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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 14 Aug 2016 23:34:30 +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/Aug/14/t1471214183p3qwxo8k645h43z.htm/, Retrieved Fri, 03 May 2024 10:06:24 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Fri, 03 May 2024 10:06:24 +0200

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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=&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=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	-0.491725	-5.0864	1e-06
2	0.144396	1.4936	0.069106
3	-0.028562	-0.2954	0.384113
4	-0.103991	-1.0757	0.142242
5	0.207975	2.1513	0.016851
6	-0.442854	-4.5809	6e-06
7	0.245203	2.5364	0.006322
8	-0.129304	-1.3375	0.091944
9	-0.012559	-0.1299	0.448438
10	0.135195	1.3985	0.082433
11	-0.411531	-4.2569	2.2e-05
12	0.80368	8.3133	0
13	-0.405956	-4.1992	2.8e-05
14	0.117412	1.2145	0.113611
15	-0.027337	-0.2828	0.388949
16	-0.103326	-1.0688	0.14378
17	0.205674	2.1275	0.017838
18	-0.401639	-4.1546	3.3e-05
19	0.198265	2.0509	0.021361
20	-0.09402	-0.9726	0.166485

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.491725 & -5.0864 & 1e-06 \tabularnewline
2 & 0.144396 & 1.4936 & 0.069106 \tabularnewline
3 & -0.028562 & -0.2954 & 0.384113 \tabularnewline
4 & -0.103991 & -1.0757 & 0.142242 \tabularnewline
5 & 0.207975 & 2.1513 & 0.016851 \tabularnewline
6 & -0.442854 & -4.5809 & 6e-06 \tabularnewline
7 & 0.245203 & 2.5364 & 0.006322 \tabularnewline
8 & -0.129304 & -1.3375 & 0.091944 \tabularnewline
9 & -0.012559 & -0.1299 & 0.448438 \tabularnewline
10 & 0.135195 & 1.3985 & 0.082433 \tabularnewline
11 & -0.411531 & -4.2569 & 2.2e-05 \tabularnewline
12 & 0.80368 & 8.3133 & 0 \tabularnewline
13 & -0.405956 & -4.1992 & 2.8e-05 \tabularnewline
14 & 0.117412 & 1.2145 & 0.113611 \tabularnewline
15 & -0.027337 & -0.2828 & 0.388949 \tabularnewline
16 & -0.103326 & -1.0688 & 0.14378 \tabularnewline
17 & 0.205674 & 2.1275 & 0.017838 \tabularnewline
18 & -0.401639 & -4.1546 & 3.3e-05 \tabularnewline
