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, 21 Dec 2010 16:39:04 +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/21/t1292949422ukzh3jnerhemmja.htm/, Retrieved Sun, 12 May 2024 10:31:38 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113738, Retrieved Sun, 12 May 2024 10:31:38 +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

144

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Multiple Regression] [Unemployment] [2010-11-30 13:40:15] [b98453cac15ba1066b407e146608df68]
- RMPD      [(Partial) Autocorrelation Function] [paper- ACF - d=1 D=1] [2010-12-21 16:39:04] [5398da98f4f83c6a353e4d3806d4bcaa] [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	4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113738&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113738&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113738&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' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.56118	-4.7286	6e-06
2	-0.046185	-0.3892	0.349161
3	0.465127	3.9192	0.000101
4	-0.422371	-3.559	0.000334
5	0.127611	1.0753	0.142947
6	0.150017	1.2641	0.105171
7	-0.236318	-1.9913	0.025151
8	0.056621	0.4771	0.317379
9	0.156983	1.3228	0.095079
10	-0.216594	-1.8251	0.0361
11	0.034605	0.2916	0.385726
12	0.162864	1.3723	0.087143
13	-0.248088	-2.0904	0.02008
14	0.082621	0.6962	0.244294
15	0.14584	1.2289	0.111589
16	-0.293689	-2.4747	0.007863
17	0.211204	1.7796	0.039707
18	0.019762	0.1665	0.434112
19	-0.218963	-1.845	0.034603

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.56118 & -4.7286 & 6e-06 \tabularnewline
2 & -0.046185 & -0.3892 & 0.349161 \tabularnewline
3 & 0.465127 & 3.9192 & 0.000101 \tabularnewline
4 & -0.422371 & -3.559 & 0.000334 \tabularnewline
5 & 0.127611 & 1.0753 & 0.142947 \tabularnewline
6 & 0.150017 & 1.2641 & 0.105171 \tabularnewline
7 & -0.236318 & -1.9913 & 0.025151 \tabularnewline
8 & 0.056621 & 0.4771 & 0.317379 \tabularnewline
9 & 0.156983 & 1.3228 & 0.095079 \tabularnewline
10 & -0.216594 & -1.8251 & 0.0361 \tabularnewline
11 & 0.034605 & 0.2916 & 0.385726 \tabularnewline
12 & 0.162864 & 1.3723 & 0.087143 \tabularnewline
13 & -0.248088 & -2.0904 & 0.02008 \tabularnewline
14 & 0.082621 & 0.6962 & 0.244294 \tabularnewline
15 & 0.14584 & 1.2289 & 0.111589 \tabularnewline
16 & -0.293689 & -2.4747 & 0.007863 \tabularnewline
17 & 0.211204 & 1.7796 & 0.039707 \tabularnewline
18 & 0.019762 & 0.1665 & 0.434112 \tabularnewline
19 & -0.218963 & -1.845 & 0.034603 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113738&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]-0.56118[/C][C]-4.7286[/C][C]6e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.046185[/C][C]-0.3892[/C][C]0.349161[/C][/ROW]
[ROW][C]3[/C][C]0.465127[/C][C]3.9192[/C][C]0.000101[/C][/ROW]
[ROW][C]4[/C][C]-0.422371[/C][C]-3.559[/C][C]0.000334[/C][/ROW]
[ROW][C]5[/C][C]0.127611[/C][C]1.0753[/C][C]0.142947[/C][/ROW]
[ROW][C]6[/C][C]0.150017[/C][C]1.2641[/C][C]0.105171[/C][/ROW]
[ROW][C]7[/C][C]-0.236318[/C][C]-1.9913[/C][C]0.025151[/C][/ROW]
[ROW][C]8[/C][C]0.056621[/C][C]0.4771[/C][C]0.317379[/C][/ROW]
[ROW][C]9[/C][C]0.156983[/C][C]1.3228[/C][C]0.095079[/C][/ROW]
[ROW][C]10[/C][C]-0.216594[/C][C]-1.8251[/C][C]0.0361[/C][/ROW]
[ROW][C]11[/C][C]0.034605[/C][C]0.2916[/C][C]0.385726[/C][/ROW]
[ROW][C]12[/C][C]0.162864[/C][C]1.3723[/C][C]0.087143[/C][/ROW]
[ROW][C]13[/C][C]-0.248088[/C][C]-2.0904[/C][C]0.02008[/C][/ROW]
[ROW][C]14[/C][C]0.082621[/C][C]0.6962[/C][C]0.244294[/C][/ROW]
[ROW][C]15[/C][C]0.14584[/C][C]1.2289[/C][C]0.111589[/C][/ROW]
[ROW][C]16[/C][C]-0.293689[/C][C]-2.4747[/C][C]0.007863[/C][/ROW]
[ROW][C]17[/C][C]0.211204[/C][C]1.7796[/C][C]0.039707[/C][/ROW]
[ROW][C]18[/C][C]0.019762[/C][C]0.1665[/C][C]0.434112[/C][/ROW]
[ROW][C]19[/C][C]-0.218963[/C][C]-1.845[/C][C]0.034603[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113738&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113738&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	-0.56118	-4.7286	6e-06
2	-0.046185	-0.3892	0.349161
3	0.465127	3.9192	0.000101
4	-0.422371	-3.559	0.000334
5	0.127611	1.0753	0.142947
6	0.150017	1.2641	0.105171
7	-0.236318	-1.9913	0.025151
8	0.056621	0.4771	0.317379
9	0.156983	1.3228	0.095079
10	-0.216594	-1.8251	0.0361
11	0.034605	0.2916	0.385726
12	0.162864	1.3723	0.087143
13	-0.248088	-2.0904	0.02008
14	0.082621	0.6962	0.244294
15	0.14584	1.2289	0.111589
16	-0.293689	-2.4747	0.007863
17	0.211204	1.7796	0.039707
18	0.019762	0.1665	0.434112
19	-0.218963	-1.845	0.034603

