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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 04 Dec 2013 07:26:09 -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/Dec/04/t1386160010lipnumnu9gezqt6.htm/, Retrieved Tue, 23 Apr 2024 09:34:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=230568, Retrieved Tue, 23 Apr 2024 09:34:29 +0000

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Estimated Impact

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

-       [(Partial) Autocorrelation Function] [D=1] [2013-12-04 12:26:09] [b86744663ec671173a5f381479557f00] [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	4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230568&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]4 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=230568&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230568&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	4 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.025635	0.2785	0.390569
2	0.104823	1.1387	0.128574
3	-0.03484	-0.3785	0.352886
4	0.127868	1.389	0.083724
5	0.110524	1.2006	0.116156
6	0.009877	0.1073	0.457372
7	-0.028437	-0.3089	0.378969
8	-0.069653	-0.7566	0.22539
9	-0.193758	-2.1048	0.018717
10	0.013791	0.1498	0.440587
11	0.084074	0.9133	0.181479
12	-0.368643	-4.0045	5.5e-05
13	-0.017491	-0.19	0.424819
14	-0.144765	-1.5725	0.059251
15	0.036424	0.3957	0.346532
16	-0.030795	-0.3345	0.369289
17	0.014895	0.1618	0.43587
18	0.099285	1.0785	0.141503
19	-0.069038	-0.7499	0.227391
20	-0.039864	-0.433	0.332888
21	0.234027	2.5422	0.006156

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.025635 & 0.2785 & 0.390569 \tabularnewline
2 & 0.104823 & 1.1387 & 0.128574 \tabularnewline
3 & -0.03484 & -0.3785 & 0.352886 \tabularnewline
4 & 0.127868 & 1.389 & 0.083724 \tabularnewline
5 & 0.110524 & 1.2006 & 0.116156 \tabularnewline
6 & 0.009877 & 0.1073 & 0.457372 \tabularnewline
7 & -0.028437 & -0.3089 & 0.378969 \tabularnewline
8 & -0.069653 & -0.7566 & 0.22539 \tabularnewline
9 & -0.193758 & -2.1048 & 0.018717 \tabularnewline
10 & 0.013791 & 0.1498 & 0.440587 \tabularnewline
11 & 0.084074 & 0.9133 & 0.181479 \tabularnewline
12 & -0.368643 & -4.0045 & 5.5e-05 \tabularnewline
13 & -0.017491 & -0.19 & 0.424819 \tabularnewline
14 & -0.144765 & -1.5725 & 0.059251 \tabularnewline
15 & 0.036424 & 0.3957 & 0.346532 \tabularnewline
16 & -0.030795 & -0.3345 & 0.369289 \tabularnewline
