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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 04 Dec 2007 14:39:06 -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/2007/Dec/04/t1196803619vc6qht6d8zlfvkf.htm/, Retrieved Thu, 16 Jan 2025 17:44:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2453, Retrieved Thu, 16 Jan 2025 17:44:29 +0000

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Estimated Impact

217

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

-       [(Partial) Autocorrelation Function] [] [2007-12-04 21:39:06] [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	'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=2453&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=2453&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2453&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	9.5394	0
1	-0.265325	-2.531	0.993455
2	-0.258423	-2.4652	0.992215
3	0.147274	1.4049	0.081727
4	0.119664	1.1415	0.128325
5	-0.258329	-2.4643	0.992197
6	-0.00565	-0.0539	0.521431
7	0.071943	0.6863	0.247136
8	-0.017348	-0.1655	0.565536
9	-0.164462	-1.5689	0.939925
10	0.087533	0.835	0.202949
11	0.093177	0.8889	0.188212
12	-0.051646	-0.4927	0.688284
13	0.004908	0.0468	0.481379
14	0.282899	2.6987	0.004149
15	-0.320935	-3.0615	0.998553
16	0.111894	1.0674	0.144307
17	-0.02247	-0.2143	0.584622
18	-0.054509	-0.52	0.697832

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 9.5394 & 0 \tabularnewline
1 & -0.265325 & -2.531 & 0.993455 \tabularnewline
2 & -0.258423 & -2.4652 & 0.992215 \tabularnewline
3 & 0.147274 & 1.4049 & 0.081727 \tabularnewline
4 & 0.119664 & 1.1415 & 0.128325 \tabularnewline
5 & -0.258329 & -2.4643 & 0.992197 \tabularnewline
6 & -0.00565 & -0.0539 & 0.521431 \tabularnewline
7 & 0.071943 & 0.6863 & 0.247136 \tabularnewline
8 & -0.017348 & -0.1655 & 0.565536 \tabularnewline
9 & -0.164462 & -1.5689 & 0.939925 \tabularnewline
10 & 0.087533 & 0.835 & 0.202949 \tabularnewline
11 & 0.093177 & 0.8889 & 0.188212 \tabularnewline
12 & -0.051646 & -0.4927 & 0.688284 \tabularnewline
13 & 0.004908 & 0.0468 & 0.481379 \tabularnewline
14 & 0.282899 & 2.6987 & 0.004149 \tabularnewline
15 & -0.320935 & -3.0615 & 0.998553 \tabularnewline
16 & 0.111894 & 1.0674 & 0.144307 \tabularnewline
17 & -0.02247 & -0.2143 & 0.584622 \tabularnewline
18 & -0.054509 & -0.52 & 0.697832 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2453&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]9.5394[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.265325[/C][C]-2.531[/C][C]0.993455[/C][/ROW]
[ROW][C]2[/C][C]-0.258423[/C][C]-2.4652[/C][C]0.992215[/C][/ROW]
[ROW][C]3[/C][C]0.147274[/C][C]1.4049[/C][C]0.081727[/C][/ROW]
[ROW][C]4[/C][C]0.119664[/C][C]1.1415[/C][C]0.128325[/C][/ROW]
[ROW][C]5[/C][C]-0.258329[/C][C]-2.4643[/C][C]0.992197[/C][/ROW]
[ROW][C]6[/C][C]-0.00565[/C][C]-0.0539[/C][C]0.521431[/C][/ROW]
[ROW][C]7[/C][C]0.071943[/C][C]0.6863[/C][C]0.247136[/C][/ROW]
[ROW][C]8[/C][C]-0.017348[/C][C]-0.1655[/C][C]0.565536[/C][/ROW]
[ROW][C]9[/C][C]-0.164462[/C][C]-1.5689[/C][C]0.939925[/C][/ROW]
[ROW][C]10[/C][C]0.087533[/C][C]0.835[/C][C]0.202949[/C][/ROW]
[ROW][C]11[/C][C]0.093177[/C][C]0.8889[/C][C]0.188212[/C][/ROW]
[ROW][C]12[/C][C]-0.051646[/C][C]-0.4927[/C][C]0.688284[/C][/ROW]
[ROW][C]13[/C][C]0.004908[/C][C]0.0468[/C][C]0.481379[/C][/ROW]
[ROW][C]14[/C][C]0.282899[/C][C]2.6987[/C][C]0.004149[/C][/ROW]
[ROW][C]15[/C][C]-0.320935[/C][C]-3.0615[/C][C]0.998553[/C][/ROW]
[ROW][C]16[/C][C]0.111894[/C][C]1.0674[/C][C]0.144307[/C][/ROW]
[ROW][C]17[/C][C]-0.02247[/C][C]-0.2143[/C][C]0.584622[/C][/ROW]
[ROW][C]18[/C][C]-0.054509[/C][C]-0.52[/C][C]0.697832[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2453&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2453&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	9.5394	0
1	-0.265325	-2.531	0.993455
2	-0.258423	-2.4652	0.992215
3	0.147274	1.4049	0.081727
4	0.119664	1.1415	0.128325
5	-0.258329	-2.4643	0.992197
6	-0.00565	-0.0539	0.521431
7	0.071943	0.6863	0.247136
8	-0.017348	-0.1655	0.565536
9	-0.164462	-1.5689	0.939925
10	0.087533	0.835	0.202949
11	0.093177	0.8889	0.188212
12	-0.051646	-0.4927	0.688284
13	0.004908	0.0468	0.481379
14	0.282899	2.6987	0.004149
15	-0.320935	-3.0615	0.998553
16	0.111894	1.0674	0.144307
17	-0.02247	-0.2143	0.584622
18	-0.054509	-0.52	0.697832

