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

Fri, 09 Dec 2011 05:46:56 -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/09/t1323427634fre9a5329hkpf7x.htm/, Retrieved Thu, 02 May 2024 15:26:20 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=153247, Retrieved Thu, 02 May 2024 15:26:20 +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

158

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

-     [Univariate Data Series] [] [2010-10-06 14:13:06] [3d53bd477a917086cfdff0f854c5e476]
-   PD  [Univariate Data Series] [rozen] [2010-12-07 20:04:29] [b98453cac15ba1066b407e146608df68]
- RMPD    [(Partial) Autocorrelation Function] [Times Series - Rozen] [2011-12-09 10:44:11] [586787d3e7267c593af3e1f6b16aa21a]
- R P         [(Partial) Autocorrelation Function] [Times Series - Rozen] [2011-12-09 10:46:56] [a0aae37dd27f4b65e222573f53b5a13b] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

1.35
1.91
1.31
1.19
1.3
1.14
1.1
1.02
1.11
1.18
1.24
1.36
1.29
1.73
1.41
1.15
1.31
1.15
1.08
1.1
1.14
1.24
1.33
1.49
1.38
1.96
1.36
1.24
1.35
1.23
1.09
1.08
1.33
1.35
1.38
1.5
1.47
2.09
1.52
1.29
1.52
1.27
1.35
1.29
1.41
1.39
1.45
1.53
1.45
2.11
1.53
1.38
1.54
1.35
1.29
1.33
1.47
1.47
1.54
1.59
1.5
2
1.51
1.4
1.62
1.44
1.29
1.28
1.4
1.39
1.46
1.49

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	'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=153247&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=153247&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=153247&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.538478	-4.1361	5.7e-05
2	0.189705	1.4572	0.075188
3	-0.199755	-1.5343	0.065145
4	0.042375	0.3255	0.372982
5	0.103901	0.7981	0.214012
6	-0.089758	-0.6894	0.246624
7	0.027866	0.214	0.415627
8	-0.014786	-0.1136	0.454982
9	0.074462	0.572	0.284763
10	-0.1027	-0.7889	0.216678
11	0.232645	1.787	0.039539
12	-0.498965	-3.8326	0.000155
13	0.451479	3.4679	0.000493
14	-0.245893	-1.8887	0.031923
15	0.251531	1.932	0.02908
16	-0.24938	-1.9155	0.030138
17	0.058876	0.4522	0.32638
18	0.118572	0.9108	0.183061

