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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 21:21:30 +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/t1445631758r1a4rmszli2vv0i.htm/, Retrieved Tue, 14 May 2024 15:26:20 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=282977, Retrieved Tue, 14 May 2024 15:26:20 +0000

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-       [(Partial) Autocorrelation Function] [] [2015-10-23 20:21:30] [0bbe3141369311cb51cf1cd235842853] [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=282977&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=282977&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282977&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	0.965625	10.0351	0
2	0.919067	9.5512	0
3	0.857705	8.9135	0
4	0.790252	8.2125	0
5	0.714457	7.4249	0
6	0.637426	6.6243	0
7	0.557389	5.7926	0
8	0.479228	4.9803	1e-06
9	0.397247	4.1283	3.6e-05
10	0.314841	3.2719	0.000717
11	0.227793	2.3673	0.009849
12	0.142877	1.4848	0.070252
13	0.057544	0.598	0.27554
14	-0.026084	-0.2711	0.393428
15	-0.111062	-1.1542	0.125485
16	-0.190937	-1.9843	0.024881
17	-0.270129	-2.8073	0.002965
18	-0.339569	-3.5289	0.000307
19	-0.403677	-4.1951	2.8e-05
20	-0.451479	-4.6919	4e-06

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.965625 & 10.0351 & 0 \tabularnewline
2 & 0.919067 & 9.5512 & 0 \tabularnewline
3 & 0.857705 & 8.9135 & 0 \tabularnewline
4 & 0.790252 & 8.2125 & 0 \tabularnewline
5 & 0.714457 & 7.4249 & 0 \tabularnewline
6 & 0.637426 & 6.6243 & 0 \tabularnewline
7 & 0.557389 & 5.7926 & 0 \tabularnewline
8 & 0.479228 & 4.9803 & 1e-06 \tabularnewline
9 & 0.397247 & 4.1283 & 3.6e-05 \tabularnewline
10 & 0.314841 & 3.2719 & 0.000717 \tabularnewline
11 & 0.227793 & 2.3673 & 0.009849 \tabularnewline
12 & 0.142877 & 1.4848 & 0.070252 \tabularnewline
13 & 0.057544 & 0.598 & 0.27554 \tabularnewline
14 & -0.026084 & -0.2711 & 0.393428 \tabularnewline
15 & -0.111062 & -1.1542 & 0.125485 \tabularnewline
16 & -0.190937 & -1.9843 & 0.024881 \tabularnewline
17 & -0.270129 & -2.8073 & 0.002965 \tabularnewline
18 & -0.339569 & -3.5289 & 0.000307 \tabularnewline
19 & -0.403677 & -4.1951 & 2.8e-05 \tabularnewline
20 & -0.451479 & -4.6919 & 4e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282977&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]0.965625[/C][C]10.0351[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.919067[/C][C]9.5512[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.857705[/C][C]8.9135[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.790252[/C][C]8.2125[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.714457[/C][C]7.4249[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.637426[/C][C]6.6243[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.557389[/C][C]5.7926[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.479228[/C][C]4.9803[/C][C]1e-06[/C][/ROW]
[ROW][C]9[/C][C]0.397247[/C][C]4.1283[/C][C]3.6e-05[/C][/ROW]
[ROW][C]10[/C][C]0.314841[/C][C]3.2719[/C][C]0.000717[/C][/ROW]
[ROW][C]11[/C][C]0.227793[/C][C]2.3673[/C][C]0.009849[/C][/ROW]
[ROW][C]12[/C][C]0.142877[/C][C]1.4848[/C][C]0.070252[/C][/ROW]
[ROW][C]13[/C][C]0.057544[/C][C]0.598[/C][C]0.27554[/C][/ROW]
[ROW][C]14[/C][C]-0.026084[/C][C]-0.2711[/C][C]0.393428[/C][/ROW]
[ROW][C]15[/C][C]-0.111062[/C][C]-1.1542[/C][C]0.125485[/C][/ROW]
[ROW][C]16[/C][C]-0.190937[/C][C]-1.9843[/C][C]0.024881[/C][/ROW]
[ROW][C]17[/C][C]-0.270129[/C][C]-2.8073[/C][C]0.002965[/C][/ROW]
[ROW][C]18[/C][C]-0.339569[/C][C]-3.5289[/C][C]0.000307[/C][/ROW]
[ROW][C]19[/C][C]-0.403677[/C][C]-4.1951[/C][C]2.8e-05[/C][/ROW]
[ROW][C]20[/C][C]-0.451479[/C][C]-4.6919[/C][C]4e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282977&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282977&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	0.965625	10.0351	0
2	0.919067	9.5512	0
3	0.857705	8.9135	0
4	0.790252	8.2125	0
5	0.714457	7.4249	0
6	0.637426	6.6243	0
7	0.557389	5.7926	0
8	0.479228	4.9803	1e-06
9	0.397247	4.1283	3.6e-05
10	0.314841	3.2719	0.000717
11	0.227793	2.3673	0.009849
12	0.142877	1.4848	0.070252
13	0.057544	0.598	0.27554
14	-0.026084	-0.2711	0.393428
15	-0.111062	-1.1542	0.125485
16	-0.190937	-1.9843	0.024881
17	-0.270129	-2.8073	0.002965
18	-0.339569	-3.5289	0.000307
19	-0.403677	-4.1951	2.8e-05
20	-0.451479	-4.6919	4e-06

