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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 13 Dec 2007 02:24:31 -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/Dec/13/t1197536978h8oin57y4ew53o1.htm/, Retrieved Sun, 05 May 2024 19:10:13 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3334, Retrieved Sun, 05 May 2024 19:10:13 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

186

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

-       [(Partial) Autocorrelation Function] [Paper (P)ACF tijd...] [2007-12-13 09:24:31] [cb172450b25aceeff04d58e88e905157] [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	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3334&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3334&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3334&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	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	7.6811	0
1	0.289068	2.2204	0.015123
2	-0.153902	-1.1821	0.879054
3	-0.186322	-1.4312	0.921171
4	0.088895	0.6828	0.248697
5	0.038393	0.2949	0.384553
6	-0.155196	-1.1921	0.880999
7	-0.049524	-0.3804	0.647494
8	0.074516	0.5724	0.284624
9	0.075827	0.5824	0.281244
10	0.057577	0.4423	0.329959
11	0.022039	0.1693	0.433075
12	0.032747	0.2515	0.401138
13	0.024999	0.192	0.424194
14	0.002729	0.021	0.491672
15	-0.126244	-0.9697	0.831922
16	-0.171154	-1.3147	0.903144

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.6811 & 0 \tabularnewline
1 & 0.289068 & 2.2204 & 0.015123 \tabularnewline
2 & -0.153902 & -1.1821 & 0.879054 \tabularnewline
3 & -0.186322 & -1.4312 & 0.921171 \tabularnewline
4 & 0.088895 & 0.6828 & 0.248697 \tabularnewline
5 & 0.038393 & 0.2949 & 0.384553 \tabularnewline
6 & -0.155196 & -1.1921 & 0.880999 \tabularnewline
7 & -0.049524 & -0.3804 & 0.647494 \tabularnewline
8 & 0.074516 & 0.5724 & 0.284624 \tabularnewline
9 & 0.075827 & 0.5824 & 0.281244 \tabularnewline
10 & 0.057577 & 0.4423 & 0.329959 \tabularnewline
11 & 0.022039 & 0.1693 & 0.433075 \tabularnewline
12 & 0.032747 & 0.2515 & 0.401138 \tabularnewline
13 & 0.024999 & 0.192 & 0.424194 \tabularnewline
14 & 0.002729 & 0.021 & 0.491672 \tabularnewline
15 & -0.126244 & -0.9697 & 0.831922 \tabularnewline
16 & -0.171154 & -1.3147 & 0.903144 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3334&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]7.6811[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.289068[/C][C]2.2204[/C][C]0.015123[/C][/ROW]
[ROW][C]2[/C][C]-0.153902[/C][C]-1.1821[/C][C]0.879054[/C][/ROW]
[ROW][C]3[/C][C]-0.186322[/C][C]-1.4312[/C][C]0.921171[/C][/ROW]
[ROW][C]4[/C][C]0.088895[/C][C]0.6828[/C][C]0.248697[/C][/ROW]
[ROW][C]5[/C][C]0.038393[/C][C]0.2949[/C][C]0.384553[/C][/ROW]
[ROW][C]6[/C][C]-0.155196[/C][C]-1.1921[/C][C]0.880999[/C][/ROW]
[ROW][C]7[/C][C]-0.049524[/C][C]-0.3804[/C][C]0.647494[/C][/ROW]
[ROW][C]8[/C][C]0.074516[/C][C]0.5724[/C][C]0.284624[/C][/ROW]
[ROW][C]9[/C][C]0.075827[/C][C]0.5824[/C][C]0.281244[/C][/ROW]
[ROW][C]10[/C][C]0.057577[/C][C]0.4423[/C][C]0.329959[/C][/ROW]
[ROW][C]11[/C][C]0.022039[/C][C]0.1693[/C][C]0.433075[/C][/ROW]
[ROW][C]12[/C][C]0.032747[/C][C]0.2515[/C][C]0.401138[/C][/ROW]
[ROW][C]13[/C][C]0.024999[/C][C]0.192[/C][C]0.424194[/C][/ROW]
[ROW][C]14[/C][C]0.002729[/C][C]0.021[/C][C]0.491672[/C][/ROW]
[ROW][C]15[/C][C]-0.126244[/C][C]-0.9697[/C][C]0.831922[/C][/ROW]
[ROW][C]16[/C][C]-0.171154[/C][C]-1.3147[/C][C]0.903144[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3334&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3334&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	7.6811	0
1	0.289068	2.2204	0.015123
2	-0.153902	-1.1821	0.879054
3	-0.186322	-1.4312	0.921171
4	0.088895	0.6828	0.248697
5	0.038393	0.2949	0.384553
6	-0.155196	-1.1921	0.880999
7	-0.049524	-0.3804	0.647494
8	0.074516	0.5724	0.284624
9	0.075827	0.5824	0.281244
10	0.057577	0.4423	0.329959
11	0.022039	0.1693	0.433075
12	0.032747	0.2515	0.401138
13	0.024999	0.192	0.424194
14	0.002729	0.021	0.491672
15	-0.126244	-0.9697	0.831922
16	-0.171154	-1.3147	0.903144

