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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 05 Jul 2016 17:08:45 +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/Jul/05/t1467734997nkim966zxd2o0bh.htm/, Retrieved Fri, 03 May 2024 08:24:09 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=295809, Retrieved Fri, 03 May 2024 08:24:09 +0000

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Estimated Impact

139

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-       [(Partial) Autocorrelation Function] [Autocorrelatie Aa...] [2016-07-05 16:08:45] [fcb50c3fd850be3d4e9c7b78a2663ee0] [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	'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295809&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295809&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295809&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	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.136637	-1.42	0.079248
2	0.097712	1.0155	0.156079
3	-0.037896	-0.3938	0.347244
4	-0.144473	-1.5014	0.068084
5	0.14664	1.5239	0.065225
6	-0.328992	-3.419	0.000444
7	0.171499	1.7823	0.038758
8	-0.149133	-1.5498	0.062053
9	-0.028223	-0.2933	0.384927
10	0.118222	1.2286	0.110946
11	-0.01426	-0.1482	0.441235
12	0.451028	4.6872	4e-06
13	-0.140143	-1.4564	0.074091
14	0.117058	1.2165	0.113223
15	-0.04753	-0.4939	0.311174
16	-0.160857	-1.6717	0.048741
17	0.16595	1.7246	0.04373
18	-0.324264	-3.3698	0.000522
19	0.166623	1.7316	0.0431
20	-0.127176	-1.3217	0.094538

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.136637 & -1.42 & 0.079248 \tabularnewline
2 & 0.097712 & 1.0155 & 0.156079 \tabularnewline
3 & -0.037896 & -0.3938 & 0.347244 \tabularnewline
4 & -0.144473 & -1.5014 & 0.068084 \tabularnewline
5 & 0.14664 & 1.5239 & 0.065225 \tabularnewline
6 & -0.328992 & -3.419 & 0.000444 \tabularnewline
7 & 0.171499 & 1.7823 & 0.038758 \tabularnewline
8 & -0.149133 & -1.5498 & 0.062053 \tabularnewline
9 & -0.028223 & -0.2933 & 0.384927 \tabularnewline
10 & 0.118222 & 1.2286 & 0.110946 \tabularnewline
11 & -0.01426 & -0.1482 & 0.441235 \tabularnewline
12 & 0.451028 & 4.6872 & 4e-06 \tabularnewline
13 & -0.140143 & -1.4564 & 0.074091 \tabularnewline
14 & 0.117058 & 1.2165 & 0.113223 \tabularnewline
15 & -0.04753 & -0.4939 & 0.311174 \tabularnewline
