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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 18 Oct 2016 21:37:06 +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/Oct/18/t1476823042c5dlivpi34whisq.htm/, Retrieved Sun, 28 Apr 2024 12:06:28 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 28 Apr 2024 12:06:28 +0200

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Estimated Impact

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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	'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.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]'Sir Ronald Aylmer Fisher' @ fisher.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	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.08151	-0.6314	0.265098
2	0.259145	2.0073	0.024612
3	0.173118	1.341	0.092493
4	-0.253162	-1.961	0.027264
5	0.253534	1.9639	0.027092
6	-0.139139	-1.0778	0.142726
7	0.119633	0.9267	0.178904
8	-0.138525	-1.073	0.143782
9	0.028201	0.2184	0.413913
10	0.16121	1.2487	0.108308
11	-0.064735	-0.5014	0.308949
12	0.560116	4.3386	2.8e-05
13	-0.108949	-0.8439	0.201035
14	0.183091	1.4182	0.080651
15	0.066405	0.5144	0.304441
16	-0.238289	-1.8458	0.03493
17	0.232501	1.8009	0.038369
18	-0.238579	-1.848	0.034764
19	0.024065	0.1864	0.426376
20	-0.093869	-0.7271	0.234995
21	-0.038286	-0.2966	0.383911
22	0.123907	0.9598	0.170509
23	-0.011403	-0.0883	0.464955
24	0.282346	2.187	0.016324

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.08151 & -0.6314 & 0.265098 \tabularnewline
2 & 0.259145 & 2.0073 & 0.024612 \tabularnewline
3 & 0.173118 & 1.341 & 0.092493 \tabularnewline
4 & -0.253162 & -1.961 & 0.027264 \tabularnewline
5 & 0.253534 & 1.9639 & 0.027092 \tabularnewline
6 & -0.139139 & -1.0778 & 0.142726 \tabularnewline
7 & 0.119633 & 0.9267 & 0.178904 \tabularnewline
8 & -0.138525 & -1.073 & 0.143782 \tabularnewline
9 & 0.028201 & 0.2184 & 0.413913 \tabularnewline
10 & 0.16121 & 1.2487 & 0.108308 \tabularnewline
11 & -0.064735 & -0.5014 & 0.308949 \tabularnewline
12 & 0.560116 & 4.3386 & 2.8e-05 \tabularnewline
13 & -0.108949 & -0.8439 & 0.201035 \tabularnewline
14 & 0.183091 & 1.4182 & 0.080651 \tabularnewline
15 & 0.066405 & 0.5144 & 0.304441 \tabularnewline
16 & -0.238289 & -1.8458 & 0.03493 \tabularnewline
17 & 0.232501 & 1.8009 & 0.038369 \tabularnewline
18 & -0.238579 & -1.848 & 0.034764 \tabularnewline
19 & 0.024065 & 0.1864 & 0.426376 \tabularnewline
20 & -0.093869 & -0.7271 & 0.234995 \tabularnewline