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.289068	2.2204	0.015123
1	-0.259114	-1.9903	0.974401
2	-0.064808	-0.4978	0.689762
3	0.159832	1.2277	0.112219
4	-0.114489	-0.8794	0.808626
5	-0.138576	-1.0644	0.854263
6	0.112411	0.8634	0.195694
7	-0.015175	-0.1166	0.546198
8	-0.005372	-0.0413	0.516388
9	0.12911	0.9917	0.162694
10	-0.019234	-0.1477	0.558475
11	0.011196	0.086	0.465881
12	0.065001	0.4993	0.309718
13	-0.019042	-0.1463	0.557893
14	-0.149641	-1.1494	0.872488
15	-0.061528	-0.4726	0.680881
16	0.177433	1.3629	0.089049

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.289068 & 2.2204 & 0.015123 \tabularnewline
1 & -0.259114 & -1.9903 & 0.974401 \tabularnewline
2 & -0.064808 & -0.4978 & 0.689762 \tabularnewline
3 & 0.159832 & 1.2277 & 0.112219 \tabularnewline
4 & -0.114489 & -0.8794 & 0.808626 \tabularnewline
5 & -0.138576 & -1.0644 & 0.854263 \tabularnewline
6 & 0.112411 & 0.8634 & 0.195694 \tabularnewline
7 & -0.015175 & -0.1166 & 0.546198 \tabularnewline
8 & -0.005372 & -0.0413 & 0.516388 \tabularnewline
9 & 0.12911 & 0.9917 & 0.162694 \tabularnewline
10 & -0.019234 & -0.1477 & 0.558475 \tabularnewline
11 & 0.011196 & 0.086 & 0.465881 \tabularnewline
12 & 0.065001 & 0.4993 & 0.309718 \tabularnewline
13 & -0.019042 & -0.1463 & 0.557893 \tabularnewline
14 & -0.149641 & -1.1494 & 0.872488 \tabularnewline
15 & -0.061528 & -0.4726 & 0.680881 \tabularnewline
16 & 0.177433 & 1.3629 & 0.089049 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3334&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]0.289068[/C][C]2.2204[/C][C]0.015123[/C][/ROW]
[ROW][C]1[/C][C]-0.259114[/C][C]-1.9903[/C][C]0.974401[/C][/ROW]
[ROW][C]2[/C][C]-0.064808[/C][C]-0.4978[/C][C]0.689762[/C][/ROW]
[ROW][C]3[/C][C]0.159832[/C][C]1.2277[/C][C]0.112219[/C][/ROW]
[ROW][C]4[/C][C]-0.114489[/C][C]-0.8794[/C][C]0.808626[/C][/ROW]
[ROW][C]5[/C][C]-0.138576[/C][C]-1.0644[/C][C]0.854263[/C][/ROW]
[ROW][C]6[/C][C]0.112411[/C][C]0.8634[/C][C]0.195694[/C][/ROW]
[ROW][C]7[/C][C]-0.015175[/C][C]-0.1166[/C][C]0.546198[/C][/ROW]
[ROW][C]8[/C][C]-0.005372[/C][C]-0.0413[/C][C]0.516388[/C][/ROW]
[ROW][C]9[/C][C]0.12911[/C][C]0.9917[/C][C]0.162694[/C][/ROW]
[ROW][C]10[/C][C]-0.019234[/C][C]-0.1477[/C][C]0.558475[/C][/ROW]
[ROW][C]11[/C][C]0.011196[/C][C]0.086[/C][C]0.465881[/C][/ROW]
[ROW][C]12[/C][C]0.065001[/C][C]0.4993[/C][C]0.309718[/C][/ROW]
[ROW][C]13[/C][C]-0.019042[/C][C]-0.1463[/C][C]0.557893[/C][/ROW]
[ROW][C]14[/C][C]-0.149641[/C][C]-1.1494[/C][C]0.872488[/C][/ROW]
[ROW][C]15[/C][C]-0.061528[/C][C]-0.4726[/C][C]0.680881[/C][/ROW]
[ROW][C]16[/C][C]0.177433[/C][C]1.3629[/C][C]0.089049[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3334&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3334&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	0.289068	2.2204	0.015123
1	-0.259114	-1.9903	0.974401
2	-0.064808	-0.4978	0.689762
3	0.159832	1.2277	0.112219
4	-0.114489	-0.8794	0.808626
5	-0.138576	-1.0644	0.854263
6	0.112411	0.8634	0.195694
7	-0.015175	-0.1166	0.546198
8	-0.005372	-0.0413	0.516388
9	0.12911	0.9917	0.162694
10	-0.019234	-0.1477	0.558475
11	0.011196	0.086	0.465881
12	0.065001	0.4993	0.309718
13	-0.019042	-0.1463	0.557893
14	-0.149641	-1.1494	0.872488
15	-0.061528	-0.4726	0.680881
16	0.177433	1.3629	0.089049

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 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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Input Parameters & R Code