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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 26 Nov 2007 13:26:31 -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/Nov/26/t119610820991r483ph35u0upz.htm/, Retrieved Thu, 02 May 2024 17:12:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6682, Retrieved Thu, 02 May 2024 17:12:39 +0000

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No (this computation is public)

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Estimated Impact

167

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-       [(Partial) Autocorrelation Function] [] [2007-11-26 20:26:31] [a5d60d21ad00400c5f1209c78aa5829c] [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	1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6682&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]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=6682&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6682&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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	9.6954	0
1	0.903464	8.7594	0
2	0.830542	8.0524	0
3	0.767693	7.4431	0
4	0.686678	6.6576	0
5	0.627079	6.0798	0
6	0.58176	5.6404	0
7	0.523956	5.0799	1e-06
8	0.457255	4.4333	1.3e-05
9	0.393922	3.8192	0.00012
10	0.330887	3.2081	0.000914
11	0.269708	2.6149	0.005198
12	0.218975	2.123	0.018189
13	0.197022	1.9102	0.029578
14	0.184891	1.7926	0.038128
15	0.157594	1.5279	0.064943
16	0.138164	1.3396	0.091811
17	0.103434	1.0028	0.159259
18	0.079593	0.7717	0.22112

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 9.6954 & 0 \tabularnewline
1 & 0.903464 & 8.7594 & 0 \tabularnewline
2 & 0.830542 & 8.0524 & 0 \tabularnewline
3 & 0.767693 & 7.4431 & 0 \tabularnewline
4 & 0.686678 & 6.6576 & 0 \tabularnewline
5 & 0.627079 & 6.0798 & 0 \tabularnewline
6 & 0.58176 & 5.6404 & 0 \tabularnewline
7 & 0.523956 & 5.0799 & 1e-06 \tabularnewline
8 & 0.457255 & 4.4333 & 1.3e-05 \tabularnewline
9 & 0.393922 & 3.8192 & 0.00012 \tabularnewline
10 & 0.330887 & 3.2081 & 0.000914 \tabularnewline
11 & 0.269708 & 2.6149 & 0.005198 \tabularnewline
12 & 0.218975 & 2.123 & 0.018189 \tabularnewline
13 & 0.197022 & 1.9102 & 0.029578 \tabularnewline
14 & 0.184891 & 1.7926 & 0.038128 \tabularnewline
15 & 0.157594 & 1.5279 & 0.064943 \tabularnewline
16 & 0.138164 & 1.3396 & 0.091811 \tabularnewline
17 & 0.103434 & 1.0028 & 0.159259 \tabularnewline
18 & 0.079593 & 0.7717 & 0.22112 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6682&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]9.6954[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.903464[/C][C]8.7594[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.830542[/C][C]8.0524[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.767693[/C][C]7.4431[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.686678[/C][C]6.6576[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.627079[/C][C]6.0798[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.58176[/C][C]5.6404[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.523956[/C][C]5.0799[/C][C]1e-06[/C][/ROW]
[ROW][C]8[/C][C]0.457255[/C][C]4.4333[/C][C]1.3e-05[/C][/ROW]
[ROW][C]9[/C][C]0.393922[/C][C]3.8192[/C][C]0.00012[/C][/ROW]
[ROW][C]10[/C][C]0.330887[/C][C]3.2081[/C][C]0.000914[/C][/ROW]
[ROW][C]11[/C][C]0.269708[/C][C]2.6149[/C][C]0.005198[/C][/ROW]
[ROW][C]12[/C][C]0.218975[/C][C]2.123[/C][C]0.018189[/C][/ROW]
[ROW][C]13[/C][C]0.197022[/C][C]1.9102[/C][C]0.029578[/C][/ROW]
[ROW][C]14[/C][C]0.184891[/C][C]1.7926[/C][C]0.038128[/C][/ROW]
[ROW][C]15[/C][C]0.157594[/C][C]1.5279[/C][C]0.064943[/C][/ROW]
[ROW][C]16[/C][C]0.138164[/C][C]1.3396[/C][C]0.091811[/C][/ROW]
[ROW][C]17[/C][C]0.103434[/C][C]1.0028[/C][C]0.159259[/C][/ROW]
[ROW][C]18[/C][C]0.079593[/C][C]0.7717[/C][C]0.22112[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6682&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6682&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	9.6954	0
1	0.903464	8.7594	0
2	0.830542	8.0524	0
3	0.767693	7.4431	0
4	0.686678	6.6576	0
5	0.627079	6.0798	0
6	0.58176	5.6404	0
7	0.523956	5.0799	1e-06
8	0.457255	4.4333	1.3e-05
9	0.393922	3.8192	0.00012
10	0.330887	3.2081	0.000914
11	0.269708	2.6149	0.005198
12	0.218975	2.123	0.018189
13	0.197022	1.9102	0.029578
14	0.184891	1.7926	0.038128
15	0.157594	1.5279	0.064943
16	0.138164	1.3396	0.091811
17	0.103434	1.0028	0.159259
18	0.079593	0.7717	0.22112

