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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 18 Oct 2016 21:28:00 +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/t14768225483amxx7eu8hw6hw4.htm/, Retrieved Sun, 28 Apr 2024 07:41:58 +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 07:41:58 +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	'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	0.562152	3.8947	0.000152
2	0.176847	1.2252	0.113233
3	0.031551	0.2186	0.413946
4	-0.230745	-1.5986	0.058231
5	-0.554562	-3.8421	0.000179
6	-0.663669	-4.598	1.6e-05
7	-0.503865	-3.4909	0.000522
8	-0.194679	-1.3488	0.091869
9	0.061111	0.4234	0.336951
10	0.191297	1.3253	0.095665
11	0.481945	3.339	0.000816
12	0.686421	4.7557	9e-06
13	0.363662	2.5195	0.007567
14	0.122892	0.8514	0.199382
15	0.051306	0.3555	0.361902
16	-0.169645	-1.1753	0.122828
17	-0.426172	-2.9526	0.002433
18	-0.490707	-3.3997	0.000683
19	-0.338756	-2.347	0.01155
20	-0.106694	-0.7392	0.231693
21	0.01185	0.0821	0.467454
22	0.101187	0.701	0.243331
23	0.324492	2.2481	0.014598
24	0.440595	3.0525	0.001847

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.562152 & 3.8947 & 0.000152 \tabularnewline
2 & 0.176847 & 1.2252 & 0.113233 \tabularnewline
3 & 0.031551 & 0.2186 & 0.413946 \tabularnewline
4 & -0.230745 & -1.5986 & 0.058231 \tabularnewline
5 & -0.554562 & -3.8421 & 0.000179 \tabularnewline
6 & -0.663669 & -4.598 & 1.6e-05 \tabularnewline
7 & -0.503865 & -3.4909 & 0.000522 \tabularnewline
8 & -0.194679 & -1.3488 & 0.091869 \tabularnewline
9 & 0.061111 & 0.4234 & 0.336951 \tabularnewline
10 & 0.191297 & 1.3253 & 0.095665 \tabularnewline
11 & 0.481945 & 3.339 & 0.000816 \tabularnewline
12 & 0.686421 & 4.7557 & 9e-06 \tabularnewline
13 & 0.363662 & 2.5195 & 0.007567 \tabularnewline
14 & 0.122892 & 0.8514 & 0.199382 \tabularnewline
15 & 0.051306 & 0.3555 & 0.361902 \tabularnewline
16 & -0.169645 & -1.1753 & 0.122828 \tabularnewline
17 & -0.426172 & -2.9526 & 0.002433 \tabularnewline
18 & -0.490707 & -3.3997 & 0.000683 \tabularnewline
19 & -0.338756 & -2.347 & 0.01155 \tabularnewline
20 & -0.106694 & -0.7392 & 0.231693 \tabularnewline
21 & 0.01185 & 0.0821 & 0.467454 \tabularnewline
22 & 0.101187 & 0.701 & 0.243331 \tabularnewline
23 & 0.324492 & 2.2481 & 0.014598 \tabularnewline
24 & 0.440595 & 3.0525 & 0.001847 \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]0.562152[/C][C]3.8947[/C][C]0.000152[/C][/ROW]
[ROW][C]2[/C][C]0.176847[/C][C]1.2252[/C][C]0.113233[/C][/ROW]
[ROW][C]3[/C][C]0.031551[/C][C]0.2186[/C][C]0.413946[/C][/ROW]
[ROW][C]4[/C][C]-0.230745[/C][C]-1.5986[/C][C]0.058231[/C][/ROW]
[ROW][C]5[/C][C]-0.554562[/C][C]-3.8421[/C][C]0.000179[/C][/ROW]
[ROW][C]6[/C][C]-0.663669[/C][C]-4.598[/C][C]1.6e-05[/C][/ROW]
[ROW][C]7[/C][C]-0.503865[/C][C]-3.4909[/C][C]0.000522[/C][/ROW]
[ROW][C]8[/C][C]-0.194679[/C][C]-1.3488[/C][C]0.091869[/C][/ROW]
[ROW][C]9[/C][C]0.061111[/C][C]0.4234[/C][C]0.336951[/C][/ROW]
[ROW][C]10[/C][C]0.191297[/C][C]1.3253[/C][C]0.095665[/C][/ROW]
