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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 25 Nov 2007 05:46:05 -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/25/t11959949569y0x0cymuj5z13g.htm/, Retrieved Tue, 21 May 2024 10:18:21 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6429, Retrieved Tue, 21 May 2024 10:18:21 +0000

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Estimated Impact

192

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-       [(Partial) Autocorrelation Function] [] [2007-11-25 12:46:05] [80e26e27d8b229550cb490fed3b7813c] [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	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6429&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6429&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6429&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	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	9	0
1	0.868318	7.8149	0
2	0.764018	6.8762	0
3	0.720541	6.4849	0
4	0.59812	5.3831	0
5	0.467994	4.2119	3.3e-05
6	0.385822	3.4724	0.000415
7	0.2942	2.6478	0.004867
8	0.170687	1.5362	0.064195
9	0.078459	0.7061	0.241066
10	0.00919	0.0827	0.467142
11	-0.104818	-0.9434	0.82585
12	-0.244359	-2.1992	0.984644
13	-0.281889	-2.537	0.99345
14	-0.31027	-2.7924	0.996738
15	-0.359541	-3.2359	0.999121
16	-0.33349	-3.0014	0.998214
17	-0.296306	-2.6667	0.995377
18	-0.282189	-2.5397	0.993497

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 9 & 0 \tabularnewline
1 & 0.868318 & 7.8149 & 0 \tabularnewline
2 & 0.764018 & 6.8762 & 0 \tabularnewline
3 & 0.720541 & 6.4849 & 0 \tabularnewline
4 & 0.59812 & 5.3831 & 0 \tabularnewline
5 & 0.467994 & 4.2119 & 3.3e-05 \tabularnewline
6 & 0.385822 & 3.4724 & 0.000415 \tabularnewline
7 & 0.2942 & 2.6478 & 0.004867 \tabularnewline
8 & 0.170687 & 1.5362 & 0.064195 \tabularnewline
9 & 0.078459 & 0.7061 & 0.241066 \tabularnewline
10 & 0.00919 & 0.0827 & 0.467142 \tabularnewline
11 & -0.104818 & -0.9434 & 0.82585 \tabularnewline
12 & -0.244359 & -2.1992 & 0.984644 \tabularnewline
13 & -0.281889 & -2.537 & 0.99345 \tabularnewline
14 & -0.31027 & -2.7924 & 0.996738 \tabularnewline
15 & -0.359541 & -3.2359 & 0.999121 \tabularnewline
16 & -0.33349 & -3.0014 & 0.998214 \tabularnewline
17 & -0.296306 & -2.6667 & 0.995377 \tabularnewline
18 & -0.282189 & -2.5397 & 0.993497 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6429&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[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.868318[/C][C]7.8149[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.764018[/C][C]6.8762[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.720541[/C][C]6.4849[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.59812[/C][C]5.3831[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.467994[/C][C]4.2119[/C][C]3.3e-05[/C][/ROW]
[ROW][C]6[/C][C]0.385822[/C][C]3.4724[/C][C]0.000415[/C][/ROW]
[ROW][C]7[/C][C]0.2942[/C][C]2.6478[/C][C]0.004867[/C][/ROW]
[ROW][C]8[/C][C]0.170687[/C][C]1.5362[/C][C]0.064195[/C][/ROW]
[ROW][C]9[/C][C]0.078459[/C][C]0.7061[/C][C]0.241066[/C][/ROW]
[ROW][C]10[/C][C]0.00919[/C][C]0.0827[/C][C]0.467142[/C][/ROW]
[ROW][C]11[/C][C]-0.104818[/C][C]-0.9434[/C][C]0.82585[/C][/ROW]
[ROW][C]12[/C][C]-0.244359[/C][C]-2.1992[/C][C]0.984644[/C][/ROW]
[ROW][C]13[/C][C]-0.281889[/C][C]-2.537[/C][C]0.99345[/C][/ROW]
[ROW][C]14[/C][C]-0.31027[/C][C]-2.7924[/C][C]0.996738[/C][/ROW]
[ROW][C]15[/C][C]-0.359541[/C][C]-3.2359[/C][C]0.999121[/C][/ROW]
[ROW][C]16[/C][C]-0.33349[/C][C]-3.0014[/C][C]0.998214[/C][/ROW]
[ROW][C]17[/C][C]-0.296306[/C][C]-2.6667[/C][C]0.995377[/C][/ROW]
[ROW][C]18[/C][C]-0.282189[/C][C]-2.5397[/C][C]0.993497[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6429&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6429&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	0
1	0.868318	7.8149	0
2	0.764018	6.8762	0
3	0.720541	6.4849	0
4	0.59812	5.3831	0
5	0.467994	4.2119	3.3e-05
6	0.385822	3.4724	0.000415
7	0.2942	2.6478	0.004867
8	0.170687	1.5362	0.064195
9	0.078459	0.7061	0.241066
10	0.00919	0.0827	0.467142
11	-0.104818	-0.9434	0.82585
12	-0.244359	-2.1992	0.984644
13	-0.281889	-2.537	0.99345
14	-0.31027	-2.7924	0.996738
15	-0.359541	-3.2359	0.999121
16	-0.33349	-3.0014	0.998214
17	-0.296306	-2.6667	0.995377
18	-0.282189	-2.5397	0.993497

