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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 28 Aug 2012 15:13:29 -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/t1346181230e3q5ct2u1r4erpk.htm/, Retrieved Fri, 03 May 2024 10:09:41 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=169540, Retrieved Fri, 03 May 2024 10:09:41 +0000

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Estimated Impact

113

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] [ACF functie niet ...] [2012-08-28 19:13:29] [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	1 seconds
R Server	'AstonUniversity' @ aston.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 & 1 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169540&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169540&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169540&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	'AstonUniversity' @ aston.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.832787	7.0664	0
2	0.762588	6.4708	0
3	0.743692	6.3104	0
4	0.768214	6.5185	0
5	0.718434	6.0961	0
6	0.648901	5.5061	0
7	0.655735	5.5641	0
8	0.639454	5.4259	0
9	0.535186	4.5412	1.1e-05
10	0.490778	4.1644	4.3e-05
11	0.491099	4.1671	4.2e-05
12	0.569044	4.8285	4e-06
13	0.418398	3.5502	0.000341
14	0.349337	2.9642	0.002056
15	0.323849	2.748	0.003787
16	0.339285	2.8789	0.002625
17	0.292353	2.4807	0.007725
18	0.230449	1.9554	0.027207

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.832787 & 7.0664 & 0 \tabularnewline
2 & 0.762588 & 6.4708 & 0 \tabularnewline
3 & 0.743692 & 6.3104 & 0 \tabularnewline
4 & 0.768214 & 6.5185 & 0 \tabularnewline
5 & 0.718434 & 6.0961 & 0 \tabularnewline
6 & 0.648901 & 5.5061 & 0 \tabularnewline
7 & 0.655735 & 5.5641 & 0 \tabularnewline
8 & 0.639454 & 5.4259 & 0 \tabularnewline
9 & 0.535186 & 4.5412 & 1.1e-05 \tabularnewline
10 & 0.490778 & 4.1644 & 4.3e-05 \tabularnewline
11 & 0.491099 & 4.1671 & 4.2e-05 \tabularnewline
12 & 0.569044 & 4.8285 & 4e-06 \tabularnewline
13 & 0.418398 & 3.5502 & 0.000341 \tabularnewline
14 & 0.349337 & 2.9642 & 0.002056 \tabularnewline
15 & 0.323849 & 2.748 & 0.003787 \tabularnewline
16 & 0.339285 & 2.8789 & 0.002625 \tabularnewline
17 & 0.292353 & 2.4807 & 0.007725 \tabularnewline
18 & 0.230449 & 1.9554 & 0.027207 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169540&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]0.832787[/C][C]7.0664[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.762588[/C][C]6.4708[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.743692[/C][C]6.3104[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.768214[/C][C]6.5185[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.718434[/C][C]6.0961[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.648901[/C][C]5.5061[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.655735[/C][C]5.5641[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.639454[/C][C]5.4259[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.535186[/C][C]4.5412[/C][C]1.1e-05[/C][/ROW]
[ROW][C]10[/C][C]0.490778[/C][C]4.1644[/C][C]4.3e-05[/C][/ROW]
[ROW][C]11[/C][C]0.491099[/C][C]4.1671[/C][C]4.2e-05[/C][/ROW]
[ROW][C]12[/C][C]0.569044[/C][C]4.8285[/C][C]4e-06[/C][/ROW]
[ROW][C]13[/C][C]0.418398[/C][C]3.5502[/C][C]0.000341[/C][/ROW]
[ROW][C]14[/C][C]0.349337[/C][C]2.9642[/C][C]0.002056[/C][/ROW]
[ROW][C]15[/C][C]0.323849[/C][C]2.748[/C][C]0.003787[/C][/ROW]
[ROW][C]16[/C][C]0.339285[/C][C]2.8789[/C][C]0.002625[/C][/ROW]
[ROW][C]17[/C][C]0.292353[/C][C]2.4807[/C][C]0.007725[/C][/ROW]
[ROW][C]18[/C][C]0.230449[/C][C]1.9554[/C][C]0.027207[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169540&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169540&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	0.832787	7.0664	0
2	0.762588	6.4708	0
3	0.743692	6.3104	0
4	0.768214	6.5185	0
5	0.718434	6.0961	0
6	0.648901	5.5061	0
7	0.655735	5.5641	0
8	0.639454	5.4259	0
9	0.535186	4.5412	1.1e-05
10	0.490778	4.1644	4.3e-05
11	0.491099	4.1671	4.2e-05
12	0.569044	4.8285	4e-06
13	0.418398	3.5502	0.000341
14	0.349337	2.9642	0.002056
15	0.323849	2.748	0.003787
16	0.339285	2.8789	0.002625
17	0.292353	2.4807	0.007725
18	0.230449	1.9554	0.027207

