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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 18 Dec 2014 16:09:23 +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/2014/Dec/18/t1418919100bq5z6rsflxmlxb3.htm/, Retrieved Fri, 17 May 2024 01:06:41 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=271109, Retrieved Fri, 17 May 2024 01:06:41 +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] [] [2014-12-18 16:09:23] [d043def4c969c6fe6dac6c6c71a7875a] [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	'Sir Maurice George Kendall' @ kendall.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 Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271109&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 Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271109&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271109&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 Maurice George Kendall' @ kendall.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.034502	-0.4512	0.326221
2	0.035935	0.4699	0.31951
3	0.075409	0.9861	0.162737
4	0.085465	1.1176	0.132652
5	0.091136	1.1918	0.117503
6	0.020446	0.2674	0.394753
7	-0.055629	-0.7274	0.233973
8	0.042266	0.5527	0.290596
9	0.012544	0.164	0.434951
10	-0.113858	-1.4889	0.069179
11	-0.008044	-0.1052	0.458172
12	-0.039124	-0.5116	0.30479
13	-0.05229	-0.6838	0.247518
14	-0.017017	-0.2225	0.412086
15	-0.104211	-1.3627	0.087379
16	-0.144192	-1.8855	0.030526
17	-0.021045	-0.2752	0.391746
18	0.022257	0.2911	0.385682
19	-0.103618	-1.355	0.088604
20	-0.017512	-0.229	0.40957
21	-0.055591	-0.727	0.234125
22	-0.058781	-0.7687	0.221578

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.034502 & -0.4512 & 0.326221 \tabularnewline
2 & 0.035935 & 0.4699 & 0.31951 \tabularnewline
3 & 0.075409 & 0.9861 & 0.162737 \tabularnewline
4 & 0.085465 & 1.1176 & 0.132652 \tabularnewline
5 & 0.091136 & 1.1918 & 0.117503 \tabularnewline
6 & 0.020446 & 0.2674 & 0.394753 \tabularnewline
7 & -0.055629 & -0.7274 & 0.233973 \tabularnewline
8 & 0.042266 & 0.5527 & 0.290596 \tabularnewline
9 & 0.012544 & 0.164 & 0.434951 \tabularnewline
10 & -0.113858 & -1.4889 & 0.069179 \tabularnewline
11 & -0.008044 & -0.1052 & 0.458172 \tabularnewline
12 & -0.039124 & -0.5116 & 0.30479 \tabularnewline
13 & -0.05229 & -0.6838 & 0.247518 \tabularnewline
14 & -0.017017 & -0.2225 & 0.412086 \tabularnewline
15 & -0.104211 & -1.3627 & 0.087379 \tabularnewline
16 & -0.144192 & -1.8855 & 0.030526 \tabularnewline
17 & -0.021045 & -0.2752 & 0.391746 \tabularnewline
18 & 0.022257 & 0.2911 & 0.385682 \tabularnewline
19 & -0.103618 & -1.355 & 0.088604 \tabularnewline
20 & -0.017512 & -0.229 & 0.40957 \tabularnewline
21 & -0.055591 & -0.727 & 0.234125 \tabularnewline
22 & -0.058781 & -0.7687 & 0.221578 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271109&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]-0.034502[/C][C]-0.4512[/C][C]0.326221[/C][/ROW]
[ROW][C]2[/C][C]0.035935[/C][C]0.4699[/C][C]0.31951[/C][/ROW]
[ROW][C]3[/C][C]0.075409[/C][C]0.9861[/C][C]0.162737[/C][/ROW]
[ROW][C]4[/C][C]0.085465[/C][C]1.1176[/C][C]0.132652[/C][/ROW]
