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Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 11 Dec 2015 12:50:57 +0000

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/2015/Dec/11/t1449838270nyg7ltk4sx8vvxd.htm/, Retrieved Thu, 16 May 2024 16:02:55 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=285924, Retrieved Thu, 16 May 2024 16:02:55 +0000

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Estimated Impact

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] [20fcaaf1d4bc4a12bf87c6c50d624c14] [Current]
- R  D      [(Partial) Autocorrelation Function] [autocorrelatie to...] [2015-12-11 12:52:40] [22b6f4a061c8797aa483199554a73d13] 
- RMPD      [Variance Reduction Matrix] [variantie totaal ...] [2015-12-11 12:59:29] [22b6f4a061c8797aa483199554a73d13] 
- RMPD      [Variance Reduction Matrix] [variantie totaal ...] [2015-12-11 13:05:33] [22b6f4a061c8797aa483199554a73d13] 

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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=285924&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=285924&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285924&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	0.040655	0.2817	0.389705
2	0.154354	1.0694	0.14512
3	0.143483	0.9941	0.162585
4	0.176578	1.2234	0.113581
5	0.012294	0.0852	0.466237
6	0.073622	0.5101	0.306171
7	0.121896	0.8445	0.201283
8	0.079576	0.5513	0.291987
9	0.152794	1.0586	0.147544
10	-0.031637	-0.2192	0.413718
11	0.03943	0.2732	0.392944
12	-0.188958	-1.3091	0.09836
13	0.078555	0.5442	0.294396
14	0.012779	0.0885	0.464909
15	0.104853	0.7264	0.235547
16	-0.029174	-0.2021	0.420337
17	0.12335	0.8546	0.19851

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.040655 & 0.2817 & 0.389705 \tabularnewline
2 & 0.154354 & 1.0694 & 0.14512 \tabularnewline
3 & 0.143483 & 0.9941 & 0.162585 \tabularnewline
4 & 0.176578 & 1.2234 & 0.113581 \tabularnewline
5 & 0.012294 & 0.0852 & 0.466237 \tabularnewline
6 & 0.073622 & 0.5101 & 0.306171 \tabularnewline
7 & 0.121896 & 0.8445 & 0.201283 \tabularnewline
8 & 0.079576 & 0.5513 & 0.291987 \tabularnewline
9 & 0.152794 & 1.0586 & 0.147544 \tabularnewline
10 & -0.031637 & -0.2192 & 0.413718 \tabularnewline
11 & 0.03943 & 0.2732 & 0.392944 \tabularnewline
12 & -0.188958 & -1.3091 & 0.09836 \tabularnewline
13 & 0.078555 & 0.5442 & 0.294396 \tabularnewline
14 & 0.012779 & 0.0885 & 0.464909 \tabularnewline
15 & 0.104853 & 0.7264 & 0.235547 \tabularnewline
16 & -0.029174 & -0.2021 & 0.420337 \tabularnewline
17 & 0.12335 & 0.8546 & 0.19851 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285924&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]0.040655[/C][C]0.2817[/C][C]0.389705[/C][/ROW]
[ROW][C]2[/C][C]0.154354[/C][C]1.0694[/C][C]0.14512[/C][/ROW]
[ROW][C]3[/C][C]0.143483[/C][C]0.9941[/C][C]0.162585[/C][/ROW]
[ROW][C]4[/C][C]0.176578[/C][C]1.2234[/C][C]0.113581[/C][/ROW]
[ROW][C]5[/C][C]0.012294[/C][C]0.0852[/C][C]0.466237[/C][/ROW]
[ROW][C]6[/C][C]0.073622[/C][C]0.5101[/C][C]0.306171[/C][/ROW]
[ROW][C]7[/C][C]0.121896[/C][C]0.8445[/C][C]0.201283[/C][/ROW]
[ROW][C]8[/C][C]0.079576[/C][C]0.5513[/C][C]0.291987[/C][/ROW]
[ROW][C]9[/C][C]0.152794[/C][C]1.0586[/C][C]0.147544[/C][/ROW]
[ROW][C]10[/C][C]-0.031637[/C][C]-0.2192[/C][C]0.413718[/C][/ROW]
[ROW][C]11[/C][C]0.03943[/C][C]0.2732[/C][C]0.392944[/C][/ROW]
[ROW][C]12[/C][C]-0.188958[/C][C]-1.3091[/C][C]0.09836[/C][/ROW]
[ROW][C]13[/C][C]0.078555[/C][C]0.5442[/C][C]0.294396[/C][/ROW]
[ROW][C]14[/C][C]0.012779[/C][C]0.0885[/C][C]0.464909[/C][/ROW]
[ROW][C]15[/C][C]0.104853[/C][C]0.7264[/C][C]0.235547[/C][/ROW]
[ROW][C]16[/C][C]-0.029174[/C][C]-0.2021[/C][C]0.420337[/C][/ROW]
[ROW][C]17[/C][C]0.12335[/C][C]0.8546[/C][C]0.19851[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285924&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285924&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	0.040655	0.2817	0.389705
2	0.154354	1.0694	0.14512
3	0.143483	0.9941	0.162585
4	0.176578	1.2234	0.113581
5	0.012294	0.0852	0.466237
6	0.073622	0.5101	0.306171
7	0.121896	0.8445	0.201283
8	0.079576	0.5513	0.291987
9	0.152794	1.0586	0.147544
10	-0.031637	-0.2192	0.413718
11	0.03943	0.2732	0.392944
12	-0.188958	-1.3091	0.09836
13	0.078555	0.5442	0.294396
14	0.012779	0.0885	0.464909
15	0.104853	0.7264	0.235547
16	-0.029174	-0.2021	0.420337
17	0.12335	0.8546	0.19851

