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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 28 Nov 2007 03:54:05 -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/28/t1196246930iidyqf51lju41s3.htm/, Retrieved Thu, 02 May 2024 10:49:46 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7011, Retrieved Thu, 02 May 2024 10:49:46 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

202

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

-       [(Partial) Autocorrelation Function] [Inducing Stationa...] [2007-11-28 10:54:05] [157a0cf3c12a7482b4e6935b4c49d48f] [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=7011&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=7011&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7011&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	8.4853	0
1	0.939557	7.9724	0
2	0.89772	7.6174	0
3	0.86648	7.3523	0
4	0.806441	6.8429	0
5	0.746781	6.3366	0
6	0.709602	6.0212	0
7	0.67291	5.7098	0
8	0.621771	5.2759	1e-06
9	0.573385	4.8653	3e-06
10	0.526452	4.4671	1.4e-05
11	0.482063	4.0904	5.5e-05
12	0.431416	3.6607	0.000238
13	0.392739	3.3325	0.000681
14	0.362034	3.072	0.0015
15	0.343064	2.911	0.002396
16	0.309761	2.6284	0.00524
17	0.287342	2.4382	0.008615

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.4853 & 0 \tabularnewline
1 & 0.939557 & 7.9724 & 0 \tabularnewline
2 & 0.89772 & 7.6174 & 0 \tabularnewline
3 & 0.86648 & 7.3523 & 0 \tabularnewline
4 & 0.806441 & 6.8429 & 0 \tabularnewline
5 & 0.746781 & 6.3366 & 0 \tabularnewline
6 & 0.709602 & 6.0212 & 0 \tabularnewline
7 & 0.67291 & 5.7098 & 0 \tabularnewline
8 & 0.621771 & 5.2759 & 1e-06 \tabularnewline
9 & 0.573385 & 4.8653 & 3e-06 \tabularnewline
10 & 0.526452 & 4.4671 & 1.4e-05 \tabularnewline
11 & 0.482063 & 4.0904 & 5.5e-05 \tabularnewline
12 & 0.431416 & 3.6607 & 0.000238 \tabularnewline
13 & 0.392739 & 3.3325 & 0.000681 \tabularnewline
14 & 0.362034 & 3.072 & 0.0015 \tabularnewline
15 & 0.343064 & 2.911 & 0.002396 \tabularnewline
16 & 0.309761 & 2.6284 & 0.00524 \tabularnewline
17 & 0.287342 & 2.4382 & 0.008615 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7011&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]8.4853[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.939557[/C][C]7.9724[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.89772[/C][C]7.6174[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.86648[/C][C]7.3523[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.806441[/C][C]6.8429[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.746781[/C][C]6.3366[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.709602[/C][C]6.0212[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.67291[/C][C]5.7098[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.621771[/C][C]5.2759[/C][C]1e-06[/C][/ROW]
[ROW][C]9[/C][C]0.573385[/C][C]4.8653[/C][C]3e-06[/C][/ROW]
[ROW][C]10[/C][C]0.526452[/C][C]4.4671[/C][C]1.4e-05[/C][/ROW]
[ROW][C]11[/C][C]0.482063[/C][C]4.0904[/C][C]5.5e-05[/C][/ROW]
[ROW][C]12[/C][C]0.431416[/C][C]3.6607[/C][C]0.000238[/C][/ROW]
[ROW][C]13[/C][C]0.392739[/C][C]3.3325[/C][C]0.000681[/C][/ROW]
[ROW][C]14[/C][C]0.362034[/C][C]3.072[/C][C]0.0015[/C][/ROW]
[ROW][C]15[/C][C]0.343064[/C][C]2.911[/C][C]0.002396[/C][/ROW]
[ROW][C]16[/C][C]0.309761[/C][C]2.6284[/C][C]0.00524[/C][/ROW]
[ROW][C]17[/C][C]0.287342[/C][C]2.4382[/C][C]0.008615[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7011&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7011&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	8.4853	0
1	0.939557	7.9724	0
2	0.89772	7.6174	0
3	0.86648	7.3523	0
4	0.806441	6.8429	0
5	0.746781	6.3366	0
6	0.709602	6.0212	0
7	0.67291	5.7098	0
8	0.621771	5.2759	1e-06
9	0.573385	4.8653	3e-06
10	0.526452	4.4671	1.4e-05
11	0.482063	4.0904	5.5e-05
12	0.431416	3.6607	0.000238
13	0.392739	3.3325	0.000681
14	0.362034	3.072	0.0015
15	0.343064	2.911	0.002396
16	0.309761	2.6284	0.00524
17	0.287342	2.4382	0.008615

