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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 02 Mar 2015 14:46:21 +0000

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/2015/Mar/02/t1425307603qq0cnhogtat0ym7.htm/, Retrieved Fri, 17 May 2024 15:19:21 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=277812, Retrieved Fri, 17 May 2024 15:19:21 +0000

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

-       [(Partial) Autocorrelation Function] [] [2015-03-02 14:46:21] [944b95db226364abcbc791a2a23b852c] [Current]

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Dataseries X:

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Histogram

Boxplots

1.3
1.2
1.1
1.4
1.5
1.4
1.1
1.1
1
1.4
1.3
1.2
1.5
1.6
1.8
1.5
1.3
1.6
1.6
1.8
1.8
1.6
1.8
2
1.3
1.1
1
1.2
1.2
1.3
1.3
1.4
1.1
0.9
1
1.1
1.4
1.5
1.8
1.8
1.8
1.7
1.5
1.1
1.3
1.6
1.9
1.9
2
2.2
2.2
2
2.3
2.6
3.2
3.2
3.1
2.8
2.3
1.9
1.9
2
2
1.8
1.6
1.4
0.2
0.3
0.4
0.7
1
1.1
0.8
0.8
1
1.1
1
0.8
1.6
1.5
1.6
1.6
1.6
1.9
2
1.9
2
2.1
2.3
2.3
2.6
2.6
2.7
2.6
2.6
2.4
2.5
2.5
2.5
2.4
2.1
2.1
2.3
2.3
2.3
2.9
2.8
2.9
3
3
2.9
2.6
2.8
2.9
3.1
2.8
2.4
1.6
1.5
1.7
1.4
1.1
0.8
1.2
0.8
0.9
0.9
1
0.9
1.1
1
0.7

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=277812&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]2 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=277812&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=277812&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	2 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.128052	1.4656	0.072574
2	-5e-06	-1e-04	0.499978
3	-0.118217	-1.3531	0.089183
4	-0.022952	-0.2627	0.396598
5	-0.032028	-0.3666	0.357265
6	0.00215	0.0246	0.490202
7	0.072412	0.8288	0.204363
8	0.140718	1.6106	0.054838
9	0.148239	1.6967	0.046066
10	-0.006933	-0.0793	0.468439
11	-0.083849	-0.9597	0.169489
12	-0.444508	-5.0876	1e-06
13	-0.096485	-1.1043	0.13574
14	-0.010344	-0.1184	0.452967
15	0.051468	0.5891	0.278411
16	0.085802	0.982	0.163944
17	0.008678	0.0993	0.460518
18	0.09023	1.0327	0.151818
19	-0.029013	-0.3321	0.370182
20	-0.149339	-1.7093	0.044886
21	-0.12413	-1.4207	0.078885