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.538478 & -4.1361 & 5.7e-05 \tabularnewline
2 & 0.189705 & 1.4572 & 0.075188 \tabularnewline
3 & -0.199755 & -1.5343 & 0.065145 \tabularnewline
4 & 0.042375 & 0.3255 & 0.372982 \tabularnewline
5 & 0.103901 & 0.7981 & 0.214012 \tabularnewline
6 & -0.089758 & -0.6894 & 0.246624 \tabularnewline
7 & 0.027866 & 0.214 & 0.415627 \tabularnewline
8 & -0.014786 & -0.1136 & 0.454982 \tabularnewline
9 & 0.074462 & 0.572 & 0.284763 \tabularnewline
10 & -0.1027 & -0.7889 & 0.216678 \tabularnewline
11 & 0.232645 & 1.787 & 0.039539 \tabularnewline
12 & -0.498965 & -3.8326 & 0.000155 \tabularnewline
13 & 0.451479 & 3.4679 & 0.000493 \tabularnewline
14 & -0.245893 & -1.8887 & 0.031923 \tabularnewline
15 & 0.251531 & 1.932 & 0.02908 \tabularnewline
16 & -0.24938 & -1.9155 & 0.030138 \tabularnewline
17 & 0.058876 & 0.4522 & 0.32638 \tabularnewline
18 & 0.118572 & 0.9108 & 0.183061 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=153247&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]-0.538478[/C][C]-4.1361[/C][C]5.7e-05[/C][/ROW]
[ROW][C]2[/C][C]0.189705[/C][C]1.4572[/C][C]0.075188[/C][/ROW]
[ROW][C]3[/C][C]-0.199755[/C][C]-1.5343[/C][C]0.065145[/C][/ROW]
[ROW][C]4[/C][C]0.042375[/C][C]0.3255[/C][C]0.372982[/C][/ROW]
[ROW][C]5[/C][C]0.103901[/C][C]0.7981[/C][C]0.214012[/C][/ROW]
[ROW][C]6[/C][C]-0.089758[/C][C]-0.6894[/C][C]0.246624[/C][/ROW]
[ROW][C]7[/C][C]0.027866[/C][C]0.214[/C][C]0.415627[/C][/ROW]
[ROW][C]8[/C][C]-0.014786[/C][C]-0.1136[/C][C]0.454982[/C][/ROW]
[ROW][C]9[/C][C]0.074462[/C][C]0.572[/C][C]0.284763[/C][/ROW]
[ROW][C]10[/C][C]-0.1027[/C][C]-0.7889[/C][C]0.216678[/C][/ROW]
[ROW][C]11[/C][C]0.232645[/C][C]1.787[/C][C]0.039539[/C][/ROW]
[ROW][C]12[/C][C]-0.498965[/C][C]-3.8326[/C][C]0.000155[/C][/ROW]
[ROW][C]13[/C][C]0.451479[/C][C]3.4679[/C][C]0.000493[/C][/ROW]
[ROW][C]14[/C][C]-0.245893[/C][C]-1.8887[/C][C]0.031923[/C][/ROW]
[ROW][C]15[/C][C]0.251531[/C][C]1.932[/C][C]0.02908[/C][/ROW]
[ROW][C]16[/C][C]-0.24938[/C][C]-1.9155[/C][C]0.030138[/C][/ROW]
[ROW][C]17[/C][C]0.058876[/C][C]0.4522[/C][C]0.32638[/C][/ROW]
[ROW][C]18[/C][C]0.118572[/C][C]0.9108[/C][C]0.183061[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=153247&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=153247&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	-0.538478	-4.1361	5.7e-05
2	0.189705	1.4572	0.075188
3	-0.199755	-1.5343	0.065145
4	0.042375	0.3255	0.372982
5	0.103901	0.7981	0.214012
6	-0.089758	-0.6894	0.246624
7	0.027866	0.214	0.415627
8	-0.014786	-0.1136	0.454982
9	0.074462	0.572	0.284763
10	-0.1027	-0.7889	0.216678
11	0.232645	1.787	0.039539
12	-0.498965	-3.8326	0.000155
13	0.451479	3.4679	0.000493
14	-0.245893	-1.8887	0.031923
15	0.251531	1.932	0.02908
16	-0.24938	-1.9155	0.030138
17	0.058876	0.4522	0.32638
18	0.118572	0.9108	0.183061

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.538478	-4.1361	5.7e-05
2	-0.141194	-1.0845	0.141271
3	-0.228786	-1.7573	0.042024
4	-0.23742	-1.8237	0.036635
5	0.013898	0.1068	0.457673
6	-0.044096	-0.3387	0.368015
7	-0.081069	-0.6227	0.26794
8	-0.009921	-0.0762	0.469758
9	0.094527	0.7261	0.23533
10	-0.056207	-0.4317	0.333754
11	0.270079	2.0745	0.021202
12	-0.376597	-2.8927	0.002671
13	0.008359	0.0642	0.474512
14	0.011232	0.0863	0.465771
15	0.098354	0.7555	0.226485
16	-0.172275	-1.3233	0.095426
17	0.010935	0.084	0.466674
18	0.111638	0.8575	0.197317

