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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 23 Nov 2007 06:31:13 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Nov/23/t1195824905tbsdjodc0m4ypvu.htm/, Retrieved Sun, 28 Apr 2024 20:56:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6170, Retrieved Sun, 28 Apr 2024 20:56:35 +0000

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Estimated Impact

170

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-       [(Partial) Autocorrelation Function] [] [2007-11-23 13:31:13] [22d719c250b0837edaa2d173fd414084] [Current]

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Summary of compuational 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 compuational 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=6170&T=0

[TABLE]
[ROW][C]Summary of compuational 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=6170&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6170&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 compuational 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
0	1	9.5917	0
1	0.438822	4.209	3e-05
2	0.129732	1.2443	0.108267
3	0.050836	0.4876	0.313497
4	-0.001357	-0.013	0.505177
5	-0.155528	-1.4918	0.93041
6	-0.109264	-1.048	0.851313
7	-0.187642	-1.7998	0.962415
8	-0.117786	-1.1298	0.869244
9	-0.213469	-2.0475	0.978271
10	-0.158162	-1.517	0.933657
11	0.014076	0.135	0.446448
12	0.112578	1.0798	0.141524
13	0.065341	0.6267	0.266193
14	0.105592	1.0128	0.156906
15	0.024892	0.2388	0.405914
16	0.013345	0.128	0.449212
17	-0.035438	-0.3399	0.632652
18	-0.033106	-0.3175	0.624225

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 9.5917 & 0 \tabularnewline
1 & 0.438822 & 4.209 & 3e-05 \tabularnewline
2 & 0.129732 & 1.2443 & 0.108267 \tabularnewline
3 & 0.050836 & 0.4876 & 0.313497 \tabularnewline
4 & -0.001357 & -0.013 & 0.505177 \tabularnewline
5 & -0.155528 & -1.4918 & 0.93041 \tabularnewline
6 & -0.109264 & -1.048 & 0.851313 \tabularnewline
7 & -0.187642 & -1.7998 & 0.962415 \tabularnewline
8 & -0.117786 & -1.1298 & 0.869244 \tabularnewline
9 & -0.213469 & -2.0475 & 0.978271 \tabularnewline
10 & -0.158162 & -1.517 & 0.933657 \tabularnewline
11 & 0.014076 & 0.135 & 0.446448 \tabularnewline
12 & 0.112578 & 1.0798 & 0.141524 \tabularnewline
13 & 0.065341 & 0.6267 & 0.266193 \tabularnewline
14 & 0.105592 & 1.0128 & 0.156906 \tabularnewline
15 & 0.024892 & 0.2388 & 0.405914 \tabularnewline
16 & 0.013345 & 0.128 & 0.449212 \tabularnewline
17 & -0.035438 & -0.3399 & 0.632652 \tabularnewline
18 & -0.033106 & -0.3175 & 0.624225 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6170&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]0[/C][C]1[/C][C]9.5917[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.438822[/C][C]4.209[/C][C]3e-05[/C][/ROW]
[ROW][C]2[/C][C]0.129732[/C][C]1.2443[/C][C]0.108267[/C][/ROW]
[ROW][C]3[/C][C]0.050836[/C][C]0.4876[/C][C]0.313497[/C][/ROW]
[ROW][C]4[/C][C]-0.001357[/C][C]-0.013[/C][C]0.505177[/C][/ROW]
[ROW][C]5[/C][C]-0.155528[/C][C]-1.4918[/C][C]0.93041[/C][/ROW]
[ROW][C]6[/C][C]-0.109264[/C][C]-1.048[/C][C]0.851313[/C][/ROW]
[ROW][C]7[/C][C]-0.187642[/C][C]-1.7998[/C][C]0.962415[/C][/ROW]
[ROW][C]8[/C][C]-0.117786[/C][C]-1.1298[/C][C]0.869244[/C][/ROW]
[ROW][C]9[/C][C]-0.213469[/C][C]-2.0475[/C][C]0.978271[/C][/ROW]
[ROW][C]10[/C][C]-0.158162[/C][C]-1.517[/C][C]0.933657[/C][/ROW]
[ROW][C]11[/C][C]0.014076[/C][C]0.135[/C][C]0.446448[/C][/ROW]
[ROW][C]12[/C][C]0.112578[/C][C]1.0798[/C][C]0.141524[/C][/ROW]
[ROW][C]13[/C][C]0.065341[/C][C]0.6267[/C][C]0.266193[/C][/ROW]
[ROW][C]14[/C][C]0.105592[/C][C]1.0128[/C][C]0.156906[/C][/ROW]
[ROW][C]15[/C][C]0.024892[/C][C]0.2388[/C][C]0.405914[/C][/ROW]
[ROW][C]16[/C][C]0.013345[/C][C]0.128[/C][C]0.449212[/C][/ROW]
[ROW][C]17[/C][C]-0.035438[/C][C]-0.3399[/C][C]0.632652[/C][/ROW]
[ROW][C]18[/C][C]-0.033106[/C][C]-0.3175[/C][C]0.624225[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6170&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6170&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
0	1	9.5917	0
1	0.438822	4.209	3e-05
2	0.129732	1.2443	0.108267
3	0.050836	0.4876	0.313497
4	-0.001357	-0.013	0.505177
5	-0.155528	-1.4918	0.93041
6	-0.109264	-1.048	0.851313
7	-0.187642	-1.7998	0.962415
8	-0.117786	-1.1298	0.869244
9	-0.213469	-2.0475	0.978271
10	-0.158162	-1.517	0.933657
11	0.014076	0.135	0.446448
12	0.112578	1.0798	0.141524
13	0.065341	0.6267	0.266193
14	0.105592	1.0128	0.156906
15	0.024892	0.2388	0.405914
16	0.013345	0.128	0.449212
17	-0.035438	-0.3399	0.632652
18	-0.033106	-0.3175	0.624225