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.128052 & 1.4656 & 0.072574 \tabularnewline
2 & -5e-06 & -1e-04 & 0.499978 \tabularnewline
3 & -0.118217 & -1.3531 & 0.089183 \tabularnewline
4 & -0.022952 & -0.2627 & 0.396598 \tabularnewline
5 & -0.032028 & -0.3666 & 0.357265 \tabularnewline
6 & 0.00215 & 0.0246 & 0.490202 \tabularnewline
7 & 0.072412 & 0.8288 & 0.204363 \tabularnewline
8 & 0.140718 & 1.6106 & 0.054838 \tabularnewline
9 & 0.148239 & 1.6967 & 0.046066 \tabularnewline
10 & -0.006933 & -0.0793 & 0.468439 \tabularnewline
11 & -0.083849 & -0.9597 & 0.169489 \tabularnewline
12 & -0.444508 & -5.0876 & 1e-06 \tabularnewline
13 & -0.096485 & -1.1043 & 0.13574 \tabularnewline
14 & -0.010344 & -0.1184 & 0.452967 \tabularnewline
15 & 0.051468 & 0.5891 & 0.278411 \tabularnewline
16 & 0.085802 & 0.982 & 0.163944 \tabularnewline
17 & 0.008678 & 0.0993 & 0.460518 \tabularnewline
18 & 0.09023 & 1.0327 & 0.151818 \tabularnewline
19 & -0.029013 & -0.3321 & 0.370182 \tabularnewline
20 & -0.149339 & -1.7093 & 0.044886 \tabularnewline
21 & -0.12413 & -1.4207 & 0.078885 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=277812&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]0.128052[/C][C]1.4656[/C][C]0.072574[/C][/ROW]
[ROW][C]2[/C][C]-5e-06[/C][C]-1e-04[/C][C]0.499978[/C][/ROW]
[ROW][C]3[/C][C]-0.118217[/C][C]-1.3531[/C][C]0.089183[/C][/ROW]
[ROW][C]4[/C][C]-0.022952[/C][C]-0.2627[/C][C]0.396598[/C][/ROW]
[ROW][C]5[/C][C]-0.032028[/C][C]-0.3666[/C][C]0.357265[/C][/ROW]
[ROW][C]6[/C][C]0.00215[/C][C]0.0246[/C][C]0.490202[/C][/ROW]
[ROW][C]7[/C][C]0.072412[/C][C]0.8288[/C][C]0.204363[/C][/ROW]
[ROW][C]8[/C][C]0.140718[/C][C]1.6106[/C][C]0.054838[/C][/ROW]
[ROW][C]9[/C][C]0.148239[/C][C]1.6967[/C][C]0.046066[/C][/ROW]
[ROW][C]10[/C][C]-0.006933[/C][C]-0.0793[/C][C]0.468439[/C][/ROW]
[ROW][C]11[/C][C]-0.083849[/C][C]-0.9597[/C][C]0.169489[/C][/ROW]
[ROW][C]12[/C][C]-0.444508[/C][C]-5.0876[/C][C]1e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.096485[/C][C]-1.1043[/C][C]0.13574[/C][/ROW]
[ROW][C]14[/C][C]-0.010344[/C][C]-0.1184[/C][C]0.452967[/C][/ROW]
[ROW][C]15[/C][C]0.051468[/C][C]0.5891[/C][C]0.278411[/C][/ROW]
[ROW][C]16[/C][C]0.085802[/C][C]0.982[/C][C]0.163944[/C][/ROW]
[ROW][C]17[/C][C]0.008678[/C][C]0.0993[/C][C]0.460518[/C][/ROW]
[ROW][C]18[/C][C]0.09023[/C][C]1.0327[/C][C]0.151818[/C][/ROW]
[ROW][C]19[/C][C]-0.029013[/C][C]-0.3321[/C][C]0.370182[/C][/ROW]
[ROW][C]20[/C][C]-0.149339[/C][C]-1.7093[/C][C]0.044886[/C][/ROW]
[ROW][C]21[/C][C]-0.12413[/C][C]-1.4207[/C][C]0.078885[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=277812&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=277812&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	0.128052	1.4656	0.072574
2	-5e-06	-1e-04	0.499978
3	-0.118217	-1.3531	0.089183
4	-0.022952	-0.2627	0.396598
5	-0.032028	-0.3666	0.357265
6	0.00215	0.0246	0.490202
7	0.072412	0.8288	0.204363
8	0.140718	1.6106	0.054838
9	0.148239	1.6967	0.046066
10	-0.006933	-0.0793	0.468439
11	-0.083849	-0.9597	0.169489
12	-0.444508	-5.0876	1e-06
13	-0.096485	-1.1043	0.13574
14	-0.010344	-0.1184	0.452967
15	0.051468	0.5891	0.278411
16	0.085802	0.982	0.163944
17	0.008678	0.0993	0.460518
18	0.09023	1.0327	0.151818
19	-0.029013	-0.3321	0.370182
20	-0.149339	-1.7093	0.044886
21	-0.12413	-1.4207	0.078885

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.128052	1.4656	0.072574
2	-0.016675	-0.1909	0.424466
3	-0.118049	-1.3511	0.08949
4	0.007551	0.0864	0.465628
5	-0.031132	-0.3563	0.361085
6	-0.004037	-0.0462	0.481609
7	0.073419	0.8403	0.201131
8	0.119348	1.366	0.087139
9	0.121035	1.3853	0.084156
10	-0.02398	-0.2745	0.39208
11	-0.054428	-0.623	0.267196
12	-0.424372	-4.8572	2e-06
13	-0.016636	-0.1904	0.424642
14	-0.015574	-0.1783	0.429401
15	-0.042712	-0.4889	0.312879
16	0.089967	1.0297	0.152518
17	-0.045525	-0.5211	0.301604
18	0.124424	1.4241	0.078397
19	0.040765	0.4666	0.320791
20	-0.053688	-0.6145	0.269978
21	0.023045	0.2638	0.396187

