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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

Wed, 13 Nov 2013 07:17:19 -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/2013/Nov/13/t1384345381f2evovv7ypub7mo.htm/, Retrieved Mon, 29 Apr 2024 06:52:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=224692, Retrieved Mon, 29 Apr 2024 06:52:47 +0000

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Paste this QR Code to cite your computation.

Original text written by user:

Howard Van den Branden

IsPrivate?

No (this computation is public)

User-defined keywords

Howard Van den Branden

Estimated Impact

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

-       [(Partial) Autocorrelation Function] [WS8: Autocorrelat...] [2013-11-13 12:17:19] [c48df00dfd28bb130a7db97d228aa375] [Current]

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Dataseries X:

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Boxplots

6,02
5,62
4,87
4,24
4,02
3,74
3,45
3,34
3,21
3,12
3,04
2,97
2,93
2,95
2,92
2,9
2,95
2,91
2,89
2,84
2,82
2,78
2,86
2,87
2,94
3,04
3,12
3,19
3,27
3,34
3,4
3,55
3,64
3,76
3,78
3,77
3,81
3,81
3,82
3,96
3,86
3,84
3,68
3,56
3,48
3,4
3,42
3,2
3,11
3,1
2,99
3,1
3
3,05
3,1
3,2
3,1
3,3
3,13
3,14

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	'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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=224692&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=224692&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=224692&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	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.805198	6.237	0
2	0.605452	4.6898	8e-06
3	0.453697	3.5143	0.000423
4	0.343424	2.6602	0.005002
5	0.235315	1.8227	0.036663
6	0.140488	1.0882	0.140426
7	0.064068	0.4963	0.310758
8	-0.009102	-0.0705	0.472015
9	-0.073454	-0.569	0.28575
10	-0.132819	-1.0288	0.15385
11	-0.181441	-1.4054	0.082524
12	-0.220793	-1.7103	0.046193
13	-0.252972	-1.9595	0.027352
14	-0.282298	-2.1867	0.016339
15	-0.305079	-2.3631	0.01069
16	-0.322192	-2.4957	0.007669
17	-0.343108	-2.6577	0.005034

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.805198 & 6.237 & 0 \tabularnewline
2 & 0.605452 & 4.6898 & 8e-06 \tabularnewline
3 & 0.453697 & 3.5143 & 0.000423 \tabularnewline
4 & 0.343424 & 2.6602 & 0.005002 \tabularnewline
5 & 0.235315 & 1.8227 & 0.036663 \tabularnewline
6 & 0.140488 & 1.0882 & 0.140426 \tabularnewline
7 & 0.064068 & 0.4963 & 0.310758 \tabularnewline
8 & -0.009102 & -0.0705 & 0.472015 \tabularnewline
9 & -0.073454 & -0.569 & 0.28575 \tabularnewline
10 & -0.132819 & -1.0288 & 0.15385 \tabularnewline
11 & -0.181441 & -1.4054 & 0.082524 \tabularnewline
12 & -0.220793 & -1.7103 & 0.046193 \tabularnewline
13 & -0.252972 & -1.9595 & 0.027352 \tabularnewline
14 & -0.282298 & -2.1867 & 0.016339 \tabularnewline
15 & -0.305079 & -2.3631 & 0.01069 \tabularnewline
16 & -0.322192 & -2.4957 & 0.007669 \tabularnewline
17 & -0.343108 & -2.6577 & 0.005034 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=224692&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]0.805198[/C][C]6.237[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.605452[/C][C]4.6898[/C][C]8e-06[/C][/ROW]
[ROW][C]3[/C][C]0.453697[/C][C]3.5143[/C][C]0.000423[/C][/ROW]
[ROW][C]4[/C][C]0.343424[/C][C]2.6602[/C][C]0.005002[/C][/ROW]
[ROW][C]5[/C][C]0.235315[/C][C]1.8227[/C][C]0.036663[/C][/ROW]
[ROW][C]6[/C][C]0.140488[/C][C]1.0882[/C][C]0.140426[/C][/ROW]
[ROW][C]7[/C][C]0.064068[/C][C]0.4963[/C][C]0.310758[/C][/ROW]
[ROW][C]8[/C][C]-0.009102[/C][C]-0.0705[/C][C]0.472015[/C][/ROW]
[ROW][C]9[/C][C]-0.073454[/C][C]-0.569[/C][C]0.28575[/C][/ROW]
[ROW][C]10[/C][C]-0.132819[/C][C]-1.0288[/C][C]0.15385[/C][/ROW]
[ROW][C]11[/C][C]-0.181441[/C][C]-1.4054[/C][C]0.082524[/C][/ROW]
[ROW][C]12[/C][C]-0.220793[/C][C]-1.7103[/C][C]0.046193[/C][/ROW]
[ROW][C]13[/C][C]-0.252972[/C][C]-1.9595[/C][C]0.027352[/C][/ROW]
[ROW][C]14[/C][C]-0.282298[/C][C]-2.1867[/C][C]0.016339[/C][/ROW]
[ROW][C]15[/C][C]-0.305079[/C][C]-2.3631[/C][C]0.01069[/C][/ROW]
[ROW][C]16[/C][C]-0.322192[/C][C]-2.4957[/C][C]0.007669[/C][/ROW]
[ROW][C]17[/C][C]-0.343108[/C][C]-2.6577[/C][C]0.005034[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=224692&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=224692&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	0.805198	6.237	0
2	0.605452	4.6898	8e-06
3	0.453697	3.5143	0.000423
4	0.343424	2.6602	0.005002
5	0.235315	1.8227	0.036663
6	0.140488	1.0882	0.140426
7	0.064068	0.4963	0.310758
8	-0.009102	-0.0705	0.472015
9	-0.073454	-0.569	0.28575
10	-0.132819	-1.0288	0.15385
11	-0.181441	-1.4054	0.082524
12	-0.220793	-1.7103	0.046193
13	-0.252972	-1.9595	0.027352
14	-0.282298	-2.1867	0.016339
15	-0.305079	-2.3631	0.01069
16	-0.322192	-2.4957	0.007669
17	-0.343108	-2.6577	0.005034