[ROW][C]11[/C][C]0.481945[/C][C]3.339[/C][C]0.000816[/C][/ROW]
[ROW][C]12[/C][C]0.686421[/C][C]4.7557[/C][C]9e-06[/C][/ROW]
[ROW][C]13[/C][C]0.363662[/C][C]2.5195[/C][C]0.007567[/C][/ROW]
[ROW][C]14[/C][C]0.122892[/C][C]0.8514[/C][C]0.199382[/C][/ROW]
[ROW][C]15[/C][C]0.051306[/C][C]0.3555[/C][C]0.361902[/C][/ROW]
[ROW][C]16[/C][C]-0.169645[/C][C]-1.1753[/C][C]0.122828[/C][/ROW]
[ROW][C]17[/C][C]-0.426172[/C][C]-2.9526[/C][C]0.002433[/C][/ROW]
[ROW][C]18[/C][C]-0.490707[/C][C]-3.3997[/C][C]0.000683[/C][/ROW]
[ROW][C]19[/C][C]-0.338756[/C][C]-2.347[/C][C]0.01155[/C][/ROW]
[ROW][C]20[/C][C]-0.106694[/C][C]-0.7392[/C][C]0.231693[/C][/ROW]
[ROW][C]21[/C][C]0.01185[/C][C]0.0821[/C][C]0.467454[/C][/ROW]
[ROW][C]22[/C][C]0.101187[/C][C]0.701[/C][C]0.243331[/C][/ROW]
[ROW][C]23[/C][C]0.324492[/C][C]2.2481[/C][C]0.014598[/C][/ROW]
[ROW][C]24[/C][C]0.440595[/C][C]3.0525[/C][C]0.001847[/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	0.562152	3.8947	0.000152
2	0.176847	1.2252	0.113233
3	0.031551	0.2186	0.413946
4	-0.230745	-1.5986	0.058231
5	-0.554562	-3.8421	0.000179
6	-0.663669	-4.598	1.6e-05
7	-0.503865	-3.4909	0.000522
8	-0.194679	-1.3488	0.091869
9	0.061111	0.4234	0.336951
10	0.191297	1.3253	0.095665
11	0.481945	3.339	0.000816
12	0.686421	4.7557	9e-06
13	0.363662	2.5195	0.007567
14	0.122892	0.8514	0.199382
15	0.051306	0.3555	0.361902
16	-0.169645	-1.1753	0.122828
17	-0.426172	-2.9526	0.002433
18	-0.490707	-3.3997	0.000683
19	-0.338756	-2.347	0.01155
20	-0.106694	-0.7392	0.231693
21	0.01185	0.0821	0.467454
22	0.101187	0.701	0.243331
23	0.324492	2.2481	0.014598
24	0.440595	3.0525	0.001847

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.562152	3.8947	0.000152
2	-0.203467	-1.4097	0.082544
3	0.040093	0.2778	0.391189
4	-0.357625	-2.4777	0.008397
5	-0.407681	-2.8245	0.003439
6	-0.347129	-2.405	0.010039
7	-0.160437	-1.1115	0.135936
8	0.104134	0.7215	0.237062
9	0.076405	0.5293	0.299501
10	-0.157531	-1.0914	0.140271
11	0.189686	1.3142	0.097516
12	0.238871	1.6549	0.05223
13	-0.278496	-1.9295	0.029797
14	0.129441	0.8968	0.187152
15	0.121858	0.8443	0.201358
16	0.061978	0.4294	0.334777
17	0.056981	0.3948	0.347378
18	-0.037856	-0.2623	0.397115
19	0.056752	0.3932	0.347961
20	0.074791	0.5182	0.303362
21	-0.083241	-0.5767	0.283415
22	0.016323	0.1131	0.455215
23	-0.064631	-0.4478	0.328165
24	-0.010677	-0.074	0.470671

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.562152 & 3.8947 & 0.000152 \tabularnewline
2 & -0.203467 & -1.4097 & 0.082544 \tabularnewline
3 & 0.040093 & 0.2778 & 0.391189 \tabularnewline
4 & -0.357625 & -2.4777 & 0.008397 \tabularnewline
5 & -0.407681 & -2.8245 & 0.003439 \tabularnewline
6 & -0.347129 & -2.405 & 0.010039 \tabularnewline
7 & -0.160437 & -1.1115 & 0.135936 \tabularnewline
8 & 0.104134 & 0.7215 & 0.237062 \tabularnewline
9 & 0.076405 & 0.5293 & 0.299501 \tabularnewline
10 & -0.157531 & -1.0914 & 0.140271 \tabularnewline
11 & 0.189686 & 1.3142 & 0.097516 \tabularnewline
