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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

Tue, 13 Dec 2016 09:48:04 +0100

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/2016/Dec/13/t1481619480dv4o2j9bhm08rku.htm/, Retrieved Sun, 05 May 2024 06:54:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299019, Retrieved Sun, 05 May 2024 06:54:51 +0000

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No (this computation is public)

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Estimated Impact

107

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

-       [(Partial) Autocorrelation Function] [autocorrelatie] [2016-12-13 08:48:04] [afe7f6443461a2cd6ee0b843643e84a9] [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	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299019&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=299019&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299019&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	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.97552	10.5067	0
2	0.951305	10.2459	0
3	0.927533	9.9898	0
4	0.903792	9.7341	0
5	0.878445	9.4611	0
6	0.853386	9.1913	0
7	0.828444	8.9226	0
8	0.803095	8.6496	0
9	0.777158	8.3702	0
10	0.751638	8.0954	0
11	0.726733	7.8272	0
12	0.702223	7.5632	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.97552 & 10.5067 & 0 \tabularnewline
2 & 0.951305 & 10.2459 & 0 \tabularnewline
3 & 0.927533 & 9.9898 & 0 \tabularnewline
4 & 0.903792 & 9.7341 & 0 \tabularnewline
5 & 0.878445 & 9.4611 & 0 \tabularnewline
6 & 0.853386 & 9.1913 & 0 \tabularnewline
7 & 0.828444 & 8.9226 & 0 \tabularnewline
8 & 0.803095 & 8.6496 & 0 \tabularnewline
9 & 0.777158 & 8.3702 & 0 \tabularnewline
10 & 0.751638 & 8.0954 & 0 \tabularnewline
11 & 0.726733 & 7.8272 & 0 \tabularnewline
12 & 0.702223 & 7.5632 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299019&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]0.97552[/C][C]10.5067[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.951305[/C][C]10.2459[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.927533[/C][C]9.9898[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.903792[/C][C]9.7341[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.878445[/C][C]9.4611[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.853386[/C][C]9.1913[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.828444[/C][C]8.9226[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.803095[/C][C]8.6496[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.777158[/C][C]8.3702[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.751638[/C][C]8.0954[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.726733[/C][C]7.8272[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.702223[/C][C]7.5632[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299019&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299019&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	0.97552	10.5067	0
2	0.951305	10.2459	0
3	0.927533	9.9898	0
4	0.903792	9.7341	0
5	0.878445	9.4611	0
6	0.853386	9.1913	0
7	0.828444	8.9226	0
8	0.803095	8.6496	0
9	0.777158	8.3702	0
10	0.751638	8.0954	0
11	0.726733	7.8272	0
12	0.702223	7.5632	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.97552	10.5067	0
2	-0.006908	-0.0744	0.470409
3	-0.003213	-0.0346	0.486227
4	-0.011604	-0.125	0.450377
5	-0.045592	-0.491	0.312162
6	-0.007869	-0.0847	0.466305
7	-0.011645	-0.1254	0.450203
8	-0.022009	-0.237	0.406518
9	-0.025252	-0.272	0.393065
10	-0.006572	-0.0708	0.471846
11	-0.002085	-0.0225	0.491059
12	-0.005393	-0.0581	0.476892

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.97552 & 10.5067 & 0 \tabularnewline
2 & -0.006908 & -0.0744 & 0.470409 \tabularnewline
3 & -0.003213 & -0.0346 & 0.486227 \tabularnewline
4 & -0.011604 & -0.125 & 0.450377 \tabularnewline
5 & -0.045592 & -0.491 & 0.312162 \tabularnewline
6 & -0.007869 & -0.0847 & 0.466305 \tabularnewline
7 & -0.011645 & -0.1254 & 0.450203 \tabularnewline
8 & -0.022009 & -0.237 & 0.406518 \tabularnewline
9 & -0.025252 & -0.272 & 0.393065 \tabularnewline
10 & -0.006572 & -0.0708 & 0.471846 \tabularnewline
11 & -0.002085 & -0.0225 & 0.491059 \tabularnewline
12 & -0.005393 & -0.0581 & 0.476892 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299019&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]0.97552[/C][C]10.5067[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.006908[/C][C]-0.0744[/C][C]0.470409[/C][/ROW]
[ROW][C]3[/C][C]-0.003213[/C][C]-0.0346[/C][C]0.486227[/C][/ROW]
[ROW][C]4[/C][C]-0.011604[/C][C]-0.125[/C][C]0.450377[/C][/ROW]
[ROW][C]5[/C][C]-0.045592[/C][C]-0.491[/C][C]0.312162[/C][/ROW]
[ROW][C]6[/C][C]-0.007869[/C][C]-0.0847[/C][C]0.466305[/C][/ROW]
[ROW][C]7[/C][C]-0.011645[/C][C]-0.1254[/C][C]0.450203[/C][/ROW]
[ROW][C]8[/C][C]-0.022009[/C][C]-0.237[/C][C]0.406518[/C][/ROW]
[ROW][C]9[/C][C]-0.025252[/C][C]-0.272[/C][C]0.393065[/C][/ROW]
[ROW][C]10[/C][C]-0.006572[/C][C]-0.0708[/C][C]0.471846[/C][/ROW]
[ROW][C]11[/C][C]-0.002085[/C][C]-0.0225[/C][C]0.491059[/C][/ROW]
[ROW][C]12[/C][C]-0.005393[/C][C]-0.0581[/C][C]0.476892[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299019&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299019&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	0.97552	10.5067	0
2	-0.006908	-0.0744	0.470409
3	-0.003213	-0.0346	0.486227
4	-0.011604	-0.125	0.450377
5	-0.045592	-0.491	0.312162
6	-0.007869	-0.0847	0.466305
7	-0.011645	-0.1254	0.450203
8	-0.022009	-0.237	0.406518
9	-0.025252	-0.272	0.393065
10	-0.006572	-0.0708	0.471846
11	-0.002085	-0.0225	0.491059
12	-0.005393	-0.0581	0.476892

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 = 12 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 12 ; 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)
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,'ACF(k)',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,'PACF(k)',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