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	-0.265325	-2.531	0.993455
1	-0.353721	-3.3743	0.999455
2	-0.04844	-0.4621	0.67744
3	0.081745	0.7798	0.218768
4	-0.181725	-1.7335	0.956807
5	-0.115085	-1.0978	0.862414
6	-0.120138	-1.146	0.87261
7	-0.059496	-0.5676	0.714131
8	-0.196484	-1.8743	0.967954
9	-0.110476	-1.0539	0.852635
10	-0.037576	-0.3584	0.639581
11	-0.036516	-0.3483	0.635806
12	0.00905	0.0863	0.465695
13	0.280432	2.6752	0.004428
14	-0.19621	-1.8717	0.967771
15	0.156892	1.4967	0.068971
16	-0.154366	-1.4726	0.92784
17	-0.056768	-0.5415	0.705268
18	0.01031	0.0984	0.460934

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & -0.265325 & -2.531 & 0.993455 \tabularnewline
1 & -0.353721 & -3.3743 & 0.999455 \tabularnewline
2 & -0.04844 & -0.4621 & 0.67744 \tabularnewline
3 & 0.081745 & 0.7798 & 0.218768 \tabularnewline
4 & -0.181725 & -1.7335 & 0.956807 \tabularnewline
5 & -0.115085 & -1.0978 & 0.862414 \tabularnewline
6 & -0.120138 & -1.146 & 0.87261 \tabularnewline
7 & -0.059496 & -0.5676 & 0.714131 \tabularnewline
8 & -0.196484 & -1.8743 & 0.967954 \tabularnewline
9 & -0.110476 & -1.0539 & 0.852635 \tabularnewline
10 & -0.037576 & -0.3584 & 0.639581 \tabularnewline
11 & -0.036516 & -0.3483 & 0.635806 \tabularnewline
12 & 0.00905 & 0.0863 & 0.465695 \tabularnewline
13 & 0.280432 & 2.6752 & 0.004428 \tabularnewline
14 & -0.19621 & -1.8717 & 0.967771 \tabularnewline
15 & 0.156892 & 1.4967 & 0.068971 \tabularnewline
16 & -0.154366 & -1.4726 & 0.92784 \tabularnewline
17 & -0.056768 & -0.5415 & 0.705268 \tabularnewline
18 & 0.01031 & 0.0984 & 0.460934 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2453&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]-0.265325[/C][C]-2.531[/C][C]0.993455[/C][/ROW]
[ROW][C]1[/C][C]-0.353721[/C][C]-3.3743[/C][C]0.999455[/C][/ROW]
[ROW][C]2[/C][C]-0.04844[/C][C]-0.4621[/C][C]0.67744[/C][/ROW]
[ROW][C]3[/C][C]0.081745[/C][C]0.7798[/C][C]0.218768[/C][/ROW]
[ROW][C]4[/C][C]-0.181725[/C][C]-1.7335[/C][C]0.956807[/C][/ROW]
[ROW][C]5[/C][C]-0.115085[/C][C]-1.0978[/C][C]0.862414[/C][/ROW]
[ROW][C]6[/C][C]-0.120138[/C][C]-1.146[/C][C]0.87261[/C][/ROW]
[ROW][C]7[/C][C]-0.059496[/C][C]-0.5676[/C][C]0.714131[/C][/ROW]
[ROW][C]8[/C][C]-0.196484[/C][C]-1.8743[/C][C]0.967954[/C][/ROW]
[ROW][C]9[/C][C]-0.110476[/C][C]-1.0539[/C][C]0.852635[/C][/ROW]
[ROW][C]10[/C][C]-0.037576[/C][C]-0.3584[/C][C]0.639581[/C][/ROW]
[ROW][C]11[/C][C]-0.036516[/C][C]-0.3483[/C][C]0.635806[/C][/ROW]
[ROW][C]12[/C][C]0.00905[/C][C]0.0863[/C][C]0.465695[/C][/ROW]
[ROW][C]13[/C][C]0.280432[/C][C]2.6752[/C][C]0.004428[/C][/ROW]
[ROW][C]14[/C][C]-0.19621[/C][C]-1.8717[/C][C]0.967771[/C][/ROW]
[ROW][C]15[/C][C]0.156892[/C][C]1.4967[/C][C]0.068971[/C][/ROW]
[ROW][C]16[/C][C]-0.154366[/C][C]-1.4726[/C][C]0.92784[/C][/ROW]
[ROW][C]17[/C][C]-0.056768[/C][C]-0.5415[/C][C]0.705268[/C][/ROW]
[ROW][C]18[/C][C]0.01031[/C][C]0.0984[/C][C]0.460934[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2453&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2453&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	-0.265325	-2.531	0.993455
1	-0.353721	-3.3743	0.999455
2	-0.04844	-0.4621	0.67744
3	0.081745	0.7798	0.218768
4	-0.181725	-1.7335	0.956807
5	-0.115085	-1.0978	0.862414
6	-0.120138	-1.146	0.87261
7	-0.059496	-0.5676	0.714131
8	-0.196484	-1.8743	0.967954
9	-0.110476	-1.0539	0.852635
10	-0.037576	-0.3584	0.639581
11	-0.036516	-0.3483	0.635806
12	0.00905	0.0863	0.465695
13	0.280432	2.6752	0.004428
14	-0.19621	-1.8717	0.967771
15	0.156892	1.4967	0.068971
16	-0.154366	-1.4726	0.92784
17	-0.056768	-0.5415	0.705268
18	0.01031	0.0984	0.460934

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 2 ; 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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