Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

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

Tue, 28 Dec 2010 19:10:02 +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/2010/Dec/28/t1293563322wzxba0g5an7f2xu.htm/, Retrieved Sun, 05 May 2024 02:37:46 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116499, Retrieved Sun, 05 May 2024 02:37:46 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

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

-       [(Partial) Autocorrelation Function] [] [2010-12-28 19:10:02] [0956ee981dded61b2e7128dae94e5715] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

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	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116499&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116499&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116499&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.079452	-1.1704	0.121561
2	-0.203949	-3.0044	0.001487
3	-0.04857	-0.7155	0.23754
4	-0.145996	-2.1507	0.016304
5	0.101543	1.4958	0.068076
6	-0.054226	-0.7988	0.212642
7	-0.019461	-0.2867	0.387314
8	0.025033	0.3688	0.356335
9	-0.045746	-0.6739	0.25055
10	0.079381	1.1693	0.121773
11	0.039296	0.5789	0.281641
12	-0.05824	-0.8579	0.195939
13	0.001638	0.0241	0.490388
14	-0.049832	-0.7341	0.231847
15	-0.010996	-0.162	0.435736
16	0.052731	0.7768	0.21907
17	0.030992	0.4565	0.324227
18	0.031305	0.4612	0.322575
19	-0.00604	-0.089	0.464594
20	-0.062768	-0.9246	0.178094
21	-0.037077	-0.5462	0.292752
22	-0.068187	-1.0045	0.158138
23	0.078445	1.1556	0.124564

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.079452 & -1.1704 & 0.121561 \tabularnewline
2 & -0.203949 & -3.0044 & 0.001487 \tabularnewline
3 & -0.04857 & -0.7155 & 0.23754 \tabularnewline
4 & -0.145996 & -2.1507 & 0.016304 \tabularnewline
5 & 0.101543 & 1.4958 & 0.068076 \tabularnewline
6 & -0.054226 & -0.7988 & 0.212642 \tabularnewline
7 & -0.019461 & -0.2867 & 0.387314 \tabularnewline
8 & 0.025033 & 0.3688 & 0.356335 \tabularnewline
9 & -0.045746 & -0.6739 & 0.25055 \tabularnewline
10 & 0.079381 & 1.1693 & 0.121773 \tabularnewline
11 & 0.039296 & 0.5789 & 0.281641 \tabularnewline
12 & -0.05824 & -0.8579 & 0.195939 \tabularnewline
13 & 0.001638 & 0.0241 & 0.490388 \tabularnewline
14 & -0.049832 & -0.7341 & 0.231847 \tabularnewline
15 & -0.010996 & -0.162 & 0.435736 \tabularnewline
16 & 0.052731 & 0.7768 & 0.21907 \tabularnewline
17 & 0.030992 & 0.4565 & 0.324227 \tabularnewline
18 & 0.031305 & 0.4612 & 0.322575 \tabularnewline
19 & -0.00604 & -0.089 & 0.464594 \tabularnewline
