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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 28 Aug 2012 15:23:19 -0400

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/2012/Aug/28/t13461818176dm242gz7dk0ss3.htm/, Retrieved Fri, 03 May 2024 07:53:18 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=169543, Retrieved Fri, 03 May 2024 07:53:18 +0000

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Estimated Impact

116

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

-     [Univariate Data Series] [] [2008-12-08 19:22:39] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMP   [(Partial) Autocorrelation Function] [] [2011-12-06 19:49:59] [b98453cac15ba1066b407e146608df68]
- R PD      [(Partial) Autocorrelation Function] [ACFF] [2012-08-28 19:23:19] [c53b4e73f301bc561a9fa0b8f84a7890] [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	3 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

\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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169543&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169543&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169543&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	3 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.147156	-1.1303	0.131456
2	0.056231	0.4319	0.333687
3	0.133348	1.0243	0.154945
4	0.11761	0.9034	0.184998
5	-0.033273	-0.2556	0.399583
6	0.120401	0.9248	0.179413
7	-0.157807	-1.2121	0.115146
8	0.243567	1.8709	0.033162
9	-0.075319	-0.5785	0.282553
10	-0.063633	-0.4888	0.313406
11	0.168971	1.2979	0.099688
12	-0.17076	-1.3116	0.097363
13	0.014208	0.1091	0.456733
14	0.048434	0.372	0.355603
15	-0.118082	-0.907	0.184047
16	0.043965	0.3377	0.368392
17	0.180218	1.3843	0.085743
18	-0.276192	-2.1215	0.019046

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.147156 & -1.1303 & 0.131456 \tabularnewline
2 & 0.056231 & 0.4319 & 0.333687 \tabularnewline
3 & 0.133348 & 1.0243 & 0.154945 \tabularnewline
4 & 0.11761 & 0.9034 & 0.184998 \tabularnewline
5 & -0.033273 & -0.2556 & 0.399583 \tabularnewline
6 & 0.120401 & 0.9248 & 0.179413 \tabularnewline
7 & -0.157807 & -1.2121 & 0.115146 \tabularnewline
8 & 0.243567 & 1.8709 & 0.033162 \tabularnewline
9 & -0.075319 & -0.5785 & 0.282553 \tabularnewline
10 & -0.063633 & -0.4888 & 0.313406 \tabularnewline
11 & 0.168971 & 1.2979 & 0.099688 \tabularnewline
12 & -0.17076 & -1.3116 & 0.097363 \tabularnewline
13 & 0.014208 & 0.1091 & 0.456733 \tabularnewline
14 & 0.048434 & 0.372 & 0.355603 \tabularnewline
15 & -0.118082 & -0.907 & 0.184047 \tabularnewline
16 & 0.043965 & 0.3377 & 0.368392 \tabularnewline
17 & 0.180218 & 1.3843 & 0.085743 \tabularnewline
18 & -0.276192 & -2.1215 & 0.019046 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169543&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]-0.147156[/C][C]-1.1303[/C][C]0.131456[/C][/ROW]
[ROW][C]2[/C][C]0.056231[/C][C]0.4319[/C][C]0.333687[/C][/ROW]
[ROW][C]3[/C][C]0.133348[/C][C]1.0243[/C][C]0.154945[/C][/ROW]
[ROW][C]4[/C][C]0.11761[/C][C]0.9034[/C][C]0.184998[/C][/ROW]
[ROW][C]5[/C][C]-0.033273[/C][C]-0.2556[/C][C]0.399583[/C][/ROW]
[ROW][C]6[/C][C]0.120401[/C][C]0.9248[/C][C]0.179413[/C][/ROW]
[ROW][C]7[/C][C]-0.157807[/C][C]-1.2121[/C][C]0.115146[/C][/ROW]
[ROW][C]8[/C][C]0.243567[/C][C]1.8709[/C][C]0.033162[/C][/ROW]
[ROW][C]9[/C][C]-0.075319[/C][C]-0.5785[/C][C]0.282553[/C][/ROW]
[ROW][C]10[/C][C]-0.063633[/C][C]-0.4888[/C][C]0.313406[/C][/ROW]
[ROW][C]11[/C][C]0.168971[/C][C]1.2979[/C][C]0.099688[/C][/ROW]
[ROW][C]12[/C][C]-0.17076[/C][C]-1.3116[/C][C]0.097363[/C][/ROW]
[ROW][C]13[/C][C]0.014208[/C][C]0.1091[/C][C]0.456733[/C][/ROW]
[ROW][C]14[/C][C]0.048434[/C][C]0.372[/C][C]0.355603[/C][/ROW]
[ROW][C]15[/C][C]-0.118082[/C][C]-0.907[/C][C]0.184047[/C][/ROW]
[ROW][C]16[/C][C]0.043965[/C][C]0.3377[/C][C]0.368392[/C][/ROW]
[ROW][C]17[/C][C]0.180218[/C][C]1.3843[/C][C]0.085743[/C][/ROW]
[ROW][C]18[/C][C]-0.276192[/C][C]-2.1215[/C][C]0.019046[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169543&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169543&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	-0.147156	-1.1303	0.131456
2	0.056231	0.4319	0.333687
3	0.133348	1.0243	0.154945
4	0.11761	0.9034	0.184998
5	-0.033273	-0.2556	0.399583
6	0.120401	0.9248	0.179413
7	-0.157807	-1.2121	0.115146
8	0.243567	1.8709	0.033162
9	-0.075319	-0.5785	0.282553
10	-0.063633	-0.4888	0.313406
11	0.168971	1.2979	0.099688
12	-0.17076	-1.3116	0.097363
13	0.014208	0.1091	0.456733
14	0.048434	0.372	0.355603
15	-0.118082	-0.907	0.184047
16	0.043965	0.3377	0.368392
17	0.180218	1.3843	0.085743
18	-0.276192	-2.1215	0.019046