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.965625	10.0351	0
2	-0.197805	-2.0557	0.021114
3	-0.22043	-2.2908	0.011959
4	-0.06592	-0.6851	0.247386
5	-0.114985	-1.195	0.11736
6	-0.018315	-0.1903	0.4247
7	-0.060387	-0.6276	0.265808
8	-0.009645	-0.1002	0.460172
9	-0.109274	-1.1356	0.129317
10	-0.06834	-0.7102	0.239552
11	-0.122143	-1.2693	0.103523
12	-0.02682	-0.2787	0.390496
13	-0.062528	-0.6498	0.258599
14	-0.06763	-0.7028	0.241837
15	-0.108522	-1.1278	0.130953
16	-0.029386	-0.3054	0.380328
17	-0.098393	-1.0225	0.154407
18	0.024334	0.2529	0.400419
19	-0.03797	-0.3946	0.346958
20	0.103724	1.0779	0.141734

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.965625 & 10.0351 & 0 \tabularnewline
2 & -0.197805 & -2.0557 & 0.021114 \tabularnewline
3 & -0.22043 & -2.2908 & 0.011959 \tabularnewline
4 & -0.06592 & -0.6851 & 0.247386 \tabularnewline
5 & -0.114985 & -1.195 & 0.11736 \tabularnewline
6 & -0.018315 & -0.1903 & 0.4247 \tabularnewline
7 & -0.060387 & -0.6276 & 0.265808 \tabularnewline
8 & -0.009645 & -0.1002 & 0.460172 \tabularnewline
9 & -0.109274 & -1.1356 & 0.129317 \tabularnewline
10 & -0.06834 & -0.7102 & 0.239552 \tabularnewline
11 & -0.122143 & -1.2693 & 0.103523 \tabularnewline
12 & -0.02682 & -0.2787 & 0.390496 \tabularnewline
13 & -0.062528 & -0.6498 & 0.258599 \tabularnewline
14 & -0.06763 & -0.7028 & 0.241837 \tabularnewline
15 & -0.108522 & -1.1278 & 0.130953 \tabularnewline
16 & -0.029386 & -0.3054 & 0.380328 \tabularnewline
17 & -0.098393 & -1.0225 & 0.154407 \tabularnewline
18 & 0.024334 & 0.2529 & 0.400419 \tabularnewline
19 & -0.03797 & -0.3946 & 0.346958 \tabularnewline
20 & 0.103724 & 1.0779 & 0.141734 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282977&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]0.965625[/C][C]10.0351[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.197805[/C][C]-2.0557[/C][C]0.021114[/C][/ROW]
[ROW][C]3[/C][C]-0.22043[/C][C]-2.2908[/C][C]0.011959[/C][/ROW]
[ROW][C]4[/C][C]-0.06592[/C][C]-0.6851[/C][C]0.247386[/C][/ROW]
[ROW][C]5[/C][C]-0.114985[/C][C]-1.195[/C][C]0.11736[/C][/ROW]
[ROW][C]6[/C][C]-0.018315[/C][C]-0.1903[/C][C]0.4247[/C][/ROW]
[ROW][C]7[/C][C]-0.060387[/C][C]-0.6276[/C][C]0.265808[/C][/ROW]
[ROW][C]8[/C][C]-0.009645[/C][C]-0.1002[/C][C]0.460172[/C][/ROW]
[ROW][C]9[/C][C]-0.109274[/C][C]-1.1356[/C][C]0.129317[/C][/ROW]
[ROW][C]10[/C][C]-0.06834[/C][C]-0.7102[/C][C]0.239552[/C][/ROW]
[ROW][C]11[/C][C]-0.122143[/C][C]-1.2693[/C][C]0.103523[/C][/ROW]
[ROW][C]12[/C][C]-0.02682[/C][C]-0.2787[/C][C]0.390496[/C][/ROW]
[ROW][C]13[/C][C]-0.062528[/C][C]-0.6498[/C][C]0.258599[/C][/ROW]
[ROW][C]14[/C][C]-0.06763[/C][C]-0.7028[/C][C]0.241837[/C][/ROW]
[ROW][C]15[/C][C]-0.108522[/C][C]-1.1278[/C][C]0.130953[/C][/ROW]
[ROW][C]16[/C][C]-0.029386[/C][C]-0.3054[/C][C]0.380328[/C][/ROW]
[ROW][C]17[/C][C]-0.098393[/C][C]-1.0225[/C][C]0.154407[/C][/ROW]
[ROW][C]18[/C][C]0.024334[/C][C]0.2529[/C][C]0.400419[/C][/ROW]
[ROW][C]19[/C][C]-0.03797[/C][C]-0.3946[/C][C]0.346958[/C][/ROW]
[ROW][C]20[/C][C]0.103724[/C][C]1.0779[/C][C]0.141734[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282977&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282977&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	0.965625	10.0351	0
2	-0.197805	-2.0557	0.021114
3	-0.22043	-2.2908	0.011959
4	-0.06592	-0.6851	0.247386
5	-0.114985	-1.195	0.11736
6	-0.018315	-0.1903	0.4247
7	-0.060387	-0.6276	0.265808
8	-0.009645	-0.1002	0.460172
9	-0.109274	-1.1356	0.129317
10	-0.06834	-0.7102	0.239552
11	-0.122143	-1.2693	0.103523
12	-0.02682	-0.2787	0.390496
13	-0.062528	-0.6498	0.258599
14	-0.06763	-0.7028	0.241837
15	-0.108522	-1.1278	0.130953
16	-0.029386	-0.3054	0.380328
17	-0.098393	-1.0225	0.154407
18	0.024334	0.2529	0.400419
19	-0.03797	-0.3946	0.346958
20	0.103724	1.0779	0.141734

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')

Free Statistics

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code