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.805198	6.237	0
2	-0.121971	-0.9448	0.174279
3	0.014251	0.1104	0.456235
4	0.008456	0.0655	0.473996
5	-0.074016	-0.5733	0.284283
6	-0.033267	-0.2577	0.398765
7	-0.028339	-0.2195	0.413498
8	-0.06789	-0.5259	0.300457
9	-0.044665	-0.346	0.365287
10	-0.062714	-0.4858	0.314447
11	-0.049916	-0.3866	0.350192
12	-0.050426	-0.3906	0.34874
13	-0.055534	-0.4302	0.33431
14	-0.06565	-0.5085	0.306475
15	-0.057613	-0.4463	0.328504
16	-0.064003	-0.4958	0.310936
17	-0.091561	-0.7092	0.240465

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.805198 & 6.237 & 0 \tabularnewline
2 & -0.121971 & -0.9448 & 0.174279 \tabularnewline
3 & 0.014251 & 0.1104 & 0.456235 \tabularnewline
4 & 0.008456 & 0.0655 & 0.473996 \tabularnewline
5 & -0.074016 & -0.5733 & 0.284283 \tabularnewline
6 & -0.033267 & -0.2577 & 0.398765 \tabularnewline
7 & -0.028339 & -0.2195 & 0.413498 \tabularnewline
8 & -0.06789 & -0.5259 & 0.300457 \tabularnewline
9 & -0.044665 & -0.346 & 0.365287 \tabularnewline
10 & -0.062714 & -0.4858 & 0.314447 \tabularnewline
11 & -0.049916 & -0.3866 & 0.350192 \tabularnewline
12 & -0.050426 & -0.3906 & 0.34874 \tabularnewline
13 & -0.055534 & -0.4302 & 0.33431 \tabularnewline
14 & -0.06565 & -0.5085 & 0.306475 \tabularnewline
15 & -0.057613 & -0.4463 & 0.328504 \tabularnewline
16 & -0.064003 & -0.4958 & 0.310936 \tabularnewline
17 & -0.091561 & -0.7092 & 0.240465 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=224692&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]0.805198[/C][C]6.237[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.121971[/C][C]-0.9448[/C][C]0.174279[/C][/ROW]
[ROW][C]3[/C][C]0.014251[/C][C]0.1104[/C][C]0.456235[/C][/ROW]
[ROW][C]4[/C][C]0.008456[/C][C]0.0655[/C][C]0.473996[/C][/ROW]
[ROW][C]5[/C][C]-0.074016[/C][C]-0.5733[/C][C]0.284283[/C][/ROW]
[ROW][C]6[/C][C]-0.033267[/C][C]-0.2577[/C][C]0.398765[/C][/ROW]
[ROW][C]7[/C][C]-0.028339[/C][C]-0.2195[/C][C]0.413498[/C][/ROW]
[ROW][C]8[/C][C]-0.06789[/C][C]-0.5259[/C][C]0.300457[/C][/ROW]
[ROW][C]9[/C][C]-0.044665[/C][C]-0.346[/C][C]0.365287[/C][/ROW]
[ROW][C]10[/C][C]-0.062714[/C][C]-0.4858[/C][C]0.314447[/C][/ROW]
[ROW][C]11[/C][C]-0.049916[/C][C]-0.3866[/C][C]0.350192[/C][/ROW]
[ROW][C]12[/C][C]-0.050426[/C][C]-0.3906[/C][C]0.34874[/C][/ROW]
[ROW][C]13[/C][C]-0.055534[/C][C]-0.4302[/C][C]0.33431[/C][/ROW]
[ROW][C]14[/C][C]-0.06565[/C][C]-0.5085[/C][C]0.306475[/C][/ROW]
[ROW][C]15[/C][C]-0.057613[/C][C]-0.4463[/C][C]0.328504[/C][/ROW]
[ROW][C]16[/C][C]-0.064003[/C][C]-0.4958[/C][C]0.310936[/C][/ROW]
[ROW][C]17[/C][C]-0.091561[/C][C]-0.7092[/C][C]0.240465[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=224692&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=224692&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	0.805198	6.237	0
2	-0.121971	-0.9448	0.174279
3	0.014251	0.1104	0.456235
4	0.008456	0.0655	0.473996
5	-0.074016	-0.5733	0.284283
6	-0.033267	-0.2577	0.398765
7	-0.028339	-0.2195	0.413498
8	-0.06789	-0.5259	0.300457
9	-0.044665	-0.346	0.365287
10	-0.062714	-0.4858	0.314447
11	-0.049916	-0.3866	0.350192
12	-0.050426	-0.3906	0.34874
13	-0.055534	-0.4302	0.33431
14	-0.06565	-0.5085	0.306475
15	-0.057613	-0.4463	0.328504
16	-0.064003	-0.4958	0.310936
17	-0.091561	-0.7092	0.240465

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):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '0'
par2 <- '1'
par1 <- 'Default'
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