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.538478 & -4.1361 & 5.7e-05 \tabularnewline
2 & -0.141194 & -1.0845 & 0.141271 \tabularnewline
3 & -0.228786 & -1.7573 & 0.042024 \tabularnewline
4 & -0.23742 & -1.8237 & 0.036635 \tabularnewline
5 & 0.013898 & 0.1068 & 0.457673 \tabularnewline
6 & -0.044096 & -0.3387 & 0.368015 \tabularnewline
7 & -0.081069 & -0.6227 & 0.26794 \tabularnewline
8 & -0.009921 & -0.0762 & 0.469758 \tabularnewline
9 & 0.094527 & 0.7261 & 0.23533 \tabularnewline
10 & -0.056207 & -0.4317 & 0.333754 \tabularnewline
11 & 0.270079 & 2.0745 & 0.021202 \tabularnewline
12 & -0.376597 & -2.8927 & 0.002671 \tabularnewline
13 & 0.008359 & 0.0642 & 0.474512 \tabularnewline
14 & 0.011232 & 0.0863 & 0.465771 \tabularnewline
15 & 0.098354 & 0.7555 & 0.226485 \tabularnewline
16 & -0.172275 & -1.3233 & 0.095426 \tabularnewline
17 & 0.010935 & 0.084 & 0.466674 \tabularnewline
18 & 0.111638 & 0.8575 & 0.197317 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=153247&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]-0.538478[/C][C]-4.1361[/C][C]5.7e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.141194[/C][C]-1.0845[/C][C]0.141271[/C][/ROW]
[ROW][C]3[/C][C]-0.228786[/C][C]-1.7573[/C][C]0.042024[/C][/ROW]
[ROW][C]4[/C][C]-0.23742[/C][C]-1.8237[/C][C]0.036635[/C][/ROW]
[ROW][C]5[/C][C]0.013898[/C][C]0.1068[/C][C]0.457673[/C][/ROW]
[ROW][C]6[/C][C]-0.044096[/C][C]-0.3387[/C][C]0.368015[/C][/ROW]
[ROW][C]7[/C][C]-0.081069[/C][C]-0.6227[/C][C]0.26794[/C][/ROW]
[ROW][C]8[/C][C]-0.009921[/C][C]-0.0762[/C][C]0.469758[/C][/ROW]
[ROW][C]9[/C][C]0.094527[/C][C]0.7261[/C][C]0.23533[/C][/ROW]
[ROW][C]10[/C][C]-0.056207[/C][C]-0.4317[/C][C]0.333754[/C][/ROW]
[ROW][C]11[/C][C]0.270079[/C][C]2.0745[/C][C]0.021202[/C][/ROW]
[ROW][C]12[/C][C]-0.376597[/C][C]-2.8927[/C][C]0.002671[/C][/ROW]
[ROW][C]13[/C][C]0.008359[/C][C]0.0642[/C][C]0.474512[/C][/ROW]
[ROW][C]14[/C][C]0.011232[/C][C]0.0863[/C][C]0.465771[/C][/ROW]
[ROW][C]15[/C][C]0.098354[/C][C]0.7555[/C][C]0.226485[/C][/ROW]
[ROW][C]16[/C][C]-0.172275[/C][C]-1.3233[/C][C]0.095426[/C][/ROW]
[ROW][C]17[/C][C]0.010935[/C][C]0.084[/C][C]0.466674[/C][/ROW]
[ROW][C]18[/C][C]0.111638[/C][C]0.8575[/C][C]0.197317[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=153247&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=153247&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	-0.538478	-4.1361	5.7e-05
2	-0.141194	-1.0845	0.141271
3	-0.228786	-1.7573	0.042024
4	-0.23742	-1.8237	0.036635
5	0.013898	0.1068	0.457673
6	-0.044096	-0.3387	0.368015
7	-0.081069	-0.6227	0.26794
8	-0.009921	-0.0762	0.469758
9	0.094527	0.7261	0.23533
10	-0.056207	-0.4317	0.333754
11	0.270079	2.0745	0.021202
12	-0.376597	-2.8927	0.002671
13	0.008359	0.0642	0.474512
14	0.011232	0.0863	0.465771
15	0.098354	0.7555	0.226485
16	-0.172275	-1.3233	0.095426
17	0.010935	0.084	0.466674
18	0.111638	0.8575	0.197317

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