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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 26 Nov 2009 10:34:55 -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/2009/Nov/26/t1259256951zog0ii0w602wrp8.htm/, Retrieved Sun, 28 Apr 2024 23:09:15 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=60195, Retrieved Sun, 28 Apr 2024 23:09:15 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

120

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

-       [(Partial) Autocorrelation Function] [] [2009-11-26 17:34:55] [14869f38c4320b00c96ca15cc00142de] [Current]
-    D    [(Partial) Autocorrelation Function] [] [2009-12-15 21:04:33] [73863f7f907331e734eff34b7de6fc83] 

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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	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60195&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60195&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60195&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.186937	1.4359	0.078158
2	-0.052916	-0.4065	0.342939
3	-0.188362	-1.4468	0.076618
4	0.04464	0.3429	0.366452
5	0.116736	0.8967	0.186771
6	-0.037779	-0.2902	0.386346
7	-0.011457	-0.088	0.465088
8	0.114558	0.8799	0.191232
9	0.250405	1.9234	0.02963
10	-0.06501	-0.4993	0.309695
11	-0.118939	-0.9136	0.182326
12	-0.195559	-1.5021	0.0692
13	0.127359	0.9783	0.16597
14	0.309612	2.3782	0.010328
15	0.098542	0.7569	0.226056
16	0.005384	0.0414	0.483577
17	-0.125044	-0.9605	0.170367
18	0.080881	0.6213	0.268411

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.186937 & 1.4359 & 0.078158 \tabularnewline
2 & -0.052916 & -0.4065 & 0.342939 \tabularnewline
3 & -0.188362 & -1.4468 & 0.076618 \tabularnewline
4 & 0.04464 & 0.3429 & 0.366452 \tabularnewline
5 & 0.116736 & 0.8967 & 0.186771 \tabularnewline
6 & -0.037779 & -0.2902 & 0.386346 \tabularnewline
7 & -0.011457 & -0.088 & 0.465088 \tabularnewline
8 & 0.114558 & 0.8799 & 0.191232 \tabularnewline
9 & 0.250405 & 1.9234 & 0.02963 \tabularnewline
10 & -0.06501 & -0.4993 & 0.309695 \tabularnewline
11 & -0.118939 & -0.9136 & 0.182326 \tabularnewline
12 & -0.195559 & -1.5021 & 0.0692 \tabularnewline
13 & 0.127359 & 0.9783 & 0.16597 \tabularnewline
14 & 0.309612 & 2.3782 & 0.010328 \tabularnewline
15 & 0.098542 & 0.7569 & 0.226056 \tabularnewline
16 & 0.005384 & 0.0414 & 0.483577 \tabularnewline
17 & -0.125044 & -0.9605 & 0.170367 \tabularnewline
18 & 0.080881 & 0.6213 & 0.268411 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60195&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]0.186937[/C][C]1.4359[/C][C]0.078158[/C][/ROW]
[ROW][C]2[/C][C]-0.052916[/C][C]-0.4065[/C][C]0.342939[/C][/ROW]
[ROW][C]3[/C][C]-0.188362[/C][C]-1.4468[/C][C]0.076618[/C][/ROW]
[ROW][C]4[/C][C]0.04464[/C][C]0.3429[/C][C]0.366452[/C][/ROW]
[ROW][C]5[/C][C]0.116736[/C][C]0.8967[/C][C]0.186771[/C][/ROW]
[ROW][C]6[/C][C]-0.037779[/C][C]-0.2902[/C][C]0.386346[/C][/ROW]
[ROW][C]7[/C][C]-0.011457[/C][C]-0.088[/C][C]0.465088[/C][/ROW]
[ROW][C]8[/C][C]0.114558[/C][C]0.8799[/C][C]0.191232[/C][/ROW]
[ROW][C]9[/C][C]0.250405[/C][C]1.9234[/C][C]0.02963[/C][/ROW]
[ROW][C]10[/C][C]-0.06501[/C][C]-0.4993[/C][C]0.309695[/C][/ROW]
[ROW][C]11[/C][C]-0.118939[/C][C]-0.9136[/C][C]0.182326[/C][/ROW]
[ROW][C]12[/C][C]-0.195559[/C][C]-1.5021[/C][C]0.0692[/C][/ROW]
[ROW][C]13[/C][C]0.127359[/C][C]0.9783[/C][C]0.16597[/C][/ROW]
[ROW][C]14[/C][C]0.309612[/C][C]2.3782[/C][C]0.010328[/C][/ROW]
[ROW][C]15[/C][C]0.098542[/C][C]0.7569[/C][C]0.226056[/C][/ROW]
[ROW][C]16[/C][C]0.005384[/C][C]0.0414[/C][C]0.483577[/C][/ROW]
[ROW][C]17[/C][C]-0.125044[/C][C]-0.9605[/C][C]0.170367[/C][/ROW]
[ROW][C]18[/C][C]0.080881[/C][C]0.6213[/C][C]0.268411[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60195&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60195&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	0.186937	1.4359	0.078158
2	-0.052916	-0.4065	0.342939
3	-0.188362	-1.4468	0.076618
4	0.04464	0.3429	0.366452
5	0.116736	0.8967	0.186771
6	-0.037779	-0.2902	0.386346
7	-0.011457	-0.088	0.465088
8	0.114558	0.8799	0.191232
9	0.250405	1.9234	0.02963
10	-0.06501	-0.4993	0.309695
11	-0.118939	-0.9136	0.182326
12	-0.195559	-1.5021	0.0692
13	0.127359	0.9783	0.16597
14	0.309612	2.3782	0.010328
15	0.098542	0.7569	0.226056
16	0.005384	0.0414	0.483577
17	-0.125044	-0.9605	0.170367
18	0.080881	0.6213	0.268411

