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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 02 Jun 2009 09:16:03 -0600

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/Jun/02/t1243955778m35knvc3nyz6gkx.htm/, Retrieved Fri, 10 May 2024 18:46:30 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41265, Retrieved Fri, 10 May 2024 18:46:30 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

123

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

-     [Standard Deviation Plot] [] [2009-06-01 15:27:11] [5c738c8b19699587b9bfe8605ebf60ee]
- RMPD    [(Partial) Autocorrelation Function] [] [2009-06-02 15:16:03] [738a25b0d97c8f3fa6714f905e8e3fd3] [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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
R Framework error message & Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values. \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41265&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[ROW][C]R Framework error message[/C][C]Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41265&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41265&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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.244052	-1.6731	0.050472
2	-0.358128	-2.4552	0.008918
3	0.094952	0.651	0.259121
4	-0.216832	-1.4865	0.071909
5	0.171211	1.1738	0.123202
6	0.122756	0.8416	0.202145
7	0.086017	0.5897	0.279108
8	-0.05809	-0.3982	0.346127
9	-0.083346	-0.5714	0.285229
10	-0.241795	-1.6577	0.052023
11	-0.063754	-0.4371	0.332029
12	0.606419	4.1574	6.8e-05
13	-0.102863	-0.7052	0.242085
14	-0.279527	-1.9163	0.030707
15	0.001593	0.0109	0.495666
16	-0.069433	-0.476	0.318136

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.244052 & -1.6731 & 0.050472 \tabularnewline
2 & -0.358128 & -2.4552 & 0.008918 \tabularnewline
3 & 0.094952 & 0.651 & 0.259121 \tabularnewline
4 & -0.216832 & -1.4865 & 0.071909 \tabularnewline
5 & 0.171211 & 1.1738 & 0.123202 \tabularnewline
6 & 0.122756 & 0.8416 & 0.202145 \tabularnewline
7 & 0.086017 & 0.5897 & 0.279108 \tabularnewline
8 & -0.05809 & -0.3982 & 0.346127 \tabularnewline
9 & -0.083346 & -0.5714 & 0.285229 \tabularnewline
10 & -0.241795 & -1.6577 & 0.052023 \tabularnewline
11 & -0.063754 & -0.4371 & 0.332029 \tabularnewline
12 & 0.606419 & 4.1574 & 6.8e-05 \tabularnewline
13 & -0.102863 & -0.7052 & 0.242085 \tabularnewline
14 & -0.279527 & -1.9163 & 0.030707 \tabularnewline
15 & 0.001593 & 0.0109 & 0.495666 \tabularnewline
16 & -0.069433 & -0.476 & 0.318136 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41265&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]-0.244052[/C][C]-1.6731[/C][C]0.050472[/C][/ROW]
[ROW][C]2[/C][C]-0.358128[/C][C]-2.4552[/C][C]0.008918[/C][/ROW]
[ROW][C]3[/C][C]0.094952[/C][C]0.651[/C][C]0.259121[/C][/ROW]
[ROW][C]4[/C][C]-0.216832[/C][C]-1.4865[/C][C]0.071909[/C][/ROW]
[ROW][C]5[/C][C]0.171211[/C][C]1.1738[/C][C]0.123202[/C][/ROW]
[ROW][C]6[/C][C]0.122756[/C][C]0.8416[/C][C]0.202145[/C][/ROW]
[ROW][C]7[/C][C]0.086017[/C][C]0.5897[/C][C]0.279108[/C][/ROW]
[ROW][C]8[/C][C]-0.05809[/C][C]-0.3982[/C][C]0.346127[/C][/ROW]
[ROW][C]9[/C][C]-0.083346[/C][C]-0.5714[/C][C]0.285229[/C][/ROW]
[ROW][C]10[/C][C]-0.241795[/C][C]-1.6577[/C][C]0.052023[/C][/ROW]
[ROW][C]11[/C][C]-0.063754[/C][C]-0.4371[/C][C]0.332029[/C][/ROW]
[ROW][C]12[/C][C]0.606419[/C][C]4.1574[/C][C]6.8e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.102863[/C][C]-0.7052[/C][C]0.242085[/C][/ROW]
[ROW][C]14[/C][C]-0.279527[/C][C]-1.9163[/C][C]0.030707[/C][/ROW]
[ROW][C]15[/C][C]0.001593[/C][C]0.0109[/C][C]0.495666[/C][/ROW]
[ROW][C]16[/C][C]-0.069433[/C][C]-0.476[/C][C]0.318136[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41265&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41265&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	-0.244052	-1.6731	0.050472
2	-0.358128	-2.4552	0.008918
3	0.094952	0.651	0.259121
4	-0.216832	-1.4865	0.071909
5	0.171211	1.1738	0.123202
6	0.122756	0.8416	0.202145
7	0.086017	0.5897	0.279108
8	-0.05809	-0.3982	0.346127
9	-0.083346	-0.5714	0.285229
10	-0.241795	-1.6577	0.052023
11	-0.063754	-0.4371	0.332029
12	0.606419	4.1574	6.8e-05
13	-0.102863	-0.7052	0.242085
14	-0.279527	-1.9163	0.030707
15	0.001593	0.0109	0.495666
16	-0.069433	-0.476	0.318136