19 & 0.198265 & 2.0509 & 0.021361 \tabularnewline
20 & -0.09402 & -0.9726 & 0.166485 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]-0.491725[/C][C]-5.0864[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]0.144396[/C][C]1.4936[/C][C]0.069106[/C][/ROW]
[ROW][C]3[/C][C]-0.028562[/C][C]-0.2954[/C][C]0.384113[/C][/ROW]
[ROW][C]4[/C][C]-0.103991[/C][C]-1.0757[/C][C]0.142242[/C][/ROW]
[ROW][C]5[/C][C]0.207975[/C][C]2.1513[/C][C]0.016851[/C][/ROW]
[ROW][C]6[/C][C]-0.442854[/C][C]-4.5809[/C][C]6e-06[/C][/ROW]
[ROW][C]7[/C][C]0.245203[/C][C]2.5364[/C][C]0.006322[/C][/ROW]
[ROW][C]8[/C][C]-0.129304[/C][C]-1.3375[/C][C]0.091944[/C][/ROW]
[ROW][C]9[/C][C]-0.012559[/C][C]-0.1299[/C][C]0.448438[/C][/ROW]
[ROW][C]10[/C][C]0.135195[/C][C]1.3985[/C][C]0.082433[/C][/ROW]
[ROW][C]11[/C][C]-0.411531[/C][C]-4.2569[/C][C]2.2e-05[/C][/ROW]
[ROW][C]12[/C][C]0.80368[/C][C]8.3133[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.405956[/C][C]-4.1992[/C][C]2.8e-05[/C][/ROW]
[ROW][C]14[/C][C]0.117412[/C][C]1.2145[/C][C]0.113611[/C][/ROW]
[ROW][C]15[/C][C]-0.027337[/C][C]-0.2828[/C][C]0.388949[/C][/ROW]
[ROW][C]16[/C][C]-0.103326[/C][C]-1.0688[/C][C]0.14378[/C][/ROW]
[ROW][C]17[/C][C]0.205674[/C][C]2.1275[/C][C]0.017838[/C][/ROW]
[ROW][C]18[/C][C]-0.401639[/C][C]-4.1546[/C][C]3.3e-05[/C][/ROW]
[ROW][C]19[/C][C]0.198265[/C][C]2.0509[/C][C]0.021361[/C][/ROW]
[ROW][C]20[/C][C]-0.09402[/C][C]-0.9726[/C][C]0.166485[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	-0.491725	-5.0864	1e-06
2	0.144396	1.4936	0.069106
3	-0.028562	-0.2954	0.384113
4	-0.103991	-1.0757	0.142242
5	0.207975	2.1513	0.016851
6	-0.442854	-4.5809	6e-06
7	0.245203	2.5364	0.006322
8	-0.129304	-1.3375	0.091944
9	-0.012559	-0.1299	0.448438
10	0.135195	1.3985	0.082433
11	-0.411531	-4.2569	2.2e-05
12	0.80368	8.3133	0
13	-0.405956	-4.1992	2.8e-05
14	0.117412	1.2145	0.113611
15	-0.027337	-0.2828	0.388949
16	-0.103326	-1.0688	0.14378
17	0.205674	2.1275	0.017838
18	-0.401639	-4.1546	3.3e-05
19	0.198265	2.0509	0.021361
20	-0.09402	-0.9726	0.166485