21 & -0.038286 & -0.2966 & 0.383911 \tabularnewline
22 & 0.123907 & 0.9598 & 0.170509 \tabularnewline
23 & -0.011403 & -0.0883 & 0.464955 \tabularnewline
24 & 0.282346 & 2.187 & 0.016324 \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]-0.08151[/C][C]-0.6314[/C][C]0.265098[/C][/ROW]
[ROW][C]2[/C][C]0.259145[/C][C]2.0073[/C][C]0.024612[/C][/ROW]
[ROW][C]3[/C][C]0.173118[/C][C]1.341[/C][C]0.092493[/C][/ROW]
[ROW][C]4[/C][C]-0.253162[/C][C]-1.961[/C][C]0.027264[/C][/ROW]
[ROW][C]5[/C][C]0.253534[/C][C]1.9639[/C][C]0.027092[/C][/ROW]
[ROW][C]6[/C][C]-0.139139[/C][C]-1.0778[/C][C]0.142726[/C][/ROW]
[ROW][C]7[/C][C]0.119633[/C][C]0.9267[/C][C]0.178904[/C][/ROW]
[ROW][C]8[/C][C]-0.138525[/C][C]-1.073[/C][C]0.143782[/C][/ROW]
[ROW][C]9[/C][C]0.028201[/C][C]0.2184[/C][C]0.413913[/C][/ROW]
[ROW][C]10[/C][C]0.16121[/C][C]1.2487[/C][C]0.108308[/C][/ROW]
[ROW][C]11[/C][C]-0.064735[/C][C]-0.5014[/C][C]0.308949[/C][/ROW]
[ROW][C]12[/C][C]0.560116[/C][C]4.3386[/C][C]2.8e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.108949[/C][C]-0.8439[/C][C]0.201035[/C][/ROW]
[ROW][C]14[/C][C]0.183091[/C][C]1.4182[/C][C]0.080651[/C][/ROW]
[ROW][C]15[/C][C]0.066405[/C][C]0.5144[/C][C]0.304441[/C][/ROW]
[ROW][C]16[/C][C]-0.238289[/C][C]-1.8458[/C][C]0.03493[/C][/ROW]
[ROW][C]17[/C][C]0.232501[/C][C]1.8009[/C][C]0.038369[/C][/ROW]
[ROW][C]18[/C][C]-0.238579[/C][C]-1.848[/C][C]0.034764[/C][/ROW]
[ROW][C]19[/C][C]0.024065[/C][C]0.1864[/C][C]0.426376[/C][/ROW]
[ROW][C]20[/C][C]-0.093869[/C][C]-0.7271[/C][C]0.234995[/C][/ROW]
[ROW][C]21[/C][C]-0.038286[/C][C]-0.2966[/C][C]0.383911[/C][/ROW]
[ROW][C]22[/C][C]0.123907[/C][C]0.9598[/C][C]0.170509[/C][/ROW]
[ROW][C]23[/C][C]-0.011403[/C][C]-0.0883[/C][C]0.464955[/C][/ROW]
[ROW][C]24[/C][C]0.282346[/C][C]2.187[/C][C]0.016324[/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	-0.08151	-0.6314	0.265098
2	0.259145	2.0073	0.024612
3	0.173118	1.341	0.092493
4	-0.253162	-1.961	0.027264
5	0.253534	1.9639	0.027092
6	-0.139139	-1.0778	0.142726
7	0.119633	0.9267	0.178904
8	-0.138525	-1.073	0.143782
9	0.028201	0.2184	0.413913
10	0.16121	1.2487	0.108308
11	-0.064735	-0.5014	0.308949
12	0.560116	4.3386	2.8e-05
13	-0.108949	-0.8439	0.201035
14	0.183091	1.4182	0.080651
15	0.066405	0.5144	0.304441
16	-0.238289	-1.8458	0.03493
17	0.232501	1.8009	0.038369
18	-0.238579	-1.848	0.034764
19	0.024065	0.1864	0.426376
20	-0.093869	-0.7271	0.234995
21	-0.038286	-0.2966	0.383911
22	0.123907	0.9598	0.170509
23	-0.011403	-0.0883	0.464955
24	0.282346	2.187	0.016324