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.939557	7.9724	0
1	0.127545	1.0823	0.141374
2	0.093343	0.792	0.215468
3	-0.236412	-2.006	0.975694
4	-0.095041	-0.8065	0.788681
5	0.122813	1.0421	0.150426
6	0.09125	0.7743	0.220651
7	-0.105557	-0.8957	0.813295
8	-0.123546	-1.0483	0.851003
9	-0.074394	-0.6313	0.735064
10	0.079614	0.6755	0.250747
11	-0.022609	-0.1918	0.575799
12	0.034864	0.2958	0.384106
13	0.010429	0.0885	0.464867
14	0.142963	1.2131	0.114532
15	-0.119436	-1.0134	0.84288
16	0.007776	0.066	0.473789
17	-0.107628	-0.9133	0.817921

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.939557 & 7.9724 & 0 \tabularnewline
1 & 0.127545 & 1.0823 & 0.141374 \tabularnewline
2 & 0.093343 & 0.792 & 0.215468 \tabularnewline
3 & -0.236412 & -2.006 & 0.975694 \tabularnewline
4 & -0.095041 & -0.8065 & 0.788681 \tabularnewline
5 & 0.122813 & 1.0421 & 0.150426 \tabularnewline
6 & 0.09125 & 0.7743 & 0.220651 \tabularnewline
7 & -0.105557 & -0.8957 & 0.813295 \tabularnewline
8 & -0.123546 & -1.0483 & 0.851003 \tabularnewline
9 & -0.074394 & -0.6313 & 0.735064 \tabularnewline
10 & 0.079614 & 0.6755 & 0.250747 \tabularnewline
11 & -0.022609 & -0.1918 & 0.575799 \tabularnewline
12 & 0.034864 & 0.2958 & 0.384106 \tabularnewline
13 & 0.010429 & 0.0885 & 0.464867 \tabularnewline
14 & 0.142963 & 1.2131 & 0.114532 \tabularnewline
15 & -0.119436 & -1.0134 & 0.84288 \tabularnewline
16 & 0.007776 & 0.066 & 0.473789 \tabularnewline
17 & -0.107628 & -0.9133 & 0.817921 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7011&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]0.939557[/C][C]7.9724[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.127545[/C][C]1.0823[/C][C]0.141374[/C][/ROW]
[ROW][C]2[/C][C]0.093343[/C][C]0.792[/C][C]0.215468[/C][/ROW]
[ROW][C]3[/C][C]-0.236412[/C][C]-2.006[/C][C]0.975694[/C][/ROW]
[ROW][C]4[/C][C]-0.095041[/C][C]-0.8065[/C][C]0.788681[/C][/ROW]
[ROW][C]5[/C][C]0.122813[/C][C]1.0421[/C][C]0.150426[/C][/ROW]
[ROW][C]6[/C][C]0.09125[/C][C]0.7743[/C][C]0.220651[/C][/ROW]
[ROW][C]7[/C][C]-0.105557[/C][C]-0.8957[/C][C]0.813295[/C][/ROW]
[ROW][C]8[/C][C]-0.123546[/C][C]-1.0483[/C][C]0.851003[/C][/ROW]
[ROW][C]9[/C][C]-0.074394[/C][C]-0.6313[/C][C]0.735064[/C][/ROW]
[ROW][C]10[/C][C]0.079614[/C][C]0.6755[/C][C]0.250747[/C][/ROW]
[ROW][C]11[/C][C]-0.022609[/C][C]-0.1918[/C][C]0.575799[/C][/ROW]
[ROW][C]12[/C][C]0.034864[/C][C]0.2958[/C][C]0.384106[/C][/ROW]
[ROW][C]13[/C][C]0.010429[/C][C]0.0885[/C][C]0.464867[/C][/ROW]
[ROW][C]14[/C][C]0.142963[/C][C]1.2131[/C][C]0.114532[/C][/ROW]
[ROW][C]15[/C][C]-0.119436[/C][C]-1.0134[/C][C]0.84288[/C][/ROW]
[ROW][C]16[/C][C]0.007776[/C][C]0.066[/C][C]0.473789[/C][/ROW]
[ROW][C]17[/C][C]-0.107628[/C][C]-0.9133[/C][C]0.817921[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7011&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7011&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	0.939557	7.9724	0
1	0.127545	1.0823	0.141374
2	0.093343	0.792	0.215468
3	-0.236412	-2.006	0.975694
4	-0.095041	-0.8065	0.788681
5	0.122813	1.0421	0.150426
6	0.09125	0.7743	0.220651
7	-0.105557	-0.8957	0.813295
8	-0.123546	-1.0483	0.851003
9	-0.074394	-0.6313	0.735064
10	0.079614	0.6755	0.250747
11	-0.022609	-0.1918	0.575799
12	0.034864	0.2958	0.384106
13	0.010429	0.0885	0.464867
14	0.142963	1.2131	0.114532
15	-0.119436	-1.0134	0.84288
16	0.007776	0.066	0.473789
17	-0.107628	-0.9133	0.817921

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = -1.2 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = -1.2 ; 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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