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.491725	-5.0864	1e-06
2	-0.128458	-1.3288	0.093374
3	-0.015561	-0.161	0.436213
4	-0.144535	-1.4951	0.068918
5	0.120757	1.2491	0.107173
6	-0.385113	-3.9836	6.2e-05
7	-0.211044	-2.1831	0.015608
8	-0.168138	-1.7392	0.042435
9	-0.217552	-2.2504	0.013235
10	-0.071591	-0.7405	0.230298
11	-0.591679	-6.1204	0
12	0.466301	4.8235	2e-06
13	0.240564	2.4884	0.007187
14	-0.004989	-0.0516	0.479469
15	-0.033383	-0.3453	0.365267
16	-0.101398	-1.0489	0.1483
17	-0.026821	-0.2774	0.390991
18	0.085313	0.8825	0.189747
19	-0.167557	-1.7332	0.042969
20	-0.066405	-0.6869	0.246816

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.491725 & -5.0864 & 1e-06 \tabularnewline
2 & -0.128458 & -1.3288 & 0.093374 \tabularnewline
3 & -0.015561 & -0.161 & 0.436213 \tabularnewline
4 & -0.144535 & -1.4951 & 0.068918 \tabularnewline
5 & 0.120757 & 1.2491 & 0.107173 \tabularnewline
6 & -0.385113 & -3.9836 & 6.2e-05 \tabularnewline
7 & -0.211044 & -2.1831 & 0.015608 \tabularnewline
8 & -0.168138 & -1.7392 & 0.042435 \tabularnewline
9 & -0.217552 & -2.2504 & 0.013235 \tabularnewline
10 & -0.071591 & -0.7405 & 0.230298 \tabularnewline
11 & -0.591679 & -6.1204 & 0 \tabularnewline
12 & 0.466301 & 4.8235 & 2e-06 \tabularnewline
13 & 0.240564 & 2.4884 & 0.007187 \tabularnewline
14 & -0.004989 & -0.0516 & 0.479469 \tabularnewline
15 & -0.033383 & -0.3453 & 0.365267 \tabularnewline
16 & -0.101398 & -1.0489 & 0.1483 \tabularnewline
17 & -0.026821 & -0.2774 & 0.390991 \tabularnewline
18 & 0.085313 & 0.8825 & 0.189747 \tabularnewline
19 & -0.167557 & -1.7332 & 0.042969 \tabularnewline
20 & -0.066405 & -0.6869 & 0.246816 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]-0.491725[/C][C]-5.0864[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.128458[/C][C]-1.3288[/C][C]0.093374[/C][/ROW]
[ROW][C]3[/C][C]-0.015561[/C][C]-0.161[/C][C]0.436213[/C][/ROW]
[ROW][C]4[/C][C]-0.144535[/C][C]-1.4951[/C][C]0.068918[/C][/ROW]
[ROW][C]5[/C][C]0.120757[/C][C]1.2491[/C][C]0.107173[/C][/ROW]
[ROW][C]6[/C][C]-0.385113[/C][C]-3.9836[/C][C]6.2e-05[/C][/ROW]
[ROW][C]7[/C][C]-0.211044[/C][C]-2.1831[/C][C]0.015608[/C][/ROW]
[ROW][C]8[/C][C]-0.168138[/C][C]-1.7392[/C][C]0.042435[/C][/ROW]
[ROW][C]9[/C][C]-0.217552[/C][C]-2.2504[/C][C]0.013235[/C][/ROW]
[ROW][C]10[/C][C]-0.071591[/C][C]-0.7405[/C][C]0.230298[/C][/ROW]
[ROW][C]11[/C][C]-0.591679[/C][C]-6.1204[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.466301[/C][C]4.8235[/C][C]2e-06[/C][/ROW]
[ROW][C]13[/C][C]0.240564[/C][C]2.4884[/C][C]0.007187[/C][/ROW]
[ROW][C]14[/C][C]-0.004989[/C][C]-0.0516[/C][C]0.479469[/C][/ROW]
[ROW][C]15[/C][C]-0.033383[/C][C]-0.3453[/C][C]0.365267[/C][/ROW]
[ROW][C]16[/C][C]-0.101398[/C][C]-1.0489[/C][C]0.1483[/C][/ROW]
[ROW][C]17[/C][C]-0.026821[/C][C]-0.2774[/C][C]0.390991[/C][/ROW]
[ROW][C]18[/C][C]0.085313[/C][C]0.8825[/C][C]0.189747[/C][/ROW]
[ROW][C]19[/C][C]-0.167557[/C][C]-1.7332[/C][C]0.042969[/C][/ROW]
[ROW][C]20[/C][C]-0.066405[/C][C]-0.6869[/C][C]0.246816[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	-0.491725	-5.0864	1e-06
2	-0.128458	-1.3288	0.093374
3	-0.015561	-0.161	0.436213
4	-0.144535	-1.4951	0.068918
5	0.120757	1.2491	0.107173
6	-0.385113	-3.9836	6.2e-05
7	-0.211044	-2.1831	0.015608
8	-0.168138	-1.7392	0.042435
9	-0.217552	-2.2504	0.013235
10	-0.071591	-0.7405	0.230298
11	-0.591679	-6.1204	0
12	0.466301	4.8235	2e-06
13	0.240564	2.4884	0.007187
14	-0.004989	-0.0516	0.479469
15	-0.033383	-0.3453	0.365267
16	-0.101398	-1.0489	0.1483
17	-0.026821	-0.2774	0.390991
18	0.085313	0.8825	0.189747
19	-0.167557	-1.7332	0.042969
20	-0.066405	-0.6869	0.246816

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 = grey ; par2 = no ;

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code