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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 01 Dec 2011 15:01:46 -0500

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/2011/Dec/01/t1322769845a716vbusw6d3na8.htm/, Retrieved Tue, 23 Apr 2024 09:31:24 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=149982, Retrieved Tue, 23 Apr 2024 09:31:24 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

151

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

-     [(Partial) Autocorrelation Function] [] [2011-12-01 19:58:02] [ee8c3a74bf3b349877806e9a50913c60]
- R P     [(Partial) Autocorrelation Function] [] [2011-12-01 20:01:46] [7dc03dd48c8acabd98b217fada4a6bc0] [Current]
-   P       [(Partial) Autocorrelation Function] [] [2011-12-01 20:04:38] [ee8c3a74bf3b349877806e9a50913c60] 
- RMP       [Spectral Analysis] [] [2011-12-01 20:13:31] [ee8c3a74bf3b349877806e9a50913c60] 
-   PD        [Spectral Analysis] [] [2011-12-01 21:22:24] [ee8c3a74bf3b349877806e9a50913c60] 
- RMP         [Standard Deviation-Mean Plot] [] [2011-12-01 21:39:37] [ee8c3a74bf3b349877806e9a50913c60] 
- R P         [Spectral Analysis] [verbetering] [2011-12-12 18:17:40] [25b6caf3839c2bdc14961e5bff2d6373] 

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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	'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=149982&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=149982&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=149982&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	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.132009	-1.5109	0.06661
2	-0.018061	-0.2067	0.418277
3	-0.088301	-1.0107	0.157023
4	0.17874	2.0458	0.02139
5	0.061772	0.707	0.240406
6	-0.376378	-4.3078	1.6e-05
7	0.054912	0.6285	0.265386
8	0.191681	2.1939	0.015003
9	-0.095812	-1.0966	0.137411
10	-0.057023	-0.6527	0.257561
11	-0.080566	-0.9221	0.179081
12	0.699421	8.0052	0
13	-0.093669	-1.0721	0.142824
14	-0.070188	-0.8033	0.211618
15	-0.125374	-1.435	0.076839
16	0.110305	1.2625	0.104506
17	0.040008	0.4579	0.323885
18	-0.409232	-4.6839	3e-06
19	0.027687	0.3169	0.375914
20	0.166236	1.9027	0.02964
21	-0.155519	-1.78	0.038697