20 & -0.062768 & -0.9246 & 0.178094 \tabularnewline
21 & -0.037077 & -0.5462 & 0.292752 \tabularnewline
22 & -0.068187 & -1.0045 & 0.158138 \tabularnewline
23 & 0.078445 & 1.1556 & 0.124564 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116499&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]-0.079452[/C][C]-1.1704[/C][C]0.121561[/C][/ROW]
[ROW][C]2[/C][C]-0.203949[/C][C]-3.0044[/C][C]0.001487[/C][/ROW]
[ROW][C]3[/C][C]-0.04857[/C][C]-0.7155[/C][C]0.23754[/C][/ROW]
[ROW][C]4[/C][C]-0.145996[/C][C]-2.1507[/C][C]0.016304[/C][/ROW]
[ROW][C]5[/C][C]0.101543[/C][C]1.4958[/C][C]0.068076[/C][/ROW]
[ROW][C]6[/C][C]-0.054226[/C][C]-0.7988[/C][C]0.212642[/C][/ROW]
[ROW][C]7[/C][C]-0.019461[/C][C]-0.2867[/C][C]0.387314[/C][/ROW]
[ROW][C]8[/C][C]0.025033[/C][C]0.3688[/C][C]0.356335[/C][/ROW]
[ROW][C]9[/C][C]-0.045746[/C][C]-0.6739[/C][C]0.25055[/C][/ROW]
[ROW][C]10[/C][C]0.079381[/C][C]1.1693[/C][C]0.121773[/C][/ROW]
[ROW][C]11[/C][C]0.039296[/C][C]0.5789[/C][C]0.281641[/C][/ROW]
[ROW][C]12[/C][C]-0.05824[/C][C]-0.8579[/C][C]0.195939[/C][/ROW]
[ROW][C]13[/C][C]0.001638[/C][C]0.0241[/C][C]0.490388[/C][/ROW]
[ROW][C]14[/C][C]-0.049832[/C][C]-0.7341[/C][C]0.231847[/C][/ROW]
[ROW][C]15[/C][C]-0.010996[/C][C]-0.162[/C][C]0.435736[/C][/ROW]
[ROW][C]16[/C][C]0.052731[/C][C]0.7768[/C][C]0.21907[/C][/ROW]
[ROW][C]17[/C][C]0.030992[/C][C]0.4565[/C][C]0.324227[/C][/ROW]
[ROW][C]18[/C][C]0.031305[/C][C]0.4612[/C][C]0.322575[/C][/ROW]
[ROW][C]19[/C][C]-0.00604[/C][C]-0.089[/C][C]0.464594[/C][/ROW]
[ROW][C]20[/C][C]-0.062768[/C][C]-0.9246[/C][C]0.178094[/C][/ROW]
[ROW][C]21[/C][C]-0.037077[/C][C]-0.5462[/C][C]0.292752[/C][/ROW]
[ROW][C]22[/C][C]-0.068187[/C][C]-1.0045[/C][C]0.158138[/C][/ROW]
[ROW][C]23[/C][C]0.078445[/C][C]1.1556[/C][C]0.124564[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116499&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116499&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	-0.079452	-1.1704	0.121561
2	-0.203949	-3.0044	0.001487
3	-0.04857	-0.7155	0.23754
4	-0.145996	-2.1507	0.016304
5	0.101543	1.4958	0.068076
6	-0.054226	-0.7988	0.212642
7	-0.019461	-0.2867	0.387314
8	0.025033	0.3688	0.356335
9	-0.045746	-0.6739	0.25055
10	0.079381	1.1693	0.121773
11	0.039296	0.5789	0.281641
12	-0.05824	-0.8579	0.195939
13	0.001638	0.0241	0.490388
14	-0.049832	-0.7341	0.231847
15	-0.010996	-0.162	0.435736
16	0.052731	0.7768	0.21907
17	0.030992	0.4565	0.324227
18	0.031305	0.4612	0.322575
19	-0.00604	-0.089	0.464594
20	-0.062768	-0.9246	0.178094
21	-0.037077	-0.5462	0.292752
22	-0.068187	-1.0045	0.158138
23	0.078445	1.1556	0.124564