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.040655	0.2817	0.389705
2	0.152954	1.0597	0.147294
3	0.135333	0.9376	0.176568
4	0.152764	1.0584	0.14759
5	-0.033466	-0.2319	0.408817
6	0.00939	0.0651	0.474199
7	0.0851	0.5896	0.279114
8	0.049011	0.3396	0.367835
9	0.129543	0.8975	0.186966
10	-0.092752	-0.6426	0.26177
11	-0.0448	-0.3104	0.378807
12	-0.247988	-1.7181	0.04611
13	0.055923	0.3874	0.35007
14	0.093846	0.6502	0.259336
15	0.15541	1.0767	0.143495
16	-0.021122	-0.1463	0.442135
17	0.040068	0.2776	0.391256

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.040655 & 0.2817 & 0.389705 \tabularnewline
2 & 0.152954 & 1.0597 & 0.147294 \tabularnewline
3 & 0.135333 & 0.9376 & 0.176568 \tabularnewline
4 & 0.152764 & 1.0584 & 0.14759 \tabularnewline
5 & -0.033466 & -0.2319 & 0.408817 \tabularnewline
6 & 0.00939 & 0.0651 & 0.474199 \tabularnewline
7 & 0.0851 & 0.5896 & 0.279114 \tabularnewline
8 & 0.049011 & 0.3396 & 0.367835 \tabularnewline
9 & 0.129543 & 0.8975 & 0.186966 \tabularnewline
10 & -0.092752 & -0.6426 & 0.26177 \tabularnewline
11 & -0.0448 & -0.3104 & 0.378807 \tabularnewline
12 & -0.247988 & -1.7181 & 0.04611 \tabularnewline
13 & 0.055923 & 0.3874 & 0.35007 \tabularnewline
14 & 0.093846 & 0.6502 & 0.259336 \tabularnewline
15 & 0.15541 & 1.0767 & 0.143495 \tabularnewline
16 & -0.021122 & -0.1463 & 0.442135 \tabularnewline
17 & 0.040068 & 0.2776 & 0.391256 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285924&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]0.040655[/C][C]0.2817[/C][C]0.389705[/C][/ROW]
[ROW][C]2[/C][C]0.152954[/C][C]1.0597[/C][C]0.147294[/C][/ROW]
[ROW][C]3[/C][C]0.135333[/C][C]0.9376[/C][C]0.176568[/C][/ROW]
[ROW][C]4[/C][C]0.152764[/C][C]1.0584[/C][C]0.14759[/C][/ROW]
[ROW][C]5[/C][C]-0.033466[/C][C]-0.2319[/C][C]0.408817[/C][/ROW]
[ROW][C]6[/C][C]0.00939[/C][C]0.0651[/C][C]0.474199[/C][/ROW]
[ROW][C]7[/C][C]0.0851[/C][C]0.5896[/C][C]0.279114[/C][/ROW]
[ROW][C]8[/C][C]0.049011[/C][C]0.3396[/C][C]0.367835[/C][/ROW]
[ROW][C]9[/C][C]0.129543[/C][C]0.8975[/C][C]0.186966[/C][/ROW]
[ROW][C]10[/C][C]-0.092752[/C][C]-0.6426[/C][C]0.26177[/C][/ROW]
[ROW][C]11[/C][C]-0.0448[/C][C]-0.3104[/C][C]0.378807[/C][/ROW]
[ROW][C]12[/C][C]-0.247988[/C][C]-1.7181[/C][C]0.04611[/C][/ROW]
[ROW][C]13[/C][C]0.055923[/C][C]0.3874[/C][C]0.35007[/C][/ROW]
[ROW][C]14[/C][C]0.093846[/C][C]0.6502[/C][C]0.259336[/C][/ROW]
[ROW][C]15[/C][C]0.15541[/C][C]1.0767[/C][C]0.143495[/C][/ROW]
[ROW][C]16[/C][C]-0.021122[/C][C]-0.1463[/C][C]0.442135[/C][/ROW]
[ROW][C]17[/C][C]0.040068[/C][C]0.2776[/C][C]0.391256[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285924&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285924&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	0.040655	0.2817	0.389705
2	0.152954	1.0597	0.147294
3	0.135333	0.9376	0.176568
4	0.152764	1.0584	0.14759
5	-0.033466	-0.2319	0.408817
6	0.00939	0.0651	0.474199
7	0.0851	0.5896	0.279114
8	0.049011	0.3396	0.367835
9	0.129543	0.8975	0.186966
10	-0.092752	-0.6426	0.26177
11	-0.0448	-0.3104	0.378807
12	-0.247988	-1.7181	0.04611
13	0.055923	0.3874	0.35007
14	0.093846	0.6502	0.259336
15	0.15541	1.0767	0.143495
16	-0.021122	-0.1463	0.442135
17	0.040068	0.2776	0.391256

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):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '1'
par3 <- '0'
par2 <- '1'
par1 <- 'Default'
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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code