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.903464	8.7594	0
1	0.077793	0.7542	0.226298
2	0.029669	0.2877	0.387122
3	-0.1209	-1.1722	0.877954
4	0.053169	0.5155	0.303708
5	0.056426	0.5471	0.292814
6	-0.062367	-0.6047	0.726573
7	-0.108096	-1.048	0.851344
8	-0.047529	-0.4608	0.677002
9	-0.021753	-0.2109	0.583291
10	-0.026632	-0.2582	0.601595
11	-0.006746	-0.0654	0.526004
12	0.124491	1.207	0.115234
13	0.08052	0.7807	0.218478
14	-0.076085	-0.7377	0.768723
15	-0.012466	-0.1209	0.547971
16	-0.08597	-0.8335	0.796666
17	0.059366	0.5756	0.283139
18	-0.045158	-0.4378	0.668741

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.903464 & 8.7594 & 0 \tabularnewline
1 & 0.077793 & 0.7542 & 0.226298 \tabularnewline
2 & 0.029669 & 0.2877 & 0.387122 \tabularnewline
3 & -0.1209 & -1.1722 & 0.877954 \tabularnewline
4 & 0.053169 & 0.5155 & 0.303708 \tabularnewline
5 & 0.056426 & 0.5471 & 0.292814 \tabularnewline
6 & -0.062367 & -0.6047 & 0.726573 \tabularnewline
7 & -0.108096 & -1.048 & 0.851344 \tabularnewline
8 & -0.047529 & -0.4608 & 0.677002 \tabularnewline
9 & -0.021753 & -0.2109 & 0.583291 \tabularnewline
10 & -0.026632 & -0.2582 & 0.601595 \tabularnewline
11 & -0.006746 & -0.0654 & 0.526004 \tabularnewline
12 & 0.124491 & 1.207 & 0.115234 \tabularnewline
13 & 0.08052 & 0.7807 & 0.218478 \tabularnewline
14 & -0.076085 & -0.7377 & 0.768723 \tabularnewline
15 & -0.012466 & -0.1209 & 0.547971 \tabularnewline
16 & -0.08597 & -0.8335 & 0.796666 \tabularnewline
17 & 0.059366 & 0.5756 & 0.283139 \tabularnewline
18 & -0.045158 & -0.4378 & 0.668741 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6682&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]0.903464[/C][C]8.7594[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.077793[/C][C]0.7542[/C][C]0.226298[/C][/ROW]
[ROW][C]2[/C][C]0.029669[/C][C]0.2877[/C][C]0.387122[/C][/ROW]
[ROW][C]3[/C][C]-0.1209[/C][C]-1.1722[/C][C]0.877954[/C][/ROW]
[ROW][C]4[/C][C]0.053169[/C][C]0.5155[/C][C]0.303708[/C][/ROW]
[ROW][C]5[/C][C]0.056426[/C][C]0.5471[/C][C]0.292814[/C][/ROW]
[ROW][C]6[/C][C]-0.062367[/C][C]-0.6047[/C][C]0.726573[/C][/ROW]
[ROW][C]7[/C][C]-0.108096[/C][C]-1.048[/C][C]0.851344[/C][/ROW]
[ROW][C]8[/C][C]-0.047529[/C][C]-0.4608[/C][C]0.677002[/C][/ROW]
[ROW][C]9[/C][C]-0.021753[/C][C]-0.2109[/C][C]0.583291[/C][/ROW]
[ROW][C]10[/C][C]-0.026632[/C][C]-0.2582[/C][C]0.601595[/C][/ROW]
[ROW][C]11[/C][C]-0.006746[/C][C]-0.0654[/C][C]0.526004[/C][/ROW]
[ROW][C]12[/C][C]0.124491[/C][C]1.207[/C][C]0.115234[/C][/ROW]
[ROW][C]13[/C][C]0.08052[/C][C]0.7807[/C][C]0.218478[/C][/ROW]
[ROW][C]14[/C][C]-0.076085[/C][C]-0.7377[/C][C]0.768723[/C][/ROW]
[ROW][C]15[/C][C]-0.012466[/C][C]-0.1209[/C][C]0.547971[/C][/ROW]
[ROW][C]16[/C][C]-0.08597[/C][C]-0.8335[/C][C]0.796666[/C][/ROW]
[ROW][C]17[/C][C]0.059366[/C][C]0.5756[/C][C]0.283139[/C][/ROW]
[ROW][C]18[/C][C]-0.045158[/C][C]-0.4378[/C][C]0.668741[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6682&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6682&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	0.903464	8.7594	0
1	0.077793	0.7542	0.226298
2	0.029669	0.2877	0.387122
3	-0.1209	-1.1722	0.877954
4	0.053169	0.5155	0.303708
5	0.056426	0.5471	0.292814
6	-0.062367	-0.6047	0.726573
7	-0.108096	-1.048	0.851344
8	-0.047529	-0.4608	0.677002
9	-0.021753	-0.2109	0.583291
10	-0.026632	-0.2582	0.601595
11	-0.006746	-0.0654	0.526004
12	0.124491	1.207	0.115234
13	0.08052	0.7807	0.218478
14	-0.076085	-0.7377	0.768723
15	-0.012466	-0.1209	0.547971
16	-0.08597	-0.8335	0.796666
17	0.059366	0.5756	0.283139
18	-0.045158	-0.4378	0.668741

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 = 0 ; par5 = 12 ;

Parameters (R input):

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