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.868318	7.8149	0
1	0.040815	0.3673	0.357162
2	0.198549	1.7869	0.038844
3	-0.311138	-2.8002	0.996809
4	-0.104139	-0.9373	0.824293
5	-0.012805	-0.1152	0.545731
6	-0.017322	-0.1559	0.56175
7	-0.143714	-1.2934	0.90023
8	-0.035777	-0.322	0.625856
9	-0.020482	-0.1843	0.572894
10	-0.176346	-1.5871	0.941808
11	-0.275974	-2.4838	0.992469
12	0.206683	1.8601	0.033247
13	0.062712	0.5644	0.287019
14	0.088678	0.7981	0.213574
15	0.099766	0.8979	0.185951
16	-0.013249	-0.1192	0.547309
17	0.022078	0.1987	0.421496
18	0.049416	0.4447	0.328845

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.868318 & 7.8149 & 0 \tabularnewline
1 & 0.040815 & 0.3673 & 0.357162 \tabularnewline
2 & 0.198549 & 1.7869 & 0.038844 \tabularnewline
3 & -0.311138 & -2.8002 & 0.996809 \tabularnewline
4 & -0.104139 & -0.9373 & 0.824293 \tabularnewline
5 & -0.012805 & -0.1152 & 0.545731 \tabularnewline
6 & -0.017322 & -0.1559 & 0.56175 \tabularnewline
7 & -0.143714 & -1.2934 & 0.90023 \tabularnewline
8 & -0.035777 & -0.322 & 0.625856 \tabularnewline
9 & -0.020482 & -0.1843 & 0.572894 \tabularnewline
10 & -0.176346 & -1.5871 & 0.941808 \tabularnewline
11 & -0.275974 & -2.4838 & 0.992469 \tabularnewline
12 & 0.206683 & 1.8601 & 0.033247 \tabularnewline
13 & 0.062712 & 0.5644 & 0.287019 \tabularnewline
14 & 0.088678 & 0.7981 & 0.213574 \tabularnewline
15 & 0.099766 & 0.8979 & 0.185951 \tabularnewline
16 & -0.013249 & -0.1192 & 0.547309 \tabularnewline
17 & 0.022078 & 0.1987 & 0.421496 \tabularnewline
18 & 0.049416 & 0.4447 & 0.328845 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6429&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]0.868318[/C][C]7.8149[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.040815[/C][C]0.3673[/C][C]0.357162[/C][/ROW]
[ROW][C]2[/C][C]0.198549[/C][C]1.7869[/C][C]0.038844[/C][/ROW]
[ROW][C]3[/C][C]-0.311138[/C][C]-2.8002[/C][C]0.996809[/C][/ROW]
[ROW][C]4[/C][C]-0.104139[/C][C]-0.9373[/C][C]0.824293[/C][/ROW]
[ROW][C]5[/C][C]-0.012805[/C][C]-0.1152[/C][C]0.545731[/C][/ROW]
[ROW][C]6[/C][C]-0.017322[/C][C]-0.1559[/C][C]0.56175[/C][/ROW]
[ROW][C]7[/C][C]-0.143714[/C][C]-1.2934[/C][C]0.90023[/C][/ROW]
[ROW][C]8[/C][C]-0.035777[/C][C]-0.322[/C][C]0.625856[/C][/ROW]
[ROW][C]9[/C][C]-0.020482[/C][C]-0.1843[/C][C]0.572894[/C][/ROW]
[ROW][C]10[/C][C]-0.176346[/C][C]-1.5871[/C][C]0.941808[/C][/ROW]
[ROW][C]11[/C][C]-0.275974[/C][C]-2.4838[/C][C]0.992469[/C][/ROW]
[ROW][C]12[/C][C]0.206683[/C][C]1.8601[/C][C]0.033247[/C][/ROW]
[ROW][C]13[/C][C]0.062712[/C][C]0.5644[/C][C]0.287019[/C][/ROW]
[ROW][C]14[/C][C]0.088678[/C][C]0.7981[/C][C]0.213574[/C][/ROW]
[ROW][C]15[/C][C]0.099766[/C][C]0.8979[/C][C]0.185951[/C][/ROW]
[ROW][C]16[/C][C]-0.013249[/C][C]-0.1192[/C][C]0.547309[/C][/ROW]
[ROW][C]17[/C][C]0.022078[/C][C]0.1987[/C][C]0.421496[/C][/ROW]
[ROW][C]18[/C][C]0.049416[/C][C]0.4447[/C][C]0.328845[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6429&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6429&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	0.868318	7.8149	0
1	0.040815	0.3673	0.357162
2	0.198549	1.7869	0.038844
3	-0.311138	-2.8002	0.996809
4	-0.104139	-0.9373	0.824293
5	-0.012805	-0.1152	0.545731
6	-0.017322	-0.1559	0.56175
7	-0.143714	-1.2934	0.90023
8	-0.035777	-0.322	0.625856
9	-0.020482	-0.1843	0.572894
10	-0.176346	-1.5871	0.941808
11	-0.275974	-2.4838	0.992469
12	0.206683	1.8601	0.033247
13	0.062712	0.5644	0.287019
14	0.088678	0.7981	0.213574
15	0.099766	0.8979	0.185951
16	-0.013249	-0.1192	0.547309
17	0.022078	0.1987	0.421496
18	0.049416	0.4447	0.328845

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

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