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.438822	4.209	3e-05
1	-0.077818	-0.7464	0.771336
2	0.029437	0.2824	0.389155
3	-0.033089	-0.3174	0.624164
4	-0.176539	-1.6933	0.953109
5	0.042766	0.4102	0.341306
6	-0.187528	-1.7987	0.962328
7	0.055555	0.5329	0.297706
8	-0.227842	-2.1854	0.9843
9	0.006128	0.0588	0.476628
10	0.122307	1.1731	0.121887
11	0.003565	0.0342	0.4864
12	0.025995	0.2493	0.40183
13	-0.012344	-0.1184	0.546994
14	-0.074226	-0.7119	0.760851
15	0.008547	0.082	0.46742
16	-0.072552	-0.6959	0.755876
17	0.010775	0.1034	0.458954
18	0.104548	1.0028	0.159297

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.438822 & 4.209 & 3e-05 \tabularnewline
1 & -0.077818 & -0.7464 & 0.771336 \tabularnewline
2 & 0.029437 & 0.2824 & 0.389155 \tabularnewline
3 & -0.033089 & -0.3174 & 0.624164 \tabularnewline
4 & -0.176539 & -1.6933 & 0.953109 \tabularnewline
5 & 0.042766 & 0.4102 & 0.341306 \tabularnewline
6 & -0.187528 & -1.7987 & 0.962328 \tabularnewline
7 & 0.055555 & 0.5329 & 0.297706 \tabularnewline
8 & -0.227842 & -2.1854 & 0.9843 \tabularnewline
9 & 0.006128 & 0.0588 & 0.476628 \tabularnewline
10 & 0.122307 & 1.1731 & 0.121887 \tabularnewline
11 & 0.003565 & 0.0342 & 0.4864 \tabularnewline
12 & 0.025995 & 0.2493 & 0.40183 \tabularnewline
13 & -0.012344 & -0.1184 & 0.546994 \tabularnewline
14 & -0.074226 & -0.7119 & 0.760851 \tabularnewline
15 & 0.008547 & 0.082 & 0.46742 \tabularnewline
16 & -0.072552 & -0.6959 & 0.755876 \tabularnewline
17 & 0.010775 & 0.1034 & 0.458954 \tabularnewline
18 & 0.104548 & 1.0028 & 0.159297 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6170&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]0[/C][C]0.438822[/C][C]4.209[/C][C]3e-05[/C][/ROW]
[ROW][C]1[/C][C]-0.077818[/C][C]-0.7464[/C][C]0.771336[/C][/ROW]
[ROW][C]2[/C][C]0.029437[/C][C]0.2824[/C][C]0.389155[/C][/ROW]
[ROW][C]3[/C][C]-0.033089[/C][C]-0.3174[/C][C]0.624164[/C][/ROW]
[ROW][C]4[/C][C]-0.176539[/C][C]-1.6933[/C][C]0.953109[/C][/ROW]
[ROW][C]5[/C][C]0.042766[/C][C]0.4102[/C][C]0.341306[/C][/ROW]
[ROW][C]6[/C][C]-0.187528[/C][C]-1.7987[/C][C]0.962328[/C][/ROW]
[ROW][C]7[/C][C]0.055555[/C][C]0.5329[/C][C]0.297706[/C][/ROW]
[ROW][C]8[/C][C]-0.227842[/C][C]-2.1854[/C][C]0.9843[/C][/ROW]
[ROW][C]9[/C][C]0.006128[/C][C]0.0588[/C][C]0.476628[/C][/ROW]
[ROW][C]10[/C][C]0.122307[/C][C]1.1731[/C][C]0.121887[/C][/ROW]
[ROW][C]11[/C][C]0.003565[/C][C]0.0342[/C][C]0.4864[/C][/ROW]
[ROW][C]12[/C][C]0.025995[/C][C]0.2493[/C][C]0.40183[/C][/ROW]
[ROW][C]13[/C][C]-0.012344[/C][C]-0.1184[/C][C]0.546994[/C][/ROW]
[ROW][C]14[/C][C]-0.074226[/C][C]-0.7119[/C][C]0.760851[/C][/ROW]
[ROW][C]15[/C][C]0.008547[/C][C]0.082[/C][C]0.46742[/C][/ROW]
[ROW][C]16[/C][C]-0.072552[/C][C]-0.6959[/C][C]0.755876[/C][/ROW]
[ROW][C]17[/C][C]0.010775[/C][C]0.1034[/C][C]0.458954[/C][/ROW]
[ROW][C]18[/C][C]0.104548[/C][C]1.0028[/C][C]0.159297[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6170&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6170&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
0	0.438822	4.209	3e-05
1	-0.077818	-0.7464	0.771336
2	0.029437	0.2824	0.389155
3	-0.033089	-0.3174	0.624164
4	-0.176539	-1.6933	0.953109
5	0.042766	0.4102	0.341306
6	-0.187528	-1.7987	0.962328
7	0.055555	0.5329	0.297706
8	-0.227842	-2.1854	0.9843
9	0.006128	0.0588	0.476628
10	0.122307	1.1731	0.121887
11	0.003565	0.0342	0.4864
12	0.025995	0.2493	0.40183
13	-0.012344	-0.1184	0.546994
14	-0.074226	-0.7119	0.760851
15	0.008547	0.082	0.46742
16	-0.072552	-0.6959	0.755876
17	0.010775	0.1034	0.458954
18	0.104548	1.0028	0.159297

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ;

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 (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='pic1.png')
racf <- acf(x,par1,main='Autocorrelation',xlab='lags',ylab='ACF')
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')
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 1:par1) {
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(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-1,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(mytstat,lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

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