16 & -0.160857 & -1.6717 & 0.048741 \tabularnewline
17 & 0.16595 & 1.7246 & 0.04373 \tabularnewline
18 & -0.324264 & -3.3698 & 0.000522 \tabularnewline
19 & 0.166623 & 1.7316 & 0.0431 \tabularnewline
20 & -0.127176 & -1.3217 & 0.094538 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295809&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]-0.136637[/C][C]-1.42[/C][C]0.079248[/C][/ROW]
[ROW][C]2[/C][C]0.097712[/C][C]1.0155[/C][C]0.156079[/C][/ROW]
[ROW][C]3[/C][C]-0.037896[/C][C]-0.3938[/C][C]0.347244[/C][/ROW]
[ROW][C]4[/C][C]-0.144473[/C][C]-1.5014[/C][C]0.068084[/C][/ROW]
[ROW][C]5[/C][C]0.14664[/C][C]1.5239[/C][C]0.065225[/C][/ROW]
[ROW][C]6[/C][C]-0.328992[/C][C]-3.419[/C][C]0.000444[/C][/ROW]
[ROW][C]7[/C][C]0.171499[/C][C]1.7823[/C][C]0.038758[/C][/ROW]
[ROW][C]8[/C][C]-0.149133[/C][C]-1.5498[/C][C]0.062053[/C][/ROW]
[ROW][C]9[/C][C]-0.028223[/C][C]-0.2933[/C][C]0.384927[/C][/ROW]
[ROW][C]10[/C][C]0.118222[/C][C]1.2286[/C][C]0.110946[/C][/ROW]
[ROW][C]11[/C][C]-0.01426[/C][C]-0.1482[/C][C]0.441235[/C][/ROW]
[ROW][C]12[/C][C]0.451028[/C][C]4.6872[/C][C]4e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.140143[/C][C]-1.4564[/C][C]0.074091[/C][/ROW]
[ROW][C]14[/C][C]0.117058[/C][C]1.2165[/C][C]0.113223[/C][/ROW]
[ROW][C]15[/C][C]-0.04753[/C][C]-0.4939[/C][C]0.311174[/C][/ROW]
[ROW][C]16[/C][C]-0.160857[/C][C]-1.6717[/C][C]0.048741[/C][/ROW]
[ROW][C]17[/C][C]0.16595[/C][C]1.7246[/C][C]0.04373[/C][/ROW]
[ROW][C]18[/C][C]-0.324264[/C][C]-3.3698[/C][C]0.000522[/C][/ROW]
[ROW][C]19[/C][C]0.166623[/C][C]1.7316[/C][C]0.0431[/C][/ROW]
[ROW][C]20[/C][C]-0.127176[/C][C]-1.3217[/C][C]0.094538[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295809&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295809&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	-0.136637	-1.42	0.079248
2	0.097712	1.0155	0.156079
3	-0.037896	-0.3938	0.347244
4	-0.144473	-1.5014	0.068084
5	0.14664	1.5239	0.065225
6	-0.328992	-3.419	0.000444
7	0.171499	1.7823	0.038758
8	-0.149133	-1.5498	0.062053
9	-0.028223	-0.2933	0.384927
10	0.118222	1.2286	0.110946
11	-0.01426	-0.1482	0.441235
12	0.451028	4.6872	4e-06
13	-0.140143	-1.4564	0.074091
14	0.117058	1.2165	0.113223
15	-0.04753	-0.4939	0.311174
16	-0.160857	-1.6717	0.048741
17	0.16595	1.7246	0.04373
18	-0.324264	-3.3698	0.000522
19	0.166623	1.7316	0.0431
20	-0.127176	-1.3217	0.094538

