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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 21 Dec 2008 10:49:59 -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/2008/Dec/21/t1229881827h13byl98z6somwd.htm/, Retrieved Sat, 18 May 2024 11:56:15 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35712, Retrieved Sat, 18 May 2024 11:56:15 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

139

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

-       [(Partial) Autocorrelation Function] [] [2008-12-21 17:49:59] [a2d5a6282476ec2b5afae6fb53d308f8] [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	1 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35712&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35712&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35712&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	1 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.863209	6.6864	0
2	0.723541	5.6045	0
3	0.626827	4.8554	4e-06
4	0.538606	4.172	4.9e-05
5	0.448423	3.4735	0.00048
6	0.346389	2.6831	0.004706
7	0.296634	2.2977	0.01254
8	0.262443	2.0329	0.023249
9	0.215053	1.6658	0.050484
10	0.148974	1.1539	0.126549
11	0.071814	0.5563	0.290047
12	0.026195	0.2029	0.419946
13	-0.009801	-0.0759	0.469868
14	-0.02512	-0.1946	0.423189
15	-0.038719	-0.2999	0.38264
16	-0.041044	-0.3179	0.375824
17	-0.051199	-0.3966	0.346541

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.863209 & 6.6864 & 0 \tabularnewline
2 & 0.723541 & 5.6045 & 0 \tabularnewline
3 & 0.626827 & 4.8554 & 4e-06 \tabularnewline
4 & 0.538606 & 4.172 & 4.9e-05 \tabularnewline
5 & 0.448423 & 3.4735 & 0.00048 \tabularnewline
6 & 0.346389 & 2.6831 & 0.004706 \tabularnewline
7 & 0.296634 & 2.2977 & 0.01254 \tabularnewline
8 & 0.262443 & 2.0329 & 0.023249 \tabularnewline
9 & 0.215053 & 1.6658 & 0.050484 \tabularnewline
10 & 0.148974 & 1.1539 & 0.126549 \tabularnewline
11 & 0.071814 & 0.5563 & 0.290047 \tabularnewline
12 & 0.026195 & 0.2029 & 0.419946 \tabularnewline
13 & -0.009801 & -0.0759 & 0.469868 \tabularnewline
14 & -0.02512 & -0.1946 & 0.423189 \tabularnewline
15 & -0.038719 & -0.2999 & 0.38264 \tabularnewline
16 & -0.041044 & -0.3179 & 0.375824 \tabularnewline
17 & -0.051199 & -0.3966 & 0.346541 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35712&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]0.863209[/C][C]6.6864[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.723541[/C][C]5.6045[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.626827[/C][C]4.8554[/C][C]4e-06[/C][/ROW]
[ROW][C]4[/C][C]0.538606[/C][C]4.172[/C][C]4.9e-05[/C][/ROW]
[ROW][C]5[/C][C]0.448423[/C][C]3.4735[/C][C]0.00048[/C][/ROW]
[ROW][C]6[/C][C]0.346389[/C][C]2.6831[/C][C]0.004706[/C][/ROW]
[ROW][C]7[/C][C]0.296634[/C][C]2.2977[/C][C]0.01254[/C][/ROW]
[ROW][C]8[/C][C]0.262443[/C][C]2.0329[/C][C]0.023249[/C][/ROW]
[ROW][C]9[/C][C]0.215053[/C][C]1.6658[/C][C]0.050484[/C][/ROW]
[ROW][C]10[/C][C]0.148974[/C][C]1.1539[/C][C]0.126549[/C][/ROW]
[ROW][C]11[/C][C]0.071814[/C][C]0.5563[/C][C]0.290047[/C][/ROW]
[ROW][C]12[/C][C]0.026195[/C][C]0.2029[/C][C]0.419946[/C][/ROW]
[ROW][C]13[/C][C]-0.009801[/C][C]-0.0759[/C][C]0.469868[/C][/ROW]
[ROW][C]14[/C][C]-0.02512[/C][C]-0.1946[/C][C]0.423189[/C][/ROW]
[ROW][C]15[/C][C]-0.038719[/C][C]-0.2999[/C][C]0.38264[/C][/ROW]
[ROW][C]16[/C][C]-0.041044[/C][C]-0.3179[/C][C]0.375824[/C][/ROW]
[ROW][C]17[/C][C]-0.051199[/C][C]-0.3966[/C][C]0.346541[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35712&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35712&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	0.863209	6.6864	0
2	0.723541	5.6045	0
3	0.626827	4.8554	4e-06
4	0.538606	4.172	4.9e-05
5	0.448423	3.4735	0.00048
6	0.346389	2.6831	0.004706
7	0.296634	2.2977	0.01254
8	0.262443	2.0329	0.023249
9	0.215053	1.6658	0.050484
10	0.148974	1.1539	0.126549
11	0.071814	0.5563	0.290047
12	0.026195	0.2029	0.419946
13	-0.009801	-0.0759	0.469868
14	-0.02512	-0.1946	0.423189
15	-0.038719	-0.2999	0.38264
16	-0.041044	-0.3179	0.375824
17	-0.051199	-0.3966	0.346541