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.08151	-0.6314	0.265098
2	0.25419	1.969	0.026791
3	0.225567	1.7472	0.042857
4	-0.321752	-2.4923	0.007736
5	0.133911	1.0373	0.151886
6	0.017035	0.132	0.447733
7	0.117709	0.9118	0.182769
8	-0.30659	-2.3748	0.010386
9	0.13904	1.077	0.142896
10	0.240386	1.862	0.03375
11	0.051197	0.3966	0.346547
12	0.390701	3.0264	0.001821
13	-0.077586	-0.601	0.275058
14	-0.03268	-0.2531	0.400513
15	-0.138129	-1.0699	0.144465
16	-0.023533	-0.1823	0.427986
17	0.019431	0.1505	0.440432
18	-0.099016	-0.767	0.223052
19	-0.111368	-0.8626	0.195883
20	0.024951	0.1933	0.4237
21	0.157931	1.2233	0.112995
22	-0.023837	-0.1846	0.427067
23	0.029087	0.2253	0.411253
24	-0.069389	-0.5375	0.296461

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.08151 & -0.6314 & 0.265098 \tabularnewline
2 & 0.25419 & 1.969 & 0.026791 \tabularnewline
3 & 0.225567 & 1.7472 & 0.042857 \tabularnewline
4 & -0.321752 & -2.4923 & 0.007736 \tabularnewline
5 & 0.133911 & 1.0373 & 0.151886 \tabularnewline
6 & 0.017035 & 0.132 & 0.447733 \tabularnewline
7 & 0.117709 & 0.9118 & 0.182769 \tabularnewline
8 & -0.30659 & -2.3748 & 0.010386 \tabularnewline
9 & 0.13904 & 1.077 & 0.142896 \tabularnewline
10 & 0.240386 & 1.862 & 0.03375 \tabularnewline
11 & 0.051197 & 0.3966 & 0.346547 \tabularnewline
12 & 0.390701 & 3.0264 & 0.001821 \tabularnewline
13 & -0.077586 & -0.601 & 0.275058 \tabularnewline
14 & -0.03268 & -0.2531 & 0.400513 \tabularnewline
15 & -0.138129 & -1.0699 & 0.144465 \tabularnewline
16 & -0.023533 & -0.1823 & 0.427986 \tabularnewline
17 & 0.019431 & 0.1505 & 0.440432 \tabularnewline
18 & -0.099016 & -0.767 & 0.223052 \tabularnewline
19 & -0.111368 & -0.8626 & 0.195883 \tabularnewline
20 & 0.024951 & 0.1933 & 0.4237 \tabularnewline
21 & 0.157931 & 1.2233 & 0.112995 \tabularnewline
22 & -0.023837 & -0.1846 & 0.427067 \tabularnewline
23 & 0.029087 & 0.2253 & 0.411253 \tabularnewline
24 & -0.069389 & -0.5375 & 0.296461 \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]-0.08151[/C][C]-0.6314[/C][C]0.265098[/C][/ROW]
[ROW][C]2[/C][C]0.25419[/C][C]1.969[/C][C]0.026791[/C][/ROW]
[ROW][C]3[/C][C]0.225567[/C][C]1.7472[/C][C]0.042857[/C][/ROW]
[ROW][C]4[/C][C]-0.321752[/C][C]-2.4923[/C][C]0.007736[/C][/ROW]
[ROW][C]5[/C][C]0.133911[/C][C]1.0373[/C][C]0.151886[/C][/ROW]
[ROW][C]6[/C][C]0.017035[/C][C]0.132[/C][C]0.447733[/C][/ROW]
[ROW][C]7[/C][C]0.117709[/C][C]0.9118[/C][C]0.182769[/C][/ROW]
[ROW][C]8[/C][C]-0.30659[/C][C]-2.3748[/C][C]0.010386[/C][/ROW]
[ROW][C]9[/C][C]0.13904[/C][C]1.077[/C][C]0.142896[/C][/ROW]
[ROW][C]10[/C][C]0.240386[/C][C]1.862[/C][C]0.03375[/C][/ROW]
[ROW][C]11[/C][C]0.051197[/C][C]0.3966[/C][C]0.346547[/C][/ROW]
[ROW][C]12[/C][C]0.390701[/C][C]3.0264[/C][C]0.001821[/C][/ROW]
[ROW][C]13[/C][C]-0.077586[/C][C]-0.601[/C][C]0.275058[/C][/ROW]
[ROW][C]14[/C][C]-0.03268[/C][C]-0.2531[/C][C]0.400513[/C][/ROW]
[ROW][C]15[/C][C]-0.138129[/C][C]-1.0699[/C][C]0.144465[/C][/ROW]
[ROW][C]16[/C][C]-0.023533[/C][C]-0.1823[/C][C]0.427986[/C][/ROW]
[ROW][C]17[/C][C]0.019431[/C][C]0.1505[/C][C]0.440432[/C][/ROW]
[ROW][C]18[/C][C]-0.099016[/C][C]-0.767[/C][C]0.223052[/C][/ROW]
[ROW][C]19[/C][C]-0.111368[/C][C]-0.8626[/C][C]0.195883[/C][/ROW]
[ROW][C]20[/C][C]0.024951[/C][C]0.1933[/C][C]0.4237[/C][/ROW]
[ROW][C]21[/C][C]0.157931[/C][C]1.2233[/C][C]0.112995[/C][/ROW]
[ROW][C]22[/C][C]-0.023837[/C][C]-0.1846[/C][C]0.427067[/C][/ROW]
[ROW][C]23[/C][C]0.029087[/C][C]0.2253[/C][C]0.411253[/C][/ROW]
[ROW][C]24[/C][C]-0.069389[/C][C]-0.5375[/C][C]0.296461[/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	-0.08151	-0.6314	0.265098
2	0.25419	1.969	0.026791
3	0.225567	1.7472	0.042857
4	-0.321752	-2.4923	0.007736
5	0.133911	1.0373	0.151886
6	0.017035	0.132	0.447733
7	0.117709	0.9118	0.182769
8	-0.30659	-2.3748	0.010386
9	0.13904	1.077	0.142896
10	0.240386	1.862	0.03375
11	0.051197	0.3966	0.346547
12	0.390701	3.0264	0.001821
13	-0.077586	-0.601	0.275058
14	-0.03268	-0.2531	0.400513
15	-0.138129	-1.0699	0.144465
16	-0.023533	-0.1823	0.427986
17	0.019431	0.1505	0.440432
18	-0.099016	-0.767	0.223052
19	-0.111368	-0.8626	0.195883
20	0.024951	0.1933	0.4237
21	0.157931	1.2233	0.112995
22	-0.023837	-0.1846	0.427067
23	0.029087	0.2253	0.411253
24	-0.069389	-0.5375	0.296461

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 = 24 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 24 ; 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)
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