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.186937	1.4359	0.078158
2	-0.091043	-0.6993	0.243552
3	-0.167754	-1.2885	0.101293
4	0.116687	0.8963	0.186871
5	0.072079	0.5536	0.290957
6	-0.112454	-0.8638	0.195604
7	0.058787	0.4516	0.326624
8	0.151781	1.1658	0.124183
9	0.173172	1.3302	0.094292
10	-0.162333	-1.2469	0.108681
11	-0.007997	-0.0614	0.475614
12	-0.122422	-0.9403	0.175439
13	0.113752	0.8737	0.1929
14	0.258157	1.9829	0.026018
15	-0.006635	-0.051	0.479762
16	0.030114	0.2313	0.408936
17	-0.098888	-0.7596	0.225266
18	0.062057	0.4767	0.31768

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.186937 & 1.4359 & 0.078158 \tabularnewline
2 & -0.091043 & -0.6993 & 0.243552 \tabularnewline
3 & -0.167754 & -1.2885 & 0.101293 \tabularnewline
4 & 0.116687 & 0.8963 & 0.186871 \tabularnewline
5 & 0.072079 & 0.5536 & 0.290957 \tabularnewline
6 & -0.112454 & -0.8638 & 0.195604 \tabularnewline
7 & 0.058787 & 0.4516 & 0.326624 \tabularnewline
8 & 0.151781 & 1.1658 & 0.124183 \tabularnewline
9 & 0.173172 & 1.3302 & 0.094292 \tabularnewline
10 & -0.162333 & -1.2469 & 0.108681 \tabularnewline
11 & -0.007997 & -0.0614 & 0.475614 \tabularnewline
12 & -0.122422 & -0.9403 & 0.175439 \tabularnewline
13 & 0.113752 & 0.8737 & 0.1929 \tabularnewline
14 & 0.258157 & 1.9829 & 0.026018 \tabularnewline
15 & -0.006635 & -0.051 & 0.479762 \tabularnewline
16 & 0.030114 & 0.2313 & 0.408936 \tabularnewline
17 & -0.098888 & -0.7596 & 0.225266 \tabularnewline
18 & 0.062057 & 0.4767 & 0.31768 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60195&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]0.186937[/C][C]1.4359[/C][C]0.078158[/C][/ROW]
[ROW][C]2[/C][C]-0.091043[/C][C]-0.6993[/C][C]0.243552[/C][/ROW]
[ROW][C]3[/C][C]-0.167754[/C][C]-1.2885[/C][C]0.101293[/C][/ROW]
[ROW][C]4[/C][C]0.116687[/C][C]0.8963[/C][C]0.186871[/C][/ROW]
[ROW][C]5[/C][C]0.072079[/C][C]0.5536[/C][C]0.290957[/C][/ROW]
[ROW][C]6[/C][C]-0.112454[/C][C]-0.8638[/C][C]0.195604[/C][/ROW]
[ROW][C]7[/C][C]0.058787[/C][C]0.4516[/C][C]0.326624[/C][/ROW]
[ROW][C]8[/C][C]0.151781[/C][C]1.1658[/C][C]0.124183[/C][/ROW]
[ROW][C]9[/C][C]0.173172[/C][C]1.3302[/C][C]0.094292[/C][/ROW]
[ROW][C]10[/C][C]-0.162333[/C][C]-1.2469[/C][C]0.108681[/C][/ROW]
[ROW][C]11[/C][C]-0.007997[/C][C]-0.0614[/C][C]0.475614[/C][/ROW]
[ROW][C]12[/C][C]-0.122422[/C][C]-0.9403[/C][C]0.175439[/C][/ROW]
[ROW][C]13[/C][C]0.113752[/C][C]0.8737[/C][C]0.1929[/C][/ROW]
[ROW][C]14[/C][C]0.258157[/C][C]1.9829[/C][C]0.026018[/C][/ROW]
[ROW][C]15[/C][C]-0.006635[/C][C]-0.051[/C][C]0.479762[/C][/ROW]
[ROW][C]16[/C][C]0.030114[/C][C]0.2313[/C][C]0.408936[/C][/ROW]
[ROW][C]17[/C][C]-0.098888[/C][C]-0.7596[/C][C]0.225266[/C][/ROW]
[ROW][C]18[/C][C]0.062057[/C][C]0.4767[/C][C]0.31768[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60195&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60195&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	0.186937	1.4359	0.078158
2	-0.091043	-0.6993	0.243552
3	-0.167754	-1.2885	0.101293
4	0.116687	0.8963	0.186871
5	0.072079	0.5536	0.290957
6	-0.112454	-0.8638	0.195604
7	0.058787	0.4516	0.326624
8	0.151781	1.1658	0.124183
9	0.173172	1.3302	0.094292
10	-0.162333	-1.2469	0.108681
11	-0.007997	-0.0614	0.475614
12	-0.122422	-0.9403	0.175439
13	0.113752	0.8737	0.1929
14	0.258157	1.9829	0.026018
15	-0.006635	-0.051	0.479762
16	0.030114	0.2313	0.408936
17	-0.098888	-0.7596	0.225266
18	0.062057	0.4767	0.31768

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 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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 (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
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')

Free Statistics

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code