[ROW][C]5[/C][C]0.091136[/C][C]1.1918[/C][C]0.117503[/C][/ROW]
[ROW][C]6[/C][C]0.020446[/C][C]0.2674[/C][C]0.394753[/C][/ROW]
[ROW][C]7[/C][C]-0.055629[/C][C]-0.7274[/C][C]0.233973[/C][/ROW]
[ROW][C]8[/C][C]0.042266[/C][C]0.5527[/C][C]0.290596[/C][/ROW]
[ROW][C]9[/C][C]0.012544[/C][C]0.164[/C][C]0.434951[/C][/ROW]
[ROW][C]10[/C][C]-0.113858[/C][C]-1.4889[/C][C]0.069179[/C][/ROW]
[ROW][C]11[/C][C]-0.008044[/C][C]-0.1052[/C][C]0.458172[/C][/ROW]
[ROW][C]12[/C][C]-0.039124[/C][C]-0.5116[/C][C]0.30479[/C][/ROW]
[ROW][C]13[/C][C]-0.05229[/C][C]-0.6838[/C][C]0.247518[/C][/ROW]
[ROW][C]14[/C][C]-0.017017[/C][C]-0.2225[/C][C]0.412086[/C][/ROW]
[ROW][C]15[/C][C]-0.104211[/C][C]-1.3627[/C][C]0.087379[/C][/ROW]
[ROW][C]16[/C][C]-0.144192[/C][C]-1.8855[/C][C]0.030526[/C][/ROW]
[ROW][C]17[/C][C]-0.021045[/C][C]-0.2752[/C][C]0.391746[/C][/ROW]
[ROW][C]18[/C][C]0.022257[/C][C]0.2911[/C][C]0.385682[/C][/ROW]
[ROW][C]19[/C][C]-0.103618[/C][C]-1.355[/C][C]0.088604[/C][/ROW]
[ROW][C]20[/C][C]-0.017512[/C][C]-0.229[/C][C]0.40957[/C][/ROW]
[ROW][C]21[/C][C]-0.055591[/C][C]-0.727[/C][C]0.234125[/C][/ROW]
[ROW][C]22[/C][C]-0.058781[/C][C]-0.7687[/C][C]0.221578[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271109&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271109&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	-0.034502	-0.4512	0.326221
2	0.035935	0.4699	0.31951
3	0.075409	0.9861	0.162737
4	0.085465	1.1176	0.132652
5	0.091136	1.1918	0.117503
6	0.020446	0.2674	0.394753
7	-0.055629	-0.7274	0.233973
8	0.042266	0.5527	0.290596
9	0.012544	0.164	0.434951
10	-0.113858	-1.4889	0.069179
11	-0.008044	-0.1052	0.458172
12	-0.039124	-0.5116	0.30479
13	-0.05229	-0.6838	0.247518
14	-0.017017	-0.2225	0.412086
15	-0.104211	-1.3627	0.087379
16	-0.144192	-1.8855	0.030526
17	-0.021045	-0.2752	0.391746
18	0.022257	0.2911	0.385682
19	-0.103618	-1.355	0.088604
20	-0.017512	-0.229	0.40957
21	-0.055591	-0.727	0.234125
22	-0.058781	-0.7687	0.221578

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.034502	-0.4512	0.326221
2	0.034786	0.4549	0.324885
3	0.077993	1.0199	0.154609
4	0.090293	1.1807	0.119674
5	0.094003	1.2293	0.110333
6	0.017294	0.2262	0.410677
7	-0.075164	-0.9829	0.163523
8	0.012603	0.1648	0.434647
9	-0.000242	-0.0032	0.498741
10	-0.120405	-1.5745	0.05861
11	-0.016658	-0.2178	0.413912
12	-0.028282	-0.3698	0.355982
13	-0.04354	-0.5694	0.284929
14	-0.002344	-0.0306	0.487794
15	-0.072047	-0.9421	0.173725
16	-0.13984	-1.8286	0.034597
17	-0.030591	-0.4	0.344819
18	0.061788	0.808	0.21011
19	-0.064912	-0.8488	0.198581
20	-0.000139	-0.0018	0.499278
21	-0.023639	-0.3091	0.378803
22	-0.072883	-0.9531	0.170952

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.034502 & -0.4512 & 0.326221 \tabularnewline
2 & 0.034786 & 0.4549 & 0.324885 \tabularnewline
3 & 0.077993 & 1.0199 & 0.154609 \tabularnewline
4 & 0.090293 & 1.1807 & 0.119674 \tabularnewline
5 & 0.094003 & 1.2293 & 0.110333 \tabularnewline
6 & 0.017294 & 0.2262 & 0.410677 \tabularnewline
7 & -0.075164 & -0.9829 & 0.163523 \tabularnewline
8 & 0.012603 & 0.1648 & 0.434647 \tabularnewline
9 & -0.000242 & -0.0032 & 0.498741 \tabularnewline
10 & -0.120405 & -1.5745 & 0.05861 \tabularnewline