17 & 0.014895 & 0.1618 & 0.43587 \tabularnewline
18 & 0.099285 & 1.0785 & 0.141503 \tabularnewline
19 & -0.069038 & -0.7499 & 0.227391 \tabularnewline
20 & -0.039864 & -0.433 & 0.332888 \tabularnewline
21 & 0.234027 & 2.5422 & 0.006156 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230568&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]0.025635[/C][C]0.2785[/C][C]0.390569[/C][/ROW]
[ROW][C]2[/C][C]0.104823[/C][C]1.1387[/C][C]0.128574[/C][/ROW]
[ROW][C]3[/C][C]-0.03484[/C][C]-0.3785[/C][C]0.352886[/C][/ROW]
[ROW][C]4[/C][C]0.127868[/C][C]1.389[/C][C]0.083724[/C][/ROW]
[ROW][C]5[/C][C]0.110524[/C][C]1.2006[/C][C]0.116156[/C][/ROW]
[ROW][C]6[/C][C]0.009877[/C][C]0.1073[/C][C]0.457372[/C][/ROW]
[ROW][C]7[/C][C]-0.028437[/C][C]-0.3089[/C][C]0.378969[/C][/ROW]
[ROW][C]8[/C][C]-0.069653[/C][C]-0.7566[/C][C]0.22539[/C][/ROW]
[ROW][C]9[/C][C]-0.193758[/C][C]-2.1048[/C][C]0.018717[/C][/ROW]
[ROW][C]10[/C][C]0.013791[/C][C]0.1498[/C][C]0.440587[/C][/ROW]
[ROW][C]11[/C][C]0.084074[/C][C]0.9133[/C][C]0.181479[/C][/ROW]
[ROW][C]12[/C][C]-0.368643[/C][C]-4.0045[/C][C]5.5e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.017491[/C][C]-0.19[/C][C]0.424819[/C][/ROW]
[ROW][C]14[/C][C]-0.144765[/C][C]-1.5725[/C][C]0.059251[/C][/ROW]
[ROW][C]15[/C][C]0.036424[/C][C]0.3957[/C][C]0.346532[/C][/ROW]
[ROW][C]16[/C][C]-0.030795[/C][C]-0.3345[/C][C]0.369289[/C][/ROW]
[ROW][C]17[/C][C]0.014895[/C][C]0.1618[/C][C]0.43587[/C][/ROW]
[ROW][C]18[/C][C]0.099285[/C][C]1.0785[/C][C]0.141503[/C][/ROW]
[ROW][C]19[/C][C]-0.069038[/C][C]-0.7499[/C][C]0.227391[/C][/ROW]
[ROW][C]20[/C][C]-0.039864[/C][C]-0.433[/C][C]0.332888[/C][/ROW]
[ROW][C]21[/C][C]0.234027[/C][C]2.5422[/C][C]0.006156[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230568&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230568&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	0.025635	0.2785	0.390569
2	0.104823	1.1387	0.128574
3	-0.03484	-0.3785	0.352886
4	0.127868	1.389	0.083724
5	0.110524	1.2006	0.116156
6	0.009877	0.1073	0.457372
7	-0.028437	-0.3089	0.378969
8	-0.069653	-0.7566	0.22539
9	-0.193758	-2.1048	0.018717
10	0.013791	0.1498	0.440587
11	0.084074	0.9133	0.181479
12	-0.368643	-4.0045	5.5e-05
13	-0.017491	-0.19	0.424819
14	-0.144765	-1.5725	0.059251
15	0.036424	0.3957	0.346532
16	-0.030795	-0.3345	0.369289
17	0.014895	0.1618	0.43587
18	0.099285	1.0785	0.141503
19	-0.069038	-0.7499	0.227391
20	-0.039864	-0.433	0.332888
21	0.234027	2.5422	0.006156

