/C][/ROW]
[ROW][C]19[/C][C]0.024566[/C][C]0.2184[/C][C]0.413859[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295590&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295590&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	0.456647	4.0588	5.8e-05
2	0.345376	3.0698	0.001468
3	0.356936	3.1725	0.001077
4	0.08237	0.7321	0.233131
5	0.010116	0.0899	0.464293
6	0.011561	0.1028	0.459209
7	-0.132948	-1.1817	0.120441
8	-0.169075	-1.5028	0.068442
9	-0.183526	-1.6312	0.053413
10	-0.187861	-1.6697	0.049464
11	-0.176301	-1.567	0.060557
12	-0.137283	-1.2202	0.113009
13	-0.222543	-1.978	0.025707
14	-0.138728	-1.233	0.110608
15	-0.156069	-1.3872	0.084645
16	-0.052023	-0.4624	0.322536
17	0.028902	0.2569	0.398968
18	0.007225	0.0642	0.474478
19	0.024566	0.2184	0.413859

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.456647	4.0588	5.8e-05
2	0.172904	1.5368	0.064168
3	0.19215	1.7079	0.045794
4	-0.220403	-1.959	0.026822
5	-0.081573	-0.725	0.235285
6	-0.001192	-0.0106	0.495788
7	-0.093993	-0.8354	0.202998
8	-0.079988	-0.7109	0.239605
9	-0.084758	-0.7533	0.226742
10	0.008837	0.0785	0.468796
11	-0.023607	-0.2098	0.417173
12	-0.003575	-0.0318	0.487367
13	-0.183821	-1.6338	0.053136
14	0.023988	0.2132	0.415855
15	-0.089438	-0.7949	0.214515
16	0.143926	1.2792	0.102278
17	0.025709	0.2285	0.409922
18	-0.037585	-0.3341	0.36961
19	-0.064881	-0.5767	0.282899

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.456647 & 4.0588 & 5.8e-05 \tabularnewline
2 & 0.172904 & 1.5368 & 0.064168 \tabularnewline
3 & 0.19215 & 1.7079 & 0.045794 \tabularnewline
4 & -0.220403 & -1.959 & 0.026822 \tabularnewline
5 & -0.081573 & -0.725 & 0.235285 \tabularnewline
6 & -0.001192 & -0.0106 & 0.495788 \tabularnewline
7 & -0.093993 & -0.8354 & 0.202998 \tabularnewline
8 & -0.079988 & -0.7109 & 0.239605 \tabularnewline
9 & -0.084758 & -0.7533 & 0.226742 \tabularnewline
10 & 0.008837 & 0.0785 & 0.468796 \tabularnewline
11 & -0.023607 & -0.2098 & 0.417173 \tabularnewline
12 & -0.003575 & -0.0318 & 0.487367 \tabularnewline
13 & -0.183821 & -1.6338 & 0.053136 \tabularnewline
14 & 0.023988 & 0.2132 & 0.415855 \tabularnewline
15 & -0.089438 & -0.7949 & 0.214515 \tabularnewline
16 & 0.143926 & 1.2792 & 0.102278 \tabularnewline
17 & 0.025709 & 0.2285 & 0.409922 \tabularnewline
18 & -0.037585 & -0.3341 & 0.36961 \tabularnewline
19 & -0.064881 & -0.5767 & 0.282899 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295590&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]0.456647[/C][C]4.0588[/C][C]5.8e-05[/C][/ROW]
[ROW][C]2[/C][C]0.172904[/C][C]1.5368[/C][C]0.064168[/C][/ROW]
[ROW][C]3[/C][C]0.19215[/C][C]1.7079[/C][C]0.045794[/C][/ROW]
[ROW][C]4[/C][C]-0.220403[/C][C]-1.959[/C][C]0.026822[/C][/ROW]
[ROW][C]5[/C][C]-0.081573[/C][C]-0.725[/C][C]0.235285[/C][/ROW]
[ROW][C]6[/C][C]-0.001192[/C][C]-0.0106[/C][C]0.495788[/C][/ROW]
[ROW][C]7[/C][C]-0.093993[/C][C]-0.8354[/C][C]0.202998[/C][/ROW]
[ROW][C]8[/C][C]-0.079988[/C][C]-0.7109[/C][C]0.239605[/C][/ROW]
[ROW][C]9[/C][C]-0.084758[/C][C]-0.7533[/C][C]0.226742[/C][/ROW]
[ROW][C]10[/C][C]0.008837[/C][C]0.0785[/C][C]0.468796[/C][/ROW]
[ROW][C]11[/C][C]-0.023607[/C][C]-0.2098[/C][C]0.417173[/C][/ROW]
[ROW][C]12[/C][C]-0.003575[/C][C]-0.0318[/C][C]0.487367[/C][/ROW]
[ROW][C]13[/C][C]-0.183821[/C][C]-1.6338[/C][C]0.053136[/C][/ROW]
[ROW][C]14[/C][C]0.023988[/C][C]0.2132[/C][C]0.415855[/C][/ROW]
[ROW][C]15[/C][C]-0.089438[/C][C]-0.7949[/C][C]0.214515[/C][/ROW]
[ROW][C]16[/C][C]0.143926[/C][C]1.2792[/C][C]0.102278[/C][/ROW]
[ROW][C]17[/C][C]0.025709[/C][C]0.2285[/C][C]0.409922[/C][/ROW]
[ROW][C]18[/C][C]-0.037585[/C][C]-0.3341[/C][C]0.36961[/C][/ROW]
[ROW][C]19[/C][C]-0.064881[/C][C]-0.5767[/C][C]0.282899[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295590&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295590&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	0.456647	4.0588	5.8e-05
2	0.172904	1.5368	0.064168
3	0.19215	1.7079	0.045794
4	-0.220403	-1.959	0.026822
5	-0.081573	-0.725	0.235285
6	-0.001192	-0.0106	0.495788
7	-0.093993	-0.8354	0.202998
8	-0.079988	-0.7109	0.239605
9	-0.084758	-0.7533	0.226742
10	0.008837	0.0785	0.468796
11	-0.023607	-0.2098	0.417173
12	-0.003575	-0.0318	0.487367
13	-0.183821	-1.6338	0.053136
14	0.023988	0.2132	0.415855
15	-0.089438	-0.7949	0.214515
16	0.143926	1.2792	0.102278
17	0.025709	0.2285	0.409922
18	-0.037585	-0.3341	0.36961
19	-0.064881	-0.5767	0.282899

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 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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)
x <- na.omit(x)
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