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.136637	-1.42	0.079248
2	0.080546	0.8371	0.202203
3	-0.01499	-0.1558	0.43825
4	-0.163041	-1.6944	0.046539
5	0.119038	1.2371	0.109371
6	-0.289119	-3.0046	0.001653
7	0.091522	0.9511	0.171834
8	-0.108948	-1.1322	0.130024
9	-0.063114	-0.6559	0.256642
10	0.052914	0.5499	0.291763
11	0.10106	1.0502	0.147974
12	0.357523	3.7155	0.000162
13	0.002217	0.023	0.490832
14	0.047747	0.4962	0.310381
15	-0.005778	-0.06	0.476116
16	-0.087674	-0.9111	0.182126
17	0.104739	1.0885	0.139403
18	-0.131857	-1.3703	0.086718
19	0.030023	0.312	0.377818
20	0.000275	0.0029	0.498864

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.136637 & -1.42 & 0.079248 \tabularnewline
2 & 0.080546 & 0.8371 & 0.202203 \tabularnewline
3 & -0.01499 & -0.1558 & 0.43825 \tabularnewline
4 & -0.163041 & -1.6944 & 0.046539 \tabularnewline
5 & 0.119038 & 1.2371 & 0.109371 \tabularnewline
6 & -0.289119 & -3.0046 & 0.001653 \tabularnewline
7 & 0.091522 & 0.9511 & 0.171834 \tabularnewline
8 & -0.108948 & -1.1322 & 0.130024 \tabularnewline
9 & -0.063114 & -0.6559 & 0.256642 \tabularnewline
10 & 0.052914 & 0.5499 & 0.291763 \tabularnewline
11 & 0.10106 & 1.0502 & 0.147974 \tabularnewline
12 & 0.357523 & 3.7155 & 0.000162 \tabularnewline
13 & 0.002217 & 0.023 & 0.490832 \tabularnewline
14 & 0.047747 & 0.4962 & 0.310381 \tabularnewline
15 & -0.005778 & -0.06 & 0.476116 \tabularnewline
16 & -0.087674 & -0.9111 & 0.182126 \tabularnewline
17 & 0.104739 & 1.0885 & 0.139403 \tabularnewline
18 & -0.131857 & -1.3703 & 0.086718 \tabularnewline
19 & 0.030023 & 0.312 & 0.377818 \tabularnewline
20 & 0.000275 & 0.0029 & 0.498864 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295809&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]-0.136637[/C][C]-1.42[/C][C]0.079248[/C][/ROW]
[ROW][C]2[/C][C]0.080546[/C][C]0.8371[/C][C]0.202203[/C][/ROW]
[ROW][C]3[/C][C]-0.01499[/C][C]-0.1558[/C][C]0.43825[/C][/ROW]
[ROW][C]4[/C][C]-0.163041[/C][C]-1.6944[/C][C]0.046539[/C][/ROW]
[ROW][C]5[/C][C]0.119038[/C][C]1.2371[/C][C]0.109371[/C][/ROW]
[ROW][C]6[/C][C]-0.289119[/C][C]-3.0046[/C][C]0.001653[/C][/ROW]
[ROW][C]7[/C][C]0.091522[/C][C]0.9511[/C][C]0.171834[/C][/ROW]
[ROW][C]8[/C][C]-0.108948[/C][C]-1.1322[/C][C]0.130024[/C][/ROW]
[ROW][C]9[/C][C]-0.063114[/C][C]-0.6559[/C][C]0.256642[/C][/ROW]
[ROW][C]10[/C][C]0.052914[/C][C]0.5499[/C][C]0.291763[/C][/ROW]
[ROW][C]11[/C][C]0.10106[/C][C]1.0502[/C][C]0.147974[/C][/ROW]
[ROW][C]12[/C][C]0.357523[/C][C]3.7155[/C][C]0.000162[/C][/ROW]
[ROW][C]13[/C][C]0.002217[/C][C]0.023[/C][C]0.490832[/C][/ROW]
[ROW][C]14[/C][C]0.047747[/C][C]0.4962[/C][C]0.310381[/C][/ROW]
[ROW][C]15[/C][C]-0.005778[/C][C]-0.06[/C][C]0.476116[/C][/ROW]
[ROW][C]16[/C][C]-0.087674[/C][C]-0.9111[/C][C]0.182126[/C][/ROW]
[ROW][C]17[/C][C]0.104739[/C][C]1.0885[/C][C]0.139403[/C][/ROW]
[ROW][C]18[/C][C]-0.131857[/C][C]-1.3703[/C][C]0.086718[/C][/ROW]
[ROW][C]19[/C][C]0.030023[/C][C]0.312[/C][C]0.377818[/C][/ROW]
[ROW][C]20[/C][C]0.000275[/C][C]0.0029[/C][C]0.498864[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295809&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295809&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	-0.136637	-1.42	0.079248
2	0.080546	0.8371	0.202203
3	-0.01499	-0.1558	0.43825
4	-0.163041	-1.6944	0.046539
5	0.119038	1.2371	0.109371
6	-0.289119	-3.0046	0.001653
7	0.091522	0.9511	0.171834
8	-0.108948	-1.1322	0.130024
9	-0.063114	-0.6559	0.256642
10	0.052914	0.5499	0.291763
11	0.10106	1.0502	0.147974
12	0.357523	3.7155	0.000162
13	0.002217	0.023	0.490832
14	0.047747	0.4962	0.310381
15	-0.005778	-0.06	0.476116
16	-0.087674	-0.9111	0.182126
17	0.104739	1.0885	0.139403
18	-0.131857	-1.3703	0.086718
19	0.030023	0.312	0.377818
20	0.000275	0.0029	0.498864

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 = 0 ; par2 = no ; par3 = 512 ;

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)
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