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.025635	0.2785	0.390569
2	0.104234	1.1323	0.129907
3	-0.040384	-0.4387	0.330847
4	0.120407	1.308	0.096715
5	0.114275	1.2413	0.108471
6	-0.022571	-0.2452	0.403369
7	-0.041608	-0.452	0.326056
8	-0.075151	-0.8164	0.207972
9	-0.22279	-2.4201	0.00852
10	0.019177	0.2083	0.41767
11	0.141098	1.5327	0.064011
12	-0.409314	-4.4463	1e-05
13	0.07694	0.8358	0.202484
14	-0.003335	-0.0362	0.48558
15	-0.094384	-1.0253	0.153665
16	0.094656	1.0282	0.152973
17	0.093159	1.012	0.156813
18	0.044048	0.4785	0.316596
19	-0.048412	-0.5259	0.299977
20	-0.045173	-0.4907	0.312273
21	0.112813	1.2255	0.11142

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.025635 & 0.2785 & 0.390569 \tabularnewline
2 & 0.104234 & 1.1323 & 0.129907 \tabularnewline
3 & -0.040384 & -0.4387 & 0.330847 \tabularnewline
4 & 0.120407 & 1.308 & 0.096715 \tabularnewline
5 & 0.114275 & 1.2413 & 0.108471 \tabularnewline
6 & -0.022571 & -0.2452 & 0.403369 \tabularnewline
7 & -0.041608 & -0.452 & 0.326056 \tabularnewline
8 & -0.075151 & -0.8164 & 0.207972 \tabularnewline
9 & -0.22279 & -2.4201 & 0.00852 \tabularnewline
10 & 0.019177 & 0.2083 & 0.41767 \tabularnewline
11 & 0.141098 & 1.5327 & 0.064011 \tabularnewline
12 & -0.409314 & -4.4463 & 1e-05 \tabularnewline
13 & 0.07694 & 0.8358 & 0.202484 \tabularnewline
14 & -0.003335 & -0.0362 & 0.48558 \tabularnewline
15 & -0.094384 & -1.0253 & 0.153665 \tabularnewline
16 & 0.094656 & 1.0282 & 0.152973 \tabularnewline
17 & 0.093159 & 1.012 & 0.156813 \tabularnewline
18 & 0.044048 & 0.4785 & 0.316596 \tabularnewline
19 & -0.048412 & -0.5259 & 0.299977 \tabularnewline
20 & -0.045173 & -0.4907 & 0.312273 \tabularnewline
21 & 0.112813 & 1.2255 & 0.11142 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230568&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]0.025635[/C][C]0.2785[/C][C]0.390569[/C][/ROW]
[ROW][C]2[/C][C]0.104234[/C][C]1.1323[/C][C]0.129907[/C][/ROW]
[ROW][C]3[/C][C]-0.040384[/C][C]-0.4387[/C][C]0.330847[/C][/ROW]
[ROW][C]4[/C][C]0.120407[/C][C]1.308[/C][C]0.096715[/C][/ROW]
[ROW][C]5[/C][C]0.114275[/C][C]1.2413[/C][C]0.108471[/C][/ROW]
[ROW][C]6[/C][C]-0.022571[/C][C]-0.2452[/C][C]0.403369[/C][/ROW]
[ROW][C]7[/C][C]-0.041608[/C][C]-0.452[/C][C]0.326056[/C][/ROW]
[ROW][C]8[/C][C]-0.075151[/C][C]-0.8164[/C][C]0.207972[/C][/ROW]
[ROW][C]9[/C][C]-0.22279[/C][C]-2.4201[/C][C]0.00852[/C][/ROW]
[ROW][C]10[/C][C]0.019177[/C][C]0.2083[/C][C]0.41767[/C][/ROW]
[ROW][C]11[/C][C]0.141098[/C][C]1.5327[/C][C]0.064011[/C][/ROW]
[ROW][C]12[/C][C]-0.409314[/C][C]-4.4463[/C][C]1e-05[/C][/ROW]
[ROW][C]13[/C][C]0.07694[/C][C]0.8358[/C][C]0.202484[/C][/ROW]
[ROW][C]14[/C][C]-0.003335[/C][C]-0.0362[/C][C]0.48558[/C][/ROW]
[ROW][C]15[/C][C]-0.094384[/C][C]-1.0253[/C][C]0.153665[/C][/ROW]
[ROW][C]16[/C][C]0.094656[/C][C]1.0282[/C][C]0.152973[/C][/ROW]
[ROW][C]17[/C][C]0.093159[/C][C]1.012[/C][C]0.156813[/C][/ROW]
[ROW][C]18[/C][C]0.044048[/C][C]0.4785[/C][C]0.316596[/C][/ROW]
[ROW][C]19[/C][C]-0.048412[/C][C]-0.5259[/C][C]0.299977[/C][/ROW]
[ROW][C]20[/C][C]-0.045173[/C][C]-0.4907[/C][C]0.312273[/C][/ROW]
[ROW][C]21[/C][C]0.112813[/C][C]1.2255[/C][C]0.11142[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230568&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230568&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	0.025635	0.2785	0.390569
2	0.104234	1.1323	0.129907
3	-0.040384	-0.4387	0.330847
4	0.120407	1.308	0.096715
5	0.114275	1.2413	0.108471
6	-0.022571	-0.2452	0.403369
7	-0.041608	-0.452	0.326056
8	-0.075151	-0.8164	0.207972
9	-0.22279	-2.4201	0.00852
10	0.019177	0.2083	0.41767
11	0.141098	1.5327	0.064011
12	-0.409314	-4.4463	1e-05
13	0.07694	0.8358	0.202484
14	-0.003335	-0.0362	0.48558
15	-0.094384	-1.0253	0.153665
16	0.094656	1.0282	0.152973
17	0.093159	1.012	0.156813
18	0.044048	0.4785	0.316596
19	-0.048412	-0.5259	0.299977
20	-0.045173	-0.4907	0.312273
21	0.112813	1.2255	0.11142

Figure 1

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Postscript link

PDF link

Figure 2

PNG link

Postscript link

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Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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