11 & -0.016658 & -0.2178 & 0.413912 \tabularnewline
12 & -0.028282 & -0.3698 & 0.355982 \tabularnewline
13 & -0.04354 & -0.5694 & 0.284929 \tabularnewline
14 & -0.002344 & -0.0306 & 0.487794 \tabularnewline
15 & -0.072047 & -0.9421 & 0.173725 \tabularnewline
16 & -0.13984 & -1.8286 & 0.034597 \tabularnewline
17 & -0.030591 & -0.4 & 0.344819 \tabularnewline
18 & 0.061788 & 0.808 & 0.21011 \tabularnewline
19 & -0.064912 & -0.8488 & 0.198581 \tabularnewline
20 & -0.000139 & -0.0018 & 0.499278 \tabularnewline
21 & -0.023639 & -0.3091 & 0.378803 \tabularnewline
22 & -0.072883 & -0.9531 & 0.170952 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271109&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]-0.034502[/C][C]-0.4512[/C][C]0.326221[/C][/ROW]
[ROW][C]2[/C][C]0.034786[/C][C]0.4549[/C][C]0.324885[/C][/ROW]
[ROW][C]3[/C][C]0.077993[/C][C]1.0199[/C][C]0.154609[/C][/ROW]
[ROW][C]4[/C][C]0.090293[/C][C]1.1807[/C][C]0.119674[/C][/ROW]
[ROW][C]5[/C][C]0.094003[/C][C]1.2293[/C][C]0.110333[/C][/ROW]
[ROW][C]6[/C][C]0.017294[/C][C]0.2262[/C][C]0.410677[/C][/ROW]
[ROW][C]7[/C][C]-0.075164[/C][C]-0.9829[/C][C]0.163523[/C][/ROW]
[ROW][C]8[/C][C]0.012603[/C][C]0.1648[/C][C]0.434647[/C][/ROW]
[ROW][C]9[/C][C]-0.000242[/C][C]-0.0032[/C][C]0.498741[/C][/ROW]
[ROW][C]10[/C][C]-0.120405[/C][C]-1.5745[/C][C]0.05861[/C][/ROW]
[ROW][C]11[/C][C]-0.016658[/C][C]-0.2178[/C][C]0.413912[/C][/ROW]
[ROW][C]12[/C][C]-0.028282[/C][C]-0.3698[/C][C]0.355982[/C][/ROW]
[ROW][C]13[/C][C]-0.04354[/C][C]-0.5694[/C][C]0.284929[/C][/ROW]
[ROW][C]14[/C][C]-0.002344[/C][C]-0.0306[/C][C]0.487794[/C][/ROW]
[ROW][C]15[/C][C]-0.072047[/C][C]-0.9421[/C][C]0.173725[/C][/ROW]
[ROW][C]16[/C][C]-0.13984[/C][C]-1.8286[/C][C]0.034597[/C][/ROW]
[ROW][C]17[/C][C]-0.030591[/C][C]-0.4[/C][C]0.344819[/C][/ROW]
[ROW][C]18[/C][C]0.061788[/C][C]0.808[/C][C]0.21011[/C][/ROW]
[ROW][C]19[/C][C]-0.064912[/C][C]-0.8488[/C][C]0.198581[/C][/ROW]
[ROW][C]20[/C][C]-0.000139[/C][C]-0.0018[/C][C]0.499278[/C][/ROW]
[ROW][C]21[/C][C]-0.023639[/C][C]-0.3091[/C][C]0.378803[/C][/ROW]
[ROW][C]22[/C][C]-0.072883[/C][C]-0.9531[/C][C]0.170952[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271109&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271109&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	-0.034502	-0.4512	0.326221
2	0.034786	0.4549	0.324885
3	0.077993	1.0199	0.154609
4	0.090293	1.1807	0.119674
5	0.094003	1.2293	0.110333
6	0.017294	0.2262	0.410677
7	-0.075164	-0.9829	0.163523
8	0.012603	0.1648	0.434647
9	-0.000242	-0.0032	0.498741
10	-0.120405	-1.5745	0.05861
11	-0.016658	-0.2178	0.413912
12	-0.028282	-0.3698	0.355982
13	-0.04354	-0.5694	0.284929
14	-0.002344	-0.0306	0.487794
15	-0.072047	-0.9421	0.173725
16	-0.13984	-1.8286	0.034597
17	-0.030591	-0.4	0.344819
18	0.061788	0.808	0.21011
19	-0.064912	-0.8488	0.198581
20	-0.000139	-0.0018	0.499278
21	-0.023639	-0.3091	0.378803
22	-0.072883	-0.9531	0.170952

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 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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)
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