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*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, 04 Dec 2009 08:19:19 -0700

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/2009/Dec/04/t1259940070aob57n6crrculnr.htm/, Retrieved Sun, 28 Apr 2024 14:58:38 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63745, Retrieved Sun, 28 Apr 2024 14:58:38 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

139

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

-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [(Partial) Autocorrelation Function] [Identifying Integ...] [2009-11-22 12:26:39] [b98453cac15ba1066b407e146608df68]
-    D        [(Partial) Autocorrelation Function] [] [2009-11-23 15:32:19] [5d885a68c2332cc44f6191ec94766bfa]
- R PD            [(Partial) Autocorrelation Function] [AutoCF d=1,D=1] [2009-12-04 15:19:19] [18c0746232b29e9668aa6bedcb8dd698] [Current]

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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	'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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63745&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63745&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63745&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.315984	2.1663	0.017697
2	0.260015	1.7826	0.040558
3	-0.401788	-2.7545	0.004167
4	-0.248872	-1.7062	0.047288
5	-0.245446	-1.6827	0.049534
6	0.064707	0.4436	0.329681
7	0.118675	0.8136	0.209989
8	0.194245	1.3317	0.094694
9	0.098253	0.6736	0.251936
10	-0.113532	-0.7783	0.220136
11	-0.238379	-1.6342	0.054445
12	-0.448522	-3.0749	0.001751
13	-0.265099	-1.8174	0.037765
14	-0.177478	-1.2167	0.114892
15	0.088161	0.6044	0.274241
16	0.074826	0.513	0.305183
17	0.159237	1.0917	0.14027

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.315984 & 2.1663 & 0.017697 \tabularnewline
2 & 0.260015 & 1.7826 & 0.040558 \tabularnewline
3 & -0.401788 & -2.7545 & 0.004167 \tabularnewline
4 & -0.248872 & -1.7062 & 0.047288 \tabularnewline
5 & -0.245446 & -1.6827 & 0.049534 \tabularnewline
6 & 0.064707 & 0.4436 & 0.329681 \tabularnewline
7 & 0.118675 & 0.8136 & 0.209989 \tabularnewline
8 & 0.194245 & 1.3317 & 0.094694 \tabularnewline
9 & 0.098253 & 0.6736 & 0.251936 \tabularnewline
10 & -0.113532 & -0.7783 & 0.220136 \tabularnewline
11 & -0.238379 & -1.6342 & 0.054445 \tabularnewline
12 & -0.448522 & -3.0749 & 0.001751 \tabularnewline
13 & -0.265099 & -1.8174 & 0.037765 \tabularnewline
14 & -0.177478 & -1.2167 & 0.114892 \tabularnewline
15 & 0.088161 & 0.6044 & 0.274241 \tabularnewline
16 & 0.074826 & 0.513 & 0.305183 \tabularnewline
17 & 0.159237 & 1.0917 & 0.14027 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63745&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]0.315984[/C][C]2.1663[/C][C]0.017697[/C][/ROW]
[ROW][C]2[/C][C]0.260015[/C][C]1.7826[/C][C]0.040558[/C][/ROW]
[ROW][C]3[/C][C]-0.401788[/C][C]-2.7545[/C][C]0.004167[/C][/ROW]
[ROW][C]4[/C][C]-0.248872[/C][C]-1.7062[/C][C]0.047288[/C][/ROW]
[ROW][C]5[/C][C]-0.245446[/C][C]-1.6827[/C][C]0.049534[/C][/ROW]
[ROW][C]6[/C][C]0.064707[/C][C]0.4436[/C][C]0.329681[/C][/ROW]
[ROW][C]7[/C][C]0.118675[/C][C]0.8136[/C][C]0.209989[/C][/ROW]
[ROW][C]8[/C][C]0.194245[/C][C]1.3317[/C][C]0.094694[/C][/ROW]
[ROW][C]9[/C][C]0.098253[/C][C]0.6736[/C][C]0.251936[/C][/ROW]
[ROW][C]10[/C][C]-0.113532[/C][C]-0.7783[/C][C]0.220136[/C][/ROW]
[ROW][C]11[/C][C]-0.238379[/C][C]-1.6342[/C][C]0.054445[/C][/ROW]
[ROW][C]12[/C][C]-0.448522[/C][C]-3.0749[/C][C]0.001751[/C][/ROW]
[ROW][C]13[/C][C]-0.265099[/C][C]-1.8174[/C][C]0.037765[/C][/ROW]
[ROW][C]14[/C][C]-0.177478[/C][C]-1.2167[/C][C]0.114892[/C][/ROW]
[ROW][C]15[/C][C]0.088161[/C][C]0.6044[/C][C]0.274241[/C][/ROW]
[ROW][C]16[/C][C]0.074826[/C][C]0.513[/C][C]0.305183[/C][/ROW]
[ROW][C]17[/C][C]0.159237[/C][C]1.0917[/C][C]0.14027[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63745&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63745&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	0.315984	2.1663	0.017697
2	0.260015	1.7826	0.040558
3	-0.401788	-2.7545	0.004167
4	-0.248872	-1.7062	0.047288
5	-0.245446	-1.6827	0.049534
6	0.064707	0.4436	0.329681
7	0.118675	0.8136	0.209989
8	0.194245	1.3317	0.094694
9	0.098253	0.6736	0.251936
10	-0.113532	-0.7783	0.220136
11	-0.238379	-1.6342	0.054445
12	-0.448522	-3.0749	0.001751
13	-0.265099	-1.8174	0.037765
14	-0.177478	-1.2167	0.114892
15	0.088161	0.6044	0.274241
16	0.074826	0.513	0.305183
17	0.159237	1.0917	0.14027