12 & 0.238871 & 1.6549 & 0.05223 \tabularnewline
13 & -0.278496 & -1.9295 & 0.029797 \tabularnewline
14 & 0.129441 & 0.8968 & 0.187152 \tabularnewline
15 & 0.121858 & 0.8443 & 0.201358 \tabularnewline
16 & 0.061978 & 0.4294 & 0.334777 \tabularnewline
17 & 0.056981 & 0.3948 & 0.347378 \tabularnewline
18 & -0.037856 & -0.2623 & 0.397115 \tabularnewline
19 & 0.056752 & 0.3932 & 0.347961 \tabularnewline
20 & 0.074791 & 0.5182 & 0.303362 \tabularnewline
21 & -0.083241 & -0.5767 & 0.283415 \tabularnewline
22 & 0.016323 & 0.1131 & 0.455215 \tabularnewline
23 & -0.064631 & -0.4478 & 0.328165 \tabularnewline
24 & -0.010677 & -0.074 & 0.470671 \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]0.562152[/C][C]3.8947[/C][C]0.000152[/C][/ROW]
[ROW][C]2[/C][C]-0.203467[/C][C]-1.4097[/C][C]0.082544[/C][/ROW]
[ROW][C]3[/C][C]0.040093[/C][C]0.2778[/C][C]0.391189[/C][/ROW]
[ROW][C]4[/C][C]-0.357625[/C][C]-2.4777[/C][C]0.008397[/C][/ROW]
[ROW][C]5[/C][C]-0.407681[/C][C]-2.8245[/C][C]0.003439[/C][/ROW]
[ROW][C]6[/C][C]-0.347129[/C][C]-2.405[/C][C]0.010039[/C][/ROW]
[ROW][C]7[/C][C]-0.160437[/C][C]-1.1115[/C][C]0.135936[/C][/ROW]
[ROW][C]8[/C][C]0.104134[/C][C]0.7215[/C][C]0.237062[/C][/ROW]
[ROW][C]9[/C][C]0.076405[/C][C]0.5293[/C][C]0.299501[/C][/ROW]
[ROW][C]10[/C][C]-0.157531[/C][C]-1.0914[/C][C]0.140271[/C][/ROW]
[ROW][C]11[/C][C]0.189686[/C][C]1.3142[/C][C]0.097516[/C][/ROW]
[ROW][C]12[/C][C]0.238871[/C][C]1.6549[/C][C]0.05223[/C][/ROW]
[ROW][C]13[/C][C]-0.278496[/C][C]-1.9295[/C][C]0.029797[/C][/ROW]
[ROW][C]14[/C][C]0.129441[/C][C]0.8968[/C][C]0.187152[/C][/ROW]
[ROW][C]15[/C][C]0.121858[/C][C]0.8443[/C][C]0.201358[/C][/ROW]
[ROW][C]16[/C][C]0.061978[/C][C]0.4294[/C][C]0.334777[/C][/ROW]
[ROW][C]17[/C][C]0.056981[/C][C]0.3948[/C][C]0.347378[/C][/ROW]
[ROW][C]18[/C][C]-0.037856[/C][C]-0.2623[/C][C]0.397115[/C][/ROW]
[ROW][C]19[/C][C]0.056752[/C][C]0.3932[/C][C]0.347961[/C][/ROW]
[ROW][C]20[/C][C]0.074791[/C][C]0.5182[/C][C]0.303362[/C][/ROW]
[ROW][C]21[/C][C]-0.083241[/C][C]-0.5767[/C][C]0.283415[/C][/ROW]
[ROW][C]22[/C][C]0.016323[/C][C]0.1131[/C][C]0.455215[/C][/ROW]
[ROW][C]23[/C][C]-0.064631[/C][C]-0.4478[/C][C]0.328165[/C][/ROW]
[ROW][C]24[/C][C]-0.010677[/C][C]-0.074[/C][C]0.470671[/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	0.562152	3.8947	0.000152
2	-0.203467	-1.4097	0.082544
3	0.040093	0.2778	0.391189
4	-0.357625	-2.4777	0.008397
5	-0.407681	-2.8245	0.003439
6	-0.347129	-2.405	0.010039
7	-0.160437	-1.1115	0.135936
8	0.104134	0.7215	0.237062
9	0.076405	0.5293	0.299501
10	-0.157531	-1.0914	0.140271
11	0.189686	1.3142	0.097516
12	0.238871	1.6549	0.05223
13	-0.278496	-1.9295	0.029797
14	0.129441	0.8968	0.187152
15	0.121858	0.8443	0.201358
16	0.061978	0.4294	0.334777
17	0.056981	0.3948	0.347378
18	-0.037856	-0.2623	0.397115
19	0.056752	0.3932	0.347961
20	0.074791	0.5182	0.303362
21	-0.083241	-0.5767	0.283415
22	0.016323	0.1131	0.455215
23	-0.064631	-0.4478	0.328165
24	-0.010677	-0.074	0.470671

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