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.244052	-1.6731	0.050472
2	-0.444143	-3.0449	0.001904
3	-0.185002	-1.2683	0.105467
4	-0.552919	-3.7906	0.000214
5	-0.310867	-2.1312	0.019166
6	-0.49422	-3.3882	0.000716
7	-0.151443	-1.0382	0.152234
8	-0.217619	-1.4919	0.071201
9	0.315893	2.1657	0.017722
10	-0.198112	-1.3582	0.090444
11	-0.397995	-2.7285	0.00446
12	-0.028645	-0.1964	0.42258
13	0.013741	0.0942	0.462673
14	0.00138	0.0095	0.496246
15	-0.227803	-1.5617	0.062529
16	0.029782	0.2042	0.41955

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.244052 & -1.6731 & 0.050472 \tabularnewline
2 & -0.444143 & -3.0449 & 0.001904 \tabularnewline
3 & -0.185002 & -1.2683 & 0.105467 \tabularnewline
4 & -0.552919 & -3.7906 & 0.000214 \tabularnewline
5 & -0.310867 & -2.1312 & 0.019166 \tabularnewline
6 & -0.49422 & -3.3882 & 0.000716 \tabularnewline
7 & -0.151443 & -1.0382 & 0.152234 \tabularnewline
8 & -0.217619 & -1.4919 & 0.071201 \tabularnewline
9 & 0.315893 & 2.1657 & 0.017722 \tabularnewline
10 & -0.198112 & -1.3582 & 0.090444 \tabularnewline
11 & -0.397995 & -2.7285 & 0.00446 \tabularnewline
12 & -0.028645 & -0.1964 & 0.42258 \tabularnewline
13 & 0.013741 & 0.0942 & 0.462673 \tabularnewline
14 & 0.00138 & 0.0095 & 0.496246 \tabularnewline
15 & -0.227803 & -1.5617 & 0.062529 \tabularnewline
16 & 0.029782 & 0.2042 & 0.41955 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41265&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]-0.244052[/C][C]-1.6731[/C][C]0.050472[/C][/ROW]
[ROW][C]2[/C][C]-0.444143[/C][C]-3.0449[/C][C]0.001904[/C][/ROW]
[ROW][C]3[/C][C]-0.185002[/C][C]-1.2683[/C][C]0.105467[/C][/ROW]
[ROW][C]4[/C][C]-0.552919[/C][C]-3.7906[/C][C]0.000214[/C][/ROW]
[ROW][C]5[/C][C]-0.310867[/C][C]-2.1312[/C][C]0.019166[/C][/ROW]
[ROW][C]6[/C][C]-0.49422[/C][C]-3.3882[/C][C]0.000716[/C][/ROW]
[ROW][C]7[/C][C]-0.151443[/C][C]-1.0382[/C][C]0.152234[/C][/ROW]
[ROW][C]8[/C][C]-0.217619[/C][C]-1.4919[/C][C]0.071201[/C][/ROW]
[ROW][C]9[/C][C]0.315893[/C][C]2.1657[/C][C]0.017722[/C][/ROW]
[ROW][C]10[/C][C]-0.198112[/C][C]-1.3582[/C][C]0.090444[/C][/ROW]
[ROW][C]11[/C][C]-0.397995[/C][C]-2.7285[/C][C]0.00446[/C][/ROW]
[ROW][C]12[/C][C]-0.028645[/C][C]-0.1964[/C][C]0.42258[/C][/ROW]
[ROW][C]13[/C][C]0.013741[/C][C]0.0942[/C][C]0.462673[/C][/ROW]
[ROW][C]14[/C][C]0.00138[/C][C]0.0095[/C][C]0.496246[/C][/ROW]
[ROW][C]15[/C][C]-0.227803[/C][C]-1.5617[/C][C]0.062529[/C][/ROW]
[ROW][C]16[/C][C]0.029782[/C][C]0.2042[/C][C]0.41955[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41265&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41265&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	-0.244052	-1.6731	0.050472
2	-0.444143	-3.0449	0.001904
3	-0.185002	-1.2683	0.105467
4	-0.552919	-3.7906	0.000214
5	-0.310867	-2.1312	0.019166
6	-0.49422	-3.3882	0.000716
7	-0.151443	-1.0382	0.152234
8	-0.217619	-1.4919	0.071201
9	0.315893	2.1657	0.017722
10	-0.198112	-1.3582	0.090444
11	-0.397995	-2.7285	0.00446
12	-0.028645	-0.1964	0.42258
13	0.013741	0.0942	0.462673
14	0.00138	0.0095	0.496246
15	-0.227803	-1.5617	0.062529
16	0.029782	0.2042	0.41955

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 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')

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