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.832787	7.0664	0
2	0.225323	1.9119	0.029933
3	0.220241	1.8688	0.032859
4	0.283403	2.4048	0.009378
5	-0.042125	-0.3574	0.360902
6	-0.112038	-0.9507	0.172476
7	0.144351	1.2249	0.11231
8	-0.038328	-0.3252	0.372979
9	-0.315401	-2.6763	0.004606
10	0.035832	0.304	0.380984
11	0.06247	0.5301	0.298845
12	0.355883	3.0198	0.001749
13	-0.485354	-4.1184	5e-05
14	-0.025457	-0.216	0.414796
15	-0.040167	-0.3408	0.367112
16	0.084331	0.7156	0.238286
17	0.032302	0.2741	0.392398
18	-0.023376	-0.1983	0.421666

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.832787 & 7.0664 & 0 \tabularnewline
2 & 0.225323 & 1.9119 & 0.029933 \tabularnewline
3 & 0.220241 & 1.8688 & 0.032859 \tabularnewline
4 & 0.283403 & 2.4048 & 0.009378 \tabularnewline
5 & -0.042125 & -0.3574 & 0.360902 \tabularnewline
6 & -0.112038 & -0.9507 & 0.172476 \tabularnewline
7 & 0.144351 & 1.2249 & 0.11231 \tabularnewline
8 & -0.038328 & -0.3252 & 0.372979 \tabularnewline
9 & -0.315401 & -2.6763 & 0.004606 \tabularnewline
10 & 0.035832 & 0.304 & 0.380984 \tabularnewline
11 & 0.06247 & 0.5301 & 0.298845 \tabularnewline
12 & 0.355883 & 3.0198 & 0.001749 \tabularnewline
13 & -0.485354 & -4.1184 & 5e-05 \tabularnewline
14 & -0.025457 & -0.216 & 0.414796 \tabularnewline
15 & -0.040167 & -0.3408 & 0.367112 \tabularnewline
16 & 0.084331 & 0.7156 & 0.238286 \tabularnewline
17 & 0.032302 & 0.2741 & 0.392398 \tabularnewline
18 & -0.023376 & -0.1983 & 0.421666 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169540&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]0.832787[/C][C]7.0664[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.225323[/C][C]1.9119[/C][C]0.029933[/C][/ROW]
[ROW][C]3[/C][C]0.220241[/C][C]1.8688[/C][C]0.032859[/C][/ROW]
[ROW][C]4[/C][C]0.283403[/C][C]2.4048[/C][C]0.009378[/C][/ROW]
[ROW][C]5[/C][C]-0.042125[/C][C]-0.3574[/C][C]0.360902[/C][/ROW]
[ROW][C]6[/C][C]-0.112038[/C][C]-0.9507[/C][C]0.172476[/C][/ROW]
[ROW][C]7[/C][C]0.144351[/C][C]1.2249[/C][C]0.11231[/C][/ROW]
[ROW][C]8[/C][C]-0.038328[/C][C]-0.3252[/C][C]0.372979[/C][/ROW]
[ROW][C]9[/C][C]-0.315401[/C][C]-2.6763[/C][C]0.004606[/C][/ROW]
[ROW][C]10[/C][C]0.035832[/C][C]0.304[/C][C]0.380984[/C][/ROW]
[ROW][C]11[/C][C]0.06247[/C][C]0.5301[/C][C]0.298845[/C][/ROW]
[ROW][C]12[/C][C]0.355883[/C][C]3.0198[/C][C]0.001749[/C][/ROW]
[ROW][C]13[/C][C]-0.485354[/C][C]-4.1184[/C][C]5e-05[/C][/ROW]
[ROW][C]14[/C][C]-0.025457[/C][C]-0.216[/C][C]0.414796[/C][/ROW]
[ROW][C]15[/C][C]-0.040167[/C][C]-0.3408[/C][C]0.367112[/C][/ROW]
[ROW][C]16[/C][C]0.084331[/C][C]0.7156[/C][C]0.238286[/C][/ROW]
[ROW][C]17[/C][C]0.032302[/C][C]0.2741[/C][C]0.392398[/C][/ROW]
[ROW][C]18[/C][C]-0.023376[/C][C]-0.1983[/C][C]0.421666[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169540&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169540&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	0.832787	7.0664	0
2	0.225323	1.9119	0.029933
3	0.220241	1.8688	0.032859
4	0.283403	2.4048	0.009378
5	-0.042125	-0.3574	0.360902
6	-0.112038	-0.9507	0.172476
7	0.144351	1.2249	0.11231
8	-0.038328	-0.3252	0.372979
9	-0.315401	-2.6763	0.004606
10	0.035832	0.304	0.380984
11	0.06247	0.5301	0.298845
12	0.355883	3.0198	0.001749
13	-0.485354	-4.1184	5e-05
14	-0.025457	-0.216	0.414796
15	-0.040167	-0.3408	0.367112
16	0.084331	0.7156	0.238286
17	0.032302	0.2741	0.392398
18	-0.023376	-0.1983	0.421666

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 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; 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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Input Parameters & R Code