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.128052 & 1.4656 & 0.072574 \tabularnewline
2 & -0.016675 & -0.1909 & 0.424466 \tabularnewline
3 & -0.118049 & -1.3511 & 0.08949 \tabularnewline
4 & 0.007551 & 0.0864 & 0.465628 \tabularnewline
5 & -0.031132 & -0.3563 & 0.361085 \tabularnewline
6 & -0.004037 & -0.0462 & 0.481609 \tabularnewline
7 & 0.073419 & 0.8403 & 0.201131 \tabularnewline
8 & 0.119348 & 1.366 & 0.087139 \tabularnewline
9 & 0.121035 & 1.3853 & 0.084156 \tabularnewline
10 & -0.02398 & -0.2745 & 0.39208 \tabularnewline
11 & -0.054428 & -0.623 & 0.267196 \tabularnewline
12 & -0.424372 & -4.8572 & 2e-06 \tabularnewline
13 & -0.016636 & -0.1904 & 0.424642 \tabularnewline
14 & -0.015574 & -0.1783 & 0.429401 \tabularnewline
15 & -0.042712 & -0.4889 & 0.312879 \tabularnewline
16 & 0.089967 & 1.0297 & 0.152518 \tabularnewline
17 & -0.045525 & -0.5211 & 0.301604 \tabularnewline
18 & 0.124424 & 1.4241 & 0.078397 \tabularnewline
19 & 0.040765 & 0.4666 & 0.320791 \tabularnewline
20 & -0.053688 & -0.6145 & 0.269978 \tabularnewline
21 & 0.023045 & 0.2638 & 0.396187 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=277812&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]0.128052[/C][C]1.4656[/C][C]0.072574[/C][/ROW]
[ROW][C]2[/C][C]-0.016675[/C][C]-0.1909[/C][C]0.424466[/C][/ROW]
[ROW][C]3[/C][C]-0.118049[/C][C]-1.3511[/C][C]0.08949[/C][/ROW]
[ROW][C]4[/C][C]0.007551[/C][C]0.0864[/C][C]0.465628[/C][/ROW]
[ROW][C]5[/C][C]-0.031132[/C][C]-0.3563[/C][C]0.361085[/C][/ROW]
[ROW][C]6[/C][C]-0.004037[/C][C]-0.0462[/C][C]0.481609[/C][/ROW]
[ROW][C]7[/C][C]0.073419[/C][C]0.8403[/C][C]0.201131[/C][/ROW]
[ROW][C]8[/C][C]0.119348[/C][C]1.366[/C][C]0.087139[/C][/ROW]
[ROW][C]9[/C][C]0.121035[/C][C]1.3853[/C][C]0.084156[/C][/ROW]
[ROW][C]10[/C][C]-0.02398[/C][C]-0.2745[/C][C]0.39208[/C][/ROW]
[ROW][C]11[/C][C]-0.054428[/C][C]-0.623[/C][C]0.267196[/C][/ROW]
[ROW][C]12[/C][C]-0.424372[/C][C]-4.8572[/C][C]2e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.016636[/C][C]-0.1904[/C][C]0.424642[/C][/ROW]
[ROW][C]14[/C][C]-0.015574[/C][C]-0.1783[/C][C]0.429401[/C][/ROW]
[ROW][C]15[/C][C]-0.042712[/C][C]-0.4889[/C][C]0.312879[/C][/ROW]
[ROW][C]16[/C][C]0.089967[/C][C]1.0297[/C][C]0.152518[/C][/ROW]
[ROW][C]17[/C][C]-0.045525[/C][C]-0.5211[/C][C]0.301604[/C][/ROW]
[ROW][C]18[/C][C]0.124424[/C][C]1.4241[/C][C]0.078397[/C][/ROW]
[ROW][C]19[/C][C]0.040765[/C][C]0.4666[/C][C]0.320791[/C][/ROW]
[ROW][C]20[/C][C]-0.053688[/C][C]-0.6145[/C][C]0.269978[/C][/ROW]
[ROW][C]21[/C][C]0.023045[/C][C]0.2638[/C][C]0.396187[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=277812&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=277812&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	0.128052	1.4656	0.072574
2	-0.016675	-0.1909	0.424466
3	-0.118049	-1.3511	0.08949
4	0.007551	0.0864	0.465628
5	-0.031132	-0.3563	0.361085
6	-0.004037	-0.0462	0.481609
7	0.073419	0.8403	0.201131
8	0.119348	1.366	0.087139
9	0.121035	1.3853	0.084156
10	-0.02398	-0.2745	0.39208
11	-0.054428	-0.623	0.267196
12	-0.424372	-4.8572	2e-06
13	-0.016636	-0.1904	0.424642
14	-0.015574	-0.1783	0.429401
15	-0.042712	-0.4889	0.312879
16	0.089967	1.0297	0.152518
17	-0.045525	-0.5211	0.301604
18	0.124424	1.4241	0.078397
19	0.040765	0.4666	0.320791
20	-0.053688	-0.6145	0.269978
21	0.023045	0.2638	0.396187

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)
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