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.132009 & -1.5109 & 0.06661 \tabularnewline
2 & -0.018061 & -0.2067 & 0.418277 \tabularnewline
3 & -0.088301 & -1.0107 & 0.157023 \tabularnewline
4 & 0.17874 & 2.0458 & 0.02139 \tabularnewline
5 & 0.061772 & 0.707 & 0.240406 \tabularnewline
6 & -0.376378 & -4.3078 & 1.6e-05 \tabularnewline
7 & 0.054912 & 0.6285 & 0.265386 \tabularnewline
8 & 0.191681 & 2.1939 & 0.015003 \tabularnewline
9 & -0.095812 & -1.0966 & 0.137411 \tabularnewline
10 & -0.057023 & -0.6527 & 0.257561 \tabularnewline
11 & -0.080566 & -0.9221 & 0.179081 \tabularnewline
12 & 0.699421 & 8.0052 & 0 \tabularnewline
13 & -0.093669 & -1.0721 & 0.142824 \tabularnewline
14 & -0.070188 & -0.8033 & 0.211618 \tabularnewline
15 & -0.125374 & -1.435 & 0.076839 \tabularnewline
16 & 0.110305 & 1.2625 & 0.104506 \tabularnewline
17 & 0.040008 & 0.4579 & 0.323885 \tabularnewline
18 & -0.409232 & -4.6839 & 3e-06 \tabularnewline
19 & 0.027687 & 0.3169 & 0.375914 \tabularnewline
20 & 0.166236 & 1.9027 & 0.02964 \tabularnewline
21 & -0.155519 & -1.78 & 0.038697 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=149982&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]-0.132009[/C][C]-1.5109[/C][C]0.06661[/C][/ROW]
[ROW][C]2[/C][C]-0.018061[/C][C]-0.2067[/C][C]0.418277[/C][/ROW]
[ROW][C]3[/C][C]-0.088301[/C][C]-1.0107[/C][C]0.157023[/C][/ROW]
[ROW][C]4[/C][C]0.17874[/C][C]2.0458[/C][C]0.02139[/C][/ROW]
[ROW][C]5[/C][C]0.061772[/C][C]0.707[/C][C]0.240406[/C][/ROW]
[ROW][C]6[/C][C]-0.376378[/C][C]-4.3078[/C][C]1.6e-05[/C][/ROW]
[ROW][C]7[/C][C]0.054912[/C][C]0.6285[/C][C]0.265386[/C][/ROW]
[ROW][C]8[/C][C]0.191681[/C][C]2.1939[/C][C]0.015003[/C][/ROW]
[ROW][C]9[/C][C]-0.095812[/C][C]-1.0966[/C][C]0.137411[/C][/ROW]
[ROW][C]10[/C][C]-0.057023[/C][C]-0.6527[/C][C]0.257561[/C][/ROW]
[ROW][C]11[/C][C]-0.080566[/C][C]-0.9221[/C][C]0.179081[/C][/ROW]
[ROW][C]12[/C][C]0.699421[/C][C]8.0052[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.093669[/C][C]-1.0721[/C][C]0.142824[/C][/ROW]
[ROW][C]14[/C][C]-0.070188[/C][C]-0.8033[/C][C]0.211618[/C][/ROW]
[ROW][C]15[/C][C]-0.125374[/C][C]-1.435[/C][C]0.076839[/C][/ROW]
[ROW][C]16[/C][C]0.110305[/C][C]1.2625[/C][C]0.104506[/C][/ROW]
[ROW][C]17[/C][C]0.040008[/C][C]0.4579[/C][C]0.323885[/C][/ROW]
[ROW][C]18[/C][C]-0.409232[/C][C]-4.6839[/C][C]3e-06[/C][/ROW]
[ROW][C]19[/C][C]0.027687[/C][C]0.3169[/C][C]0.375914[/C][/ROW]
[ROW][C]20[/C][C]0.166236[/C][C]1.9027[/C][C]0.02964[/C][/ROW]
[ROW][C]21[/C][C]-0.155519[/C][C]-1.78[/C][C]0.038697[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=149982&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=149982&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	-0.132009	-1.5109	0.06661
2	-0.018061	-0.2067	0.418277
3	-0.088301	-1.0107	0.157023
4	0.17874	2.0458	0.02139
5	0.061772	0.707	0.240406
6	-0.376378	-4.3078	1.6e-05
7	0.054912	0.6285	0.265386
8	0.191681	2.1939	0.015003
9	-0.095812	-1.0966	0.137411
10	-0.057023	-0.6527	0.257561
11	-0.080566	-0.9221	0.179081
12	0.699421	8.0052	0
13	-0.093669	-1.0721	0.142824
14	-0.070188	-0.8033	0.211618
15	-0.125374	-1.435	0.076839
16	0.110305	1.2625	0.104506
17	0.040008	0.4579	0.323885
18	-0.409232	-4.6839	3e-06
19	0.027687	0.3169	0.375914
20	0.166236	1.9027	0.02964
21	-0.155519	-1.78	0.038697

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.132009	-1.5109	0.06661
2	-0.036116	-0.4134	0.340005
3	-0.09736	-1.1143	0.133587
4	0.157005	1.797	0.03732
5	0.105273	1.2049	0.115207
6	-0.374282	-4.2839	1.8e-05
7	-0.003107	-0.0356	0.485845
8	0.228269	2.6127	0.005017
9	-0.193032	-2.2094	0.014444
10	0.031967	0.3659	0.357522
11	0.03448	0.3946	0.346877
12	0.603027	6.902	0
13	0.070345	0.8051	0.211099
14	-0.069863	-0.7996	0.212689
15	-0.165733	-1.8969	0.030022
16	-0.149046	-1.7059	0.045197
17	-0.00066	-0.0076	0.496992
18	-0.139053	-1.5915	0.05695
19	-0.07137	-0.8169	0.207744
20	0.031861	0.3647	0.357976
21	-0.182556	-2.0894	0.019301