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.079452	-1.1704	0.121561
2	-0.211597	-3.117	0.001037
3	-0.089565	-1.3194	0.094217
4	-0.216255	-3.1856	0.000828
5	0.031592	0.4654	0.321066
6	-0.140195	-2.0652	0.020046
7	-0.039127	-0.5764	0.28248
8	-0.056683	-0.835	0.202318
9	-0.058032	-0.8549	0.196784
10	0.023112	0.3405	0.366922
11	0.032999	0.4861	0.31369
12	-0.039314	-0.5791	0.281551
13	0.001407	0.0207	0.49174
14	-0.046885	-0.6907	0.245258
15	-0.032591	-0.4801	0.315822
16	0.012001	0.1768	0.429919
17	0.038439	0.5662	0.285907
18	0.033526	0.4939	0.310951
19	0.031857	0.4693	0.319667
20	-0.033837	-0.4985	0.309335
21	-0.044648	-0.6577	0.255714
22	-0.099027	-1.4588	0.073038
23	0.040627	0.5985	0.275074

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.079452 & -1.1704 & 0.121561 \tabularnewline
2 & -0.211597 & -3.117 & 0.001037 \tabularnewline
3 & -0.089565 & -1.3194 & 0.094217 \tabularnewline
4 & -0.216255 & -3.1856 & 0.000828 \tabularnewline
5 & 0.031592 & 0.4654 & 0.321066 \tabularnewline
6 & -0.140195 & -2.0652 & 0.020046 \tabularnewline
7 & -0.039127 & -0.5764 & 0.28248 \tabularnewline
8 & -0.056683 & -0.835 & 0.202318 \tabularnewline
9 & -0.058032 & -0.8549 & 0.196784 \tabularnewline
10 & 0.023112 & 0.3405 & 0.366922 \tabularnewline
11 & 0.032999 & 0.4861 & 0.31369 \tabularnewline
12 & -0.039314 & -0.5791 & 0.281551 \tabularnewline
13 & 0.001407 & 0.0207 & 0.49174 \tabularnewline
14 & -0.046885 & -0.6907 & 0.245258 \tabularnewline
15 & -0.032591 & -0.4801 & 0.315822 \tabularnewline
16 & 0.012001 & 0.1768 & 0.429919 \tabularnewline
17 & 0.038439 & 0.5662 & 0.285907 \tabularnewline
18 & 0.033526 & 0.4939 & 0.310951 \tabularnewline
19 & 0.031857 & 0.4693 & 0.319667 \tabularnewline
20 & -0.033837 & -0.4985 & 0.309335 \tabularnewline
21 & -0.044648 & -0.6577 & 0.255714 \tabularnewline
22 & -0.099027 & -1.4588 & 0.073038 \tabularnewline
23 & 0.040627 & 0.5985 & 0.275074 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116499&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]-0.079452[/C][C]-1.1704[/C][C]0.121561[/C][/ROW]
[ROW][C]2[/C][C]-0.211597[/C][C]-3.117[/C][C]0.001037[/C][/ROW]
[ROW][C]3[/C][C]-0.089565[/C][C]-1.3194[/C][C]0.094217[/C][/ROW]
[ROW][C]4[/C][C]-0.216255[/C][C]-3.1856[/C][C]0.000828[/C][/ROW]
[ROW][C]5[/C][C]0.031592[/C][C]0.4654[/C][C]0.321066[/C][/ROW]
[ROW][C]6[/C][C]-0.140195[/C][C]-2.0652[/C][C]0.020046[/C][/ROW]
[ROW][C]7[/C][C]-0.039127[/C][C]-0.5764[/C][C]0.28248[/C][/ROW]
[ROW][C]8[/C][C]-0.056683[/C][C]-0.835[/C][C]0.202318[/C][/ROW]
[ROW][C]9[/C][C]-0.058032[/C][C]-0.8549[/C][C]0.196784[/C][/ROW]
[ROW][C]10[/C][C]0.023112[/C][C]0.3405[/C][C]0.366922[/C][/ROW]
[ROW][C]11[/C][C]0.032999[/C][C]0.4861[/C][C]0.31369[/C][/ROW]
[ROW][C]12[/C][C]-0.039314[/C][C]-0.5791[/C][C]0.281551[/C][/ROW]
[ROW][C]13[/C][C]0.001407[/C][C]0.0207[/C][C]0.49174[/C][/ROW]
[ROW][C]14[/C][C]-0.046885[/C][C]-0.6907[/C][C]0.245258[/C][/ROW]
[ROW][C]15[/C][C]-0.032591[/C][C]-0.4801[/C][C]0.315822[/C][/ROW]
[ROW][C]16[/C][C]0.012001[/C][C]0.1768[/C][C]0.429919[/C][/ROW]
[ROW][C]17[/C][C]0.038439[/C][C]0.5662[/C][C]0.285907[/C][/ROW]
[ROW][C]18[/C][C]0.033526[/C][C]0.4939[/C][C]0.310951[/C][/ROW]
[ROW][C]19[/C][C]0.031857[/C][C]0.4693[/C][C]0.319667[/C][/ROW]
[ROW][C]20[/C][C]-0.033837[/C][C]-0.4985[/C][C]0.309335[/C][/ROW]
[ROW][C]21[/C][C]-0.044648[/C][C]-0.6577[/C][C]0.255714[/C][/ROW]
[ROW][C]22[/C][C]-0.099027[/C][C]-1.4588[/C][C]0.073038[/C][/ROW]
[ROW][C]23[/C][C]0.040627[/C][C]0.5985[/C][C]0.275074[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116499&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116499&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	-0.079452	-1.1704	0.121561
2	-0.211597	-3.117	0.001037
3	-0.089565	-1.3194	0.094217
4	-0.216255	-3.1856	0.000828
5	0.031592	0.4654	0.321066
6	-0.140195	-2.0652	0.020046
7	-0.039127	-0.5764	0.28248
8	-0.056683	-0.835	0.202318
9	-0.058032	-0.8549	0.196784
10	0.023112	0.3405	0.366922
11	0.032999	0.4861	0.31369
12	-0.039314	-0.5791	0.281551
13	0.001407	0.0207	0.49174
14	-0.046885	-0.6907	0.245258
15	-0.032591	-0.4801	0.315822
16	0.012001	0.1768	0.429919
17	0.038439	0.5662	0.285907
18	0.033526	0.4939	0.310951
19	0.031857	0.4693	0.319667
20	-0.033837	-0.4985	0.309335
21	-0.044648	-0.6577	0.255714
22	-0.099027	-1.4588	0.073038
23	0.040627	0.5985	0.275074

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 = 1 ; par5 = 1 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 1 ; 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