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.863209	6.6864	0
2	-0.084704	-0.6561	0.25713
3	0.088811	0.6879	0.247075
4	-0.032792	-0.254	0.400179
5	-0.044601	-0.3455	0.365471
6	-0.102109	-0.7909	0.21605
7	0.139687	1.082	0.141789
8	-0.006829	-0.0529	0.478994
9	-0.038973	-0.3019	0.381892
10	-0.099841	-0.7734	0.22117
11	-0.098526	-0.7632	0.224174
12	0.028431	0.2202	0.413223
13	-0.002088	-0.0162	0.493576
14	0.081832	0.6339	0.264289
15	-0.023362	-0.181	0.428503
16	0.024437	0.1893	0.425254
17	-0.091689	-0.7102	0.240161

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.863209 & 6.6864 & 0 \tabularnewline
2 & -0.084704 & -0.6561 & 0.25713 \tabularnewline
3 & 0.088811 & 0.6879 & 0.247075 \tabularnewline
4 & -0.032792 & -0.254 & 0.400179 \tabularnewline
5 & -0.044601 & -0.3455 & 0.365471 \tabularnewline
6 & -0.102109 & -0.7909 & 0.21605 \tabularnewline
7 & 0.139687 & 1.082 & 0.141789 \tabularnewline
8 & -0.006829 & -0.0529 & 0.478994 \tabularnewline
9 & -0.038973 & -0.3019 & 0.381892 \tabularnewline
10 & -0.099841 & -0.7734 & 0.22117 \tabularnewline
11 & -0.098526 & -0.7632 & 0.224174 \tabularnewline
12 & 0.028431 & 0.2202 & 0.413223 \tabularnewline
13 & -0.002088 & -0.0162 & 0.493576 \tabularnewline
14 & 0.081832 & 0.6339 & 0.264289 \tabularnewline
15 & -0.023362 & -0.181 & 0.428503 \tabularnewline
16 & 0.024437 & 0.1893 & 0.425254 \tabularnewline
17 & -0.091689 & -0.7102 & 0.240161 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35712&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]0.863209[/C][C]6.6864[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.084704[/C][C]-0.6561[/C][C]0.25713[/C][/ROW]
[ROW][C]3[/C][C]0.088811[/C][C]0.6879[/C][C]0.247075[/C][/ROW]
[ROW][C]4[/C][C]-0.032792[/C][C]-0.254[/C][C]0.400179[/C][/ROW]
[ROW][C]5[/C][C]-0.044601[/C][C]-0.3455[/C][C]0.365471[/C][/ROW]
[ROW][C]6[/C][C]-0.102109[/C][C]-0.7909[/C][C]0.21605[/C][/ROW]
[ROW][C]7[/C][C]0.139687[/C][C]1.082[/C][C]0.141789[/C][/ROW]
[ROW][C]8[/C][C]-0.006829[/C][C]-0.0529[/C][C]0.478994[/C][/ROW]
[ROW][C]9[/C][C]-0.038973[/C][C]-0.3019[/C][C]0.381892[/C][/ROW]
[ROW][C]10[/C][C]-0.099841[/C][C]-0.7734[/C][C]0.22117[/C][/ROW]
[ROW][C]11[/C][C]-0.098526[/C][C]-0.7632[/C][C]0.224174[/C][/ROW]
[ROW][C]12[/C][C]0.028431[/C][C]0.2202[/C][C]0.413223[/C][/ROW]
[ROW][C]13[/C][C]-0.002088[/C][C]-0.0162[/C][C]0.493576[/C][/ROW]
[ROW][C]14[/C][C]0.081832[/C][C]0.6339[/C][C]0.264289[/C][/ROW]
[ROW][C]15[/C][C]-0.023362[/C][C]-0.181[/C][C]0.428503[/C][/ROW]
[ROW][C]16[/C][C]0.024437[/C][C]0.1893[/C][C]0.425254[/C][/ROW]
[ROW][C]17[/C][C]-0.091689[/C][C]-0.7102[/C][C]0.240161[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35712&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35712&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	0.863209	6.6864	0
2	-0.084704	-0.6561	0.25713
3	0.088811	0.6879	0.247075
4	-0.032792	-0.254	0.400179
5	-0.044601	-0.3455	0.365471
6	-0.102109	-0.7909	0.21605
7	0.139687	1.082	0.141789
8	-0.006829	-0.0529	0.478994
9	-0.038973	-0.3019	0.381892
10	-0.099841	-0.7734	0.22117
11	-0.098526	-0.7632	0.224174
12	0.028431	0.2202	0.413223
13	-0.002088	-0.0162	0.493576
14	0.081832	0.6339	0.264289
15	-0.023362	-0.181	0.428503
16	0.024437	0.1893	0.425254
17	-0.091689	-0.7102	0.240161

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 4 ;

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 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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Dataset

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Input Parameters & R Code