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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 11 Dec 2015 12:52:40 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Dec/11/t14498385415n6uvfrjxcmh8qd.htm/, Retrieved Thu, 16 May 2024 16:17:48 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=285926, Retrieved Thu, 16 May 2024 16:17:48 +0000

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMPD  [(Partial) Autocorrelation Function] [autocorrelatie to...] [2015-12-11 12:50:57] [22b6f4a061c8797aa483199554a73d13]
- R  D      [(Partial) Autocorrelation Function] [autocorrelatie to...] [2015-12-11 12:52:40] [20fcaaf1d4bc4a12bf87c6c50d624c14] [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	'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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285926&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285926&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285926&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' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.152167	1.0542	0.148525
2	0.069122	0.4789	0.317095
3	0.119232	0.8261	0.206428
4	0.088078	0.6102	0.272298
5	0.053469	0.3704	0.35634
6	0.116751	0.8089	0.211288
7	0.225785	1.5643	0.06216
8	0.151762	1.0514	0.149162
9	0.275405	1.9081	0.031187
10	0.153179	1.0613	0.146942
11	-0.049519	-0.3431	0.36652
12	-0.246169	-1.7055	0.047282
13	0.054532	0.3778	0.353619
14	0.159266	1.1034	0.137671
15	0.151269	1.048	0.149938
16	0.007552	0.0523	0.479245
17	0.141893	0.9831	0.165253

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.152167 & 1.0542 & 0.148525 \tabularnewline
2 & 0.069122 & 0.4789 & 0.317095 \tabularnewline
3 & 0.119232 & 0.8261 & 0.206428 \tabularnewline
4 & 0.088078 & 0.6102 & 0.272298 \tabularnewline
5 & 0.053469 & 0.3704 & 0.35634 \tabularnewline
6 & 0.116751 & 0.8089 & 0.211288 \tabularnewline
7 & 0.225785 & 1.5643 & 0.06216 \tabularnewline
8 & 0.151762 & 1.0514 & 0.149162 \tabularnewline
9 & 0.275405 & 1.9081 & 0.031187 \tabularnewline
10 & 0.153179 & 1.0613 & 0.146942 \tabularnewline
11 & -0.049519 & -0.3431 & 0.36652 \tabularnewline
12 & -0.246169 & -1.7055 & 0.047282 \tabularnewline
13 & 0.054532 & 0.3778 & 0.353619 \tabularnewline
14 & 0.159266 & 1.1034 & 0.137671 \tabularnewline
15 & 0.151269 & 1.048 & 0.149938 \tabularnewline
16 & 0.007552 & 0.0523 & 0.479245 \tabularnewline
17 & 0.141893 & 0.9831 & 0.165253 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285926&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]0.152167[/C][C]1.0542[/C][C]0.148525[/C][/ROW]
[ROW][C]2[/C][C]0.069122[/C][C]0.4789[/C][C]0.317095[/C][/ROW]
[ROW][C]3[/C][C]0.119232[/C][C]0.8261[/C][C]0.206428[/C][/ROW]
[ROW][C]4[/C][C]0.088078[/C][C]0.6102[/C][C]0.272298[/C][/ROW]
[ROW][C]5[/C][C]0.053469[/C][C]0.3704[/C][C]0.35634[/C][/ROW]
[ROW][C]6[/C][C]0.116751[/C][C]0.8089[/C][C]0.211288[/C][/ROW]
[ROW][C]7[/C][C]0.225785[/C][C]1.5643[/C][C]0.06216[/C][/ROW]
[ROW][C]8[/C][C]0.151762[/C][C]1.0514[/C][C]0.149162[/C][/ROW]
[ROW][C]9[/C][C]0.275405[/C][C]1.9081[/C][C]0.031187[/C][/ROW]
[ROW][C]10[/C][C]0.153179[/C][C]1.0613[/C][C]0.146942[/C][/ROW]
[ROW][C]11[/C][C]-0.049519[/C][C]-0.3431[/C][C]0.36652[/C][/ROW]
[ROW][C]12[/C][C]-0.246169[/C][C]-1.7055[/C][C]0.047282[/C][/ROW]
[ROW][C]13[/C][C]0.054532[/C][C]0.3778[/C][C]0.353619[/C][/ROW]
[ROW][C]14[/C][C]0.159266[/C][C]1.1034[/C][C]0.137671[/C][/ROW]
[ROW][C]15[/C][C]0.151269[/C][C]1.048[/C][C]0.149938[/C][/ROW]
[ROW][C]16[/C][C]0.007552[/C][C]0.0523[/C][C]0.479245[/C][/ROW]
[ROW][C]17[/C][C]0.141893[/C][C]0.9831[/C][C]0.165253[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285926&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285926&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	0.152167	1.0542	0.148525
2	0.069122	0.4789	0.317095
3	0.119232	0.8261	0.206428
4	0.088078	0.6102	0.272298
5	0.053469	0.3704	0.35634
6	0.116751	0.8089	0.211288
7	0.225785	1.5643	0.06216
8	0.151762	1.0514	0.149162
9	0.275405	1.9081	0.031187
10	0.153179	1.0613	0.146942
11	-0.049519	-0.3431	0.36652
12	-0.246169	-1.7055	0.047282
13	0.054532	0.3778	0.353619
14	0.159266	1.1034	0.137671
15	0.151269	1.048	0.149938
16	0.007552	0.0523	0.479245
17	0.141893	0.9831	0.165253