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.147156	-1.1303	0.131456
2	0.035342	0.2715	0.393491
3	0.149962	1.1519	0.127008
4	0.163462	1.2556	0.10711
5	-0.005508	-0.0423	0.483199
6	0.081585	0.6267	0.266649
7	-0.17821	-1.3689	0.088116
8	0.187637	1.4413	0.077398
9	-0.030169	-0.2317	0.408774
10	-0.078981	-0.6067	0.2732
11	0.153741	1.1809	0.121189
12	-0.221941	-1.7048	0.04675
13	0.05459	0.4193	0.338256
14	-0.031797	-0.2442	0.403948
15	-0.053697	-0.4125	0.340751
16	0.063273	0.486	0.31438
17	0.16226	1.2463	0.108782
18	-0.162363	-1.2471	0.108638

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.147156 & -1.1303 & 0.131456 \tabularnewline
2 & 0.035342 & 0.2715 & 0.393491 \tabularnewline
3 & 0.149962 & 1.1519 & 0.127008 \tabularnewline
4 & 0.163462 & 1.2556 & 0.10711 \tabularnewline
5 & -0.005508 & -0.0423 & 0.483199 \tabularnewline
6 & 0.081585 & 0.6267 & 0.266649 \tabularnewline
7 & -0.17821 & -1.3689 & 0.088116 \tabularnewline
8 & 0.187637 & 1.4413 & 0.077398 \tabularnewline
9 & -0.030169 & -0.2317 & 0.408774 \tabularnewline
10 & -0.078981 & -0.6067 & 0.2732 \tabularnewline
11 & 0.153741 & 1.1809 & 0.121189 \tabularnewline
12 & -0.221941 & -1.7048 & 0.04675 \tabularnewline
13 & 0.05459 & 0.4193 & 0.338256 \tabularnewline
14 & -0.031797 & -0.2442 & 0.403948 \tabularnewline
15 & -0.053697 & -0.4125 & 0.340751 \tabularnewline
16 & 0.063273 & 0.486 & 0.31438 \tabularnewline
17 & 0.16226 & 1.2463 & 0.108782 \tabularnewline
18 & -0.162363 & -1.2471 & 0.108638 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169543&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]-0.147156[/C][C]-1.1303[/C][C]0.131456[/C][/ROW]
[ROW][C]2[/C][C]0.035342[/C][C]0.2715[/C][C]0.393491[/C][/ROW]
[ROW][C]3[/C][C]0.149962[/C][C]1.1519[/C][C]0.127008[/C][/ROW]
[ROW][C]4[/C][C]0.163462[/C][C]1.2556[/C][C]0.10711[/C][/ROW]
[ROW][C]5[/C][C]-0.005508[/C][C]-0.0423[/C][C]0.483199[/C][/ROW]
[ROW][C]6[/C][C]0.081585[/C][C]0.6267[/C][C]0.266649[/C][/ROW]
[ROW][C]7[/C][C]-0.17821[/C][C]-1.3689[/C][C]0.088116[/C][/ROW]
[ROW][C]8[/C][C]0.187637[/C][C]1.4413[/C][C]0.077398[/C][/ROW]
[ROW][C]9[/C][C]-0.030169[/C][C]-0.2317[/C][C]0.408774[/C][/ROW]
[ROW][C]10[/C][C]-0.078981[/C][C]-0.6067[/C][C]0.2732[/C][/ROW]
[ROW][C]11[/C][C]0.153741[/C][C]1.1809[/C][C]0.121189[/C][/ROW]
[ROW][C]12[/C][C]-0.221941[/C][C]-1.7048[/C][C]0.04675[/C][/ROW]
[ROW][C]13[/C][C]0.05459[/C][C]0.4193[/C][C]0.338256[/C][/ROW]
[ROW][C]14[/C][C]-0.031797[/C][C]-0.2442[/C][C]0.403948[/C][/ROW]
[ROW][C]15[/C][C]-0.053697[/C][C]-0.4125[/C][C]0.340751[/C][/ROW]
[ROW][C]16[/C][C]0.063273[/C][C]0.486[/C][C]0.31438[/C][/ROW]
[ROW][C]17[/C][C]0.16226[/C][C]1.2463[/C][C]0.108782[/C][/ROW]
[ROW][C]18[/C][C]-0.162363[/C][C]-1.2471[/C][C]0.108638[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169543&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169543&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	-0.147156	-1.1303	0.131456
2	0.035342	0.2715	0.393491
3	0.149962	1.1519	0.127008
4	0.163462	1.2556	0.10711
5	-0.005508	-0.0423	0.483199
6	0.081585	0.6267	0.266649
7	-0.17821	-1.3689	0.088116
8	0.187637	1.4413	0.077398
9	-0.030169	-0.2317	0.408774
10	-0.078981	-0.6067	0.2732
11	0.153741	1.1809	0.121189
12	-0.221941	-1.7048	0.04675
13	0.05459	0.4193	0.338256
14	-0.031797	-0.2442	0.403948
15	-0.053697	-0.4125	0.340751
16	0.063273	0.486	0.31438
17	0.16226	1.2463	0.108782
18	-0.162363	-1.2471	0.108638

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

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 ; par8 = ;

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 (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
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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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code