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.315984	2.1663	0.017697
2	0.177935	1.2199	0.114302
3	-0.602939	-4.1335	7.3e-05
4	0.003843	0.0263	0.489545
5	0.245701	1.6844	0.049364
6	-0.106914	-0.733	0.23361
7	-0.06697	-0.4591	0.324131
8	0.150682	1.033	0.15344
9	0.051734	0.3547	0.362212
10	-0.363601	-2.4927	0.008129
11	-0.132661	-0.9095	0.18387
12	-0.176339	-1.2089	0.11637
13	-0.144441	-0.9902	0.163564
14	-0.092556	-0.6345	0.264404
15	-0.200137	-1.3721	0.088278
16	-0.18999	-1.3025	0.099545
17	0.100684	0.6903	0.246715

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.315984 & 2.1663 & 0.017697 \tabularnewline
2 & 0.177935 & 1.2199 & 0.114302 \tabularnewline
3 & -0.602939 & -4.1335 & 7.3e-05 \tabularnewline
4 & 0.003843 & 0.0263 & 0.489545 \tabularnewline
5 & 0.245701 & 1.6844 & 0.049364 \tabularnewline
6 & -0.106914 & -0.733 & 0.23361 \tabularnewline
7 & -0.06697 & -0.4591 & 0.324131 \tabularnewline
8 & 0.150682 & 1.033 & 0.15344 \tabularnewline
9 & 0.051734 & 0.3547 & 0.362212 \tabularnewline
10 & -0.363601 & -2.4927 & 0.008129 \tabularnewline
11 & -0.132661 & -0.9095 & 0.18387 \tabularnewline
12 & -0.176339 & -1.2089 & 0.11637 \tabularnewline
13 & -0.144441 & -0.9902 & 0.163564 \tabularnewline
14 & -0.092556 & -0.6345 & 0.264404 \tabularnewline
15 & -0.200137 & -1.3721 & 0.088278 \tabularnewline
16 & -0.18999 & -1.3025 & 0.099545 \tabularnewline
17 & 0.100684 & 0.6903 & 0.246715 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63745&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]0.315984[/C][C]2.1663[/C][C]0.017697[/C][/ROW]
[ROW][C]2[/C][C]0.177935[/C][C]1.2199[/C][C]0.114302[/C][/ROW]
[ROW][C]3[/C][C]-0.602939[/C][C]-4.1335[/C][C]7.3e-05[/C][/ROW]
[ROW][C]4[/C][C]0.003843[/C][C]0.0263[/C][C]0.489545[/C][/ROW]
[ROW][C]5[/C][C]0.245701[/C][C]1.6844[/C][C]0.049364[/C][/ROW]
[ROW][C]6[/C][C]-0.106914[/C][C]-0.733[/C][C]0.23361[/C][/ROW]
[ROW][C]7[/C][C]-0.06697[/C][C]-0.4591[/C][C]0.324131[/C][/ROW]
[ROW][C]8[/C][C]0.150682[/C][C]1.033[/C][C]0.15344[/C][/ROW]
[ROW][C]9[/C][C]0.051734[/C][C]0.3547[/C][C]0.362212[/C][/ROW]
[ROW][C]10[/C][C]-0.363601[/C][C]-2.4927[/C][C]0.008129[/C][/ROW]
[ROW][C]11[/C][C]-0.132661[/C][C]-0.9095[/C][C]0.18387[/C][/ROW]
[ROW][C]12[/C][C]-0.176339[/C][C]-1.2089[/C][C]0.11637[/C][/ROW]
[ROW][C]13[/C][C]-0.144441[/C][C]-0.9902[/C][C]0.163564[/C][/ROW]
[ROW][C]14[/C][C]-0.092556[/C][C]-0.6345[/C][C]0.264404[/C][/ROW]
[ROW][C]15[/C][C]-0.200137[/C][C]-1.3721[/C][C]0.088278[/C][/ROW]
[ROW][C]16[/C][C]-0.18999[/C][C]-1.3025[/C][C]0.099545[/C][/ROW]
[ROW][C]17[/C][C]0.100684[/C][C]0.6903[/C][C]0.246715[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63745&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63745&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	0.315984	2.1663	0.017697
2	0.177935	1.2199	0.114302
3	-0.602939	-4.1335	7.3e-05
4	0.003843	0.0263	0.489545
5	0.245701	1.6844	0.049364
6	-0.106914	-0.733	0.23361
7	-0.06697	-0.4591	0.324131
8	0.150682	1.033	0.15344
9	0.051734	0.3547	0.362212
10	-0.363601	-2.4927	0.008129
11	-0.132661	-0.9095	0.18387
12	-0.176339	-1.2089	0.11637
13	-0.144441	-0.9902	0.163564
14	-0.092556	-0.6345	0.264404
15	-0.200137	-1.3721	0.088278
16	-0.18999	-1.3025	0.099545
17	0.100684	0.6903	0.246715

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 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

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 (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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
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 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

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code