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.56118	-4.7286	6e-06
2	-0.527105	-4.4415	1.6e-05
3	0.262255	2.2098	0.015172
4	0.097987	0.8257	0.205883
5	0.022765	0.1918	0.424214
6	-0.027707	-0.2335	0.408036
7	-0.015869	-0.1337	0.447002
8	-0.186428	-1.5709	0.060329
9	0.045282	0.3816	0.351966
10	0.026007	0.2191	0.413586
11	-0.102302	-0.862	0.195792
12	-0.020154	-0.1698	0.432816
13	-0.064654	-0.5448	0.293806
14	-0.133001	-1.1207	0.133099
15	0.032966	0.2778	0.390997
16	-0.078642	-0.6626	0.254851
17	-0.002947	-0.0248	0.49013
18	0.010995	0.0926	0.463223
19	-0.032288	-0.2721	0.393182

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.56118 & -4.7286 & 6e-06 \tabularnewline
2 & -0.527105 & -4.4415 & 1.6e-05 \tabularnewline
3 & 0.262255 & 2.2098 & 0.015172 \tabularnewline
4 & 0.097987 & 0.8257 & 0.205883 \tabularnewline
5 & 0.022765 & 0.1918 & 0.424214 \tabularnewline
6 & -0.027707 & -0.2335 & 0.408036 \tabularnewline
7 & -0.015869 & -0.1337 & 0.447002 \tabularnewline
8 & -0.186428 & -1.5709 & 0.060329 \tabularnewline
9 & 0.045282 & 0.3816 & 0.351966 \tabularnewline
10 & 0.026007 & 0.2191 & 0.413586 \tabularnewline
11 & -0.102302 & -0.862 & 0.195792 \tabularnewline
12 & -0.020154 & -0.1698 & 0.432816 \tabularnewline
13 & -0.064654 & -0.5448 & 0.293806 \tabularnewline
14 & -0.133001 & -1.1207 & 0.133099 \tabularnewline
15 & 0.032966 & 0.2778 & 0.390997 \tabularnewline
16 & -0.078642 & -0.6626 & 0.254851 \tabularnewline
17 & -0.002947 & -0.0248 & 0.49013 \tabularnewline
18 & 0.010995 & 0.0926 & 0.463223 \tabularnewline
19 & -0.032288 & -0.2721 & 0.393182 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113738&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]-0.56118[/C][C]-4.7286[/C][C]6e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.527105[/C][C]-4.4415[/C][C]1.6e-05[/C][/ROW]
[ROW][C]3[/C][C]0.262255[/C][C]2.2098[/C][C]0.015172[/C][/ROW]
[ROW][C]4[/C][C]0.097987[/C][C]0.8257[/C][C]0.205883[/C][/ROW]
[ROW][C]5[/C][C]0.022765[/C][C]0.1918[/C][C]0.424214[/C][/ROW]
[ROW][C]6[/C][C]-0.027707[/C][C]-0.2335[/C][C]0.408036[/C][/ROW]
[ROW][C]7[/C][C]-0.015869[/C][C]-0.1337[/C][C]0.447002[/C][/ROW]
[ROW][C]8[/C][C]-0.186428[/C][C]-1.5709[/C][C]0.060329[/C][/ROW]
[ROW][C]9[/C][C]0.045282[/C][C]0.3816[/C][C]0.351966[/C][/ROW]
[ROW][C]10[/C][C]0.026007[/C][C]0.2191[/C][C]0.413586[/C][/ROW]
[ROW][C]11[/C][C]-0.102302[/C][C]-0.862[/C][C]0.195792[/C][/ROW]
[ROW][C]12[/C][C]-0.020154[/C][C]-0.1698[/C][C]0.432816[/C][/ROW]
[ROW][C]13[/C][C]-0.064654[/C][C]-0.5448[/C][C]0.293806[/C][/ROW]
[ROW][C]14[/C][C]-0.133001[/C][C]-1.1207[/C][C]0.133099[/C][/ROW]
[ROW][C]15[/C][C]0.032966[/C][C]0.2778[/C][C]0.390997[/C][/ROW]
[ROW][C]16[/C][C]-0.078642[/C][C]-0.6626[/C][C]0.254851[/C][/ROW]
[ROW][C]17[/C][C]-0.002947[/C][C]-0.0248[/C][C]0.49013[/C][/ROW]
[ROW][C]18[/C][C]0.010995[/C][C]0.0926[/C][C]0.463223[/C][/ROW]
[ROW][C]19[/C][C]-0.032288[/C][C]-0.2721[/C][C]0.393182[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113738&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113738&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	-0.56118	-4.7286	6e-06
2	-0.527105	-4.4415	1.6e-05
3	0.262255	2.2098	0.015172
4	0.097987	0.8257	0.205883
5	0.022765	0.1918	0.424214
6	-0.027707	-0.2335	0.408036
7	-0.015869	-0.1337	0.447002
8	-0.186428	-1.5709	0.060329
9	0.045282	0.3816	0.351966
10	0.026007	0.2191	0.413586
11	-0.102302	-0.862	0.195792
12	-0.020154	-0.1698	0.432816
13	-0.064654	-0.5448	0.293806
14	-0.133001	-1.1207	0.133099
15	0.032966	0.2778	0.390997
16	-0.078642	-0.6626	0.254851
17	-0.002947	-0.0248	0.49013
18	0.010995	0.0926	0.463223
19	-0.032288	-0.2721	0.393182

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 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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