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.152167	1.0542	0.148525
2	0.047057	0.326	0.372913
3	0.104699	0.7254	0.235872
4	0.055229	0.3826	0.351839
5	0.023874	0.1654	0.434662
6	0.092127	0.6383	0.263165
7	0.189919	1.3158	0.097246
8	0.089624	0.6209	0.26879
9	0.233843	1.6201	0.05588
10	0.062767	0.4349	0.332806
11	-0.133438	-0.9245	0.179929
12	-0.355493	-2.4629	0.00871
13	0.001777	0.0123	0.495115
14	0.136496	0.9457	0.174526
15	0.177234	1.2279	0.112734
16	-0.13037	-0.9032	0.185456
17	0.03462	0.2399	0.405733

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.152167 & 1.0542 & 0.148525 \tabularnewline
2 & 0.047057 & 0.326 & 0.372913 \tabularnewline
3 & 0.104699 & 0.7254 & 0.235872 \tabularnewline
4 & 0.055229 & 0.3826 & 0.351839 \tabularnewline
5 & 0.023874 & 0.1654 & 0.434662 \tabularnewline
6 & 0.092127 & 0.6383 & 0.263165 \tabularnewline
7 & 0.189919 & 1.3158 & 0.097246 \tabularnewline
8 & 0.089624 & 0.6209 & 0.26879 \tabularnewline
9 & 0.233843 & 1.6201 & 0.05588 \tabularnewline
10 & 0.062767 & 0.4349 & 0.332806 \tabularnewline
11 & -0.133438 & -0.9245 & 0.179929 \tabularnewline
12 & -0.355493 & -2.4629 & 0.00871 \tabularnewline
13 & 0.001777 & 0.0123 & 0.495115 \tabularnewline
14 & 0.136496 & 0.9457 & 0.174526 \tabularnewline
15 & 0.177234 & 1.2279 & 0.112734 \tabularnewline
16 & -0.13037 & -0.9032 & 0.185456 \tabularnewline
17 & 0.03462 & 0.2399 & 0.405733 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285926&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]0.152167[/C][C]1.0542[/C][C]0.148525[/C][/ROW]
[ROW][C]2[/C][C]0.047057[/C][C]0.326[/C][C]0.372913[/C][/ROW]
[ROW][C]3[/C][C]0.104699[/C][C]0.7254[/C][C]0.235872[/C][/ROW]
[ROW][C]4[/C][C]0.055229[/C][C]0.3826[/C][C]0.351839[/C][/ROW]
[ROW][C]5[/C][C]0.023874[/C][C]0.1654[/C][C]0.434662[/C][/ROW]
[ROW][C]6[/C][C]0.092127[/C][C]0.6383[/C][C]0.263165[/C][/ROW]
[ROW][C]7[/C][C]0.189919[/C][C]1.3158[/C][C]0.097246[/C][/ROW]
[ROW][C]8[/C][C]0.089624[/C][C]0.6209[/C][C]0.26879[/C][/ROW]
[ROW][C]9[/C][C]0.233843[/C][C]1.6201[/C][C]0.05588[/C][/ROW]
[ROW][C]10[/C][C]0.062767[/C][C]0.4349[/C][C]0.332806[/C][/ROW]
[ROW][C]11[/C][C]-0.133438[/C][C]-0.9245[/C][C]0.179929[/C][/ROW]
[ROW][C]12[/C][C]-0.355493[/C][C]-2.4629[/C][C]0.00871[/C][/ROW]
[ROW][C]13[/C][C]0.001777[/C][C]0.0123[/C][C]0.495115[/C][/ROW]
[ROW][C]14[/C][C]0.136496[/C][C]0.9457[/C][C]0.174526[/C][/ROW]
[ROW][C]15[/C][C]0.177234[/C][C]1.2279[/C][C]0.112734[/C][/ROW]
[ROW][C]16[/C][C]-0.13037[/C][C]-0.9032[/C][C]0.185456[/C][/ROW]
[ROW][C]17[/C][C]0.03462[/C][C]0.2399[/C][C]0.405733[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285926&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285926&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	0.152167	1.0542	0.148525
2	0.047057	0.326	0.372913
3	0.104699	0.7254	0.235872
4	0.055229	0.3826	0.351839
5	0.023874	0.1654	0.434662
6	0.092127	0.6383	0.263165
7	0.189919	1.3158	0.097246
8	0.089624	0.6209	0.26879
9	0.233843	1.6201	0.05588
10	0.062767	0.4349	0.332806
11	-0.133438	-0.9245	0.179929
12	-0.355493	-2.4629	0.00871
13	0.001777	0.0123	0.495115
14	0.136496	0.9457	0.174526
15	0.177234	1.2279	0.112734
16	-0.13037	-0.9032	0.185456
17	0.03462	0.2399	0.405733

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)
x <- na.omit(x)
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