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.132009 & -1.5109 & 0.06661 \tabularnewline
2 & -0.036116 & -0.4134 & 0.340005 \tabularnewline
3 & -0.09736 & -1.1143 & 0.133587 \tabularnewline
4 & 0.157005 & 1.797 & 0.03732 \tabularnewline
5 & 0.105273 & 1.2049 & 0.115207 \tabularnewline
6 & -0.374282 & -4.2839 & 1.8e-05 \tabularnewline
7 & -0.003107 & -0.0356 & 0.485845 \tabularnewline
8 & 0.228269 & 2.6127 & 0.005017 \tabularnewline
9 & -0.193032 & -2.2094 & 0.014444 \tabularnewline
10 & 0.031967 & 0.3659 & 0.357522 \tabularnewline
11 & 0.03448 & 0.3946 & 0.346877 \tabularnewline
12 & 0.603027 & 6.902 & 0 \tabularnewline
13 & 0.070345 & 0.8051 & 0.211099 \tabularnewline
14 & -0.069863 & -0.7996 & 0.212689 \tabularnewline
15 & -0.165733 & -1.8969 & 0.030022 \tabularnewline
16 & -0.149046 & -1.7059 & 0.045197 \tabularnewline
17 & -0.00066 & -0.0076 & 0.496992 \tabularnewline
18 & -0.139053 & -1.5915 & 0.05695 \tabularnewline
19 & -0.07137 & -0.8169 & 0.207744 \tabularnewline
20 & 0.031861 & 0.3647 & 0.357976 \tabularnewline
21 & -0.182556 & -2.0894 & 0.019301 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=149982&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]-0.132009[/C][C]-1.5109[/C][C]0.06661[/C][/ROW]
[ROW][C]2[/C][C]-0.036116[/C][C]-0.4134[/C][C]0.340005[/C][/ROW]
[ROW][C]3[/C][C]-0.09736[/C][C]-1.1143[/C][C]0.133587[/C][/ROW]
[ROW][C]4[/C][C]0.157005[/C][C]1.797[/C][C]0.03732[/C][/ROW]
[ROW][C]5[/C][C]0.105273[/C][C]1.2049[/C][C]0.115207[/C][/ROW]
[ROW][C]6[/C][C]-0.374282[/C][C]-4.2839[/C][C]1.8e-05[/C][/ROW]
[ROW][C]7[/C][C]-0.003107[/C][C]-0.0356[/C][C]0.485845[/C][/ROW]
[ROW][C]8[/C][C]0.228269[/C][C]2.6127[/C][C]0.005017[/C][/ROW]
[ROW][C]9[/C][C]-0.193032[/C][C]-2.2094[/C][C]0.014444[/C][/ROW]
[ROW][C]10[/C][C]0.031967[/C][C]0.3659[/C][C]0.357522[/C][/ROW]
[ROW][C]11[/C][C]0.03448[/C][C]0.3946[/C][C]0.346877[/C][/ROW]
[ROW][C]12[/C][C]0.603027[/C][C]6.902[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.070345[/C][C]0.8051[/C][C]0.211099[/C][/ROW]
[ROW][C]14[/C][C]-0.069863[/C][C]-0.7996[/C][C]0.212689[/C][/ROW]
[ROW][C]15[/C][C]-0.165733[/C][C]-1.8969[/C][C]0.030022[/C][/ROW]
[ROW][C]16[/C][C]-0.149046[/C][C]-1.7059[/C][C]0.045197[/C][/ROW]
[ROW][C]17[/C][C]-0.00066[/C][C]-0.0076[/C][C]0.496992[/C][/ROW]
[ROW][C]18[/C][C]-0.139053[/C][C]-1.5915[/C][C]0.05695[/C][/ROW]
[ROW][C]19[/C][C]-0.07137[/C][C]-0.8169[/C][C]0.207744[/C][/ROW]
[ROW][C]20[/C][C]0.031861[/C][C]0.3647[/C][C]0.357976[/C][/ROW]
[ROW][C]21[/C][C]-0.182556[/C][C]-2.0894[/C][C]0.019301[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=149982&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=149982&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	-0.132009	-1.5109	0.06661
2	-0.036116	-0.4134	0.340005
3	-0.09736	-1.1143	0.133587
4	0.157005	1.797	0.03732
5	0.105273	1.2049	0.115207
6	-0.374282	-4.2839	1.8e-05
7	-0.003107	-0.0356	0.485845
8	0.228269	2.6127	0.005017
9	-0.193032	-2.2094	0.014444
10	0.031967	0.3659	0.357522
11	0.03448	0.3946	0.346877
12	0.603027	6.902	0
13	0.070345	0.8051	0.211099
14	-0.069863	-0.7996	0.212689
15	-0.165733	-1.8969	0.030022
16	-0.149046	-1.7059	0.045197
17	-0.00066	-0.0076	0.496992
18	-0.139053	-1.5915	0.05695
19	-0.07137	-0.8169	0.207744
20	0.031861	0.3647	0.357976
21	-0.182556	-2.0894	0.019301

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