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Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 27 Dec 2010 10:22:55 +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/2010/Dec/27/t1293446488tp5f1jrbs7hzh4g.htm/, Retrieved Mon, 06 May 2024 21:36:38 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115896, Retrieved Mon, 06 May 2024 21:36:38 +0000

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Estimated Impact

119

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-       [(Partial) Autocorrelation Function] [] [2010-12-27 10:22:55] [c984196f1244e05baf3e7c2e52d47a33] [Current]

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8.5
8.6
8.5
8.2
8.1
7.9
8.6
8.7
8.7
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8
8.2
8.1
8.1
8
7.9
7.9
8
8
7.9
8
7.7
7.2
7.5
7.3
7
7
7
7.2
7.3
7.1
6.8
6.4
6.1
6.5
7.7
.9
7.5
6.9
6.6
6.9
7.7
8
8
7.7
7.3
7.4
8.1
8.3
8.1
7.9
7.9
8.3
8.6

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115896&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115896&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115896&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	2 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.233141	1.632	0.054547
2	0.318446	2.2291	0.015212
3	0.375289	2.627	0.005733
4	0.360441	2.5231	0.007464
5	0.264775	1.8534	0.034923
6	0.166513	1.1656	0.124712
7	0.115603	0.8092	0.21115
8	0.053174	0.3722	0.355668
9	0.027798	0.1946	0.423261
10	0.024891	0.1742	0.431199
11	0.056371	0.3946	0.347427
12	-0.366004	-2.562	0.006766
13	-0.01554	-0.1088	0.456911
14	-0.074231	-0.5196	0.302834
15	-0.151336	-1.0594	0.147317
16	-0.177373	-1.2416	0.110146
17	-0.137028	-0.9592	0.171084

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.233141 & 1.632 & 0.054547 \tabularnewline
2 & 0.318446 & 2.2291 & 0.015212 \tabularnewline
3 & 0.375289 & 2.627 & 0.005733 \tabularnewline
4 & 0.360441 & 2.5231 & 0.007464 \tabularnewline
5 & 0.264775 & 1.8534 & 0.034923 \tabularnewline
6 & 0.166513 & 1.1656 & 0.124712 \tabularnewline
7 & 0.115603 & 0.8092 & 0.21115 \tabularnewline
8 & 0.053174 & 0.3722 & 0.355668 \tabularnewline
9 & 0.027798 & 0.1946 & 0.423261 \tabularnewline
10 & 0.024891 & 0.1742 & 0.431199 \tabularnewline
11 & 0.056371 & 0.3946 & 0.347427 \tabularnewline
12 & -0.366004 & -2.562 & 0.006766 \tabularnewline
13 & -0.01554 & -0.1088 & 0.456911 \tabularnewline
14 & -0.074231 & -0.5196 & 0.302834 \tabularnewline
15 & -0.151336 & -1.0594 & 0.147317 \tabularnewline
16 & -0.177373 & -1.2416 & 0.110146 \tabularnewline
17 & -0.137028 & -0.9592 & 0.171084 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115896&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]0.233141[/C][C]1.632[/C][C]0.054547[/C][/ROW]
[ROW][C]2[/C][C]0.318446[/C][C]2.2291[/C][C]0.015212[/C][/ROW]
[ROW][C]3[/C][C]0.375289[/C][C]2.627[/C][C]0.005733[/C][/ROW]
[ROW][C]4[/C][C]0.360441[/C][C]2.5231[/C][C]0.007464[/C][/ROW]
[ROW][C]5[/C][C]0.264775[/C][C]1.8534[/C][C]0.034923[/C][/ROW]
[ROW][C]6[/C][C]0.166513[/C][C]1.1656[/C][C]0.124712[/C][/ROW]
[ROW][C]7[/C][C]0.115603[/C][C]0.8092[/C][C]0.21115[/C][/ROW]
[ROW][C]8[/C][C]0.053174[/C][C]0.3722[/C][C]0.355668[/C][/ROW]
[ROW][C]9[/C][C]0.027798[/C][C]0.1946[/C][C]0.423261[/C][/ROW]
[ROW][C]10[/C][C]0.024891[/C][C]0.1742[/C][C]0.431199[/C][/ROW]
[ROW][C]11[/C][C]0.056371[/C][C]0.3946[/C][C]0.347427[/C][/ROW]
[ROW][C]12[/C][C]-0.366004[/C][C]-2.562[/C][C]0.006766[/C][/ROW]
[ROW][C]13[/C][C]-0.01554[/C][C]-0.1088[/C][C]0.456911[/C][/ROW]
[ROW][C]14[/C][C]-0.074231[/C][C]-0.5196[/C][C]0.302834[/C][/ROW]
[ROW][C]15[/C][C]-0.151336[/C][C]-1.0594[/C][C]0.147317[/C][/ROW]
[ROW][C]16[/C][C]-0.177373[/C][C]-1.2416[/C][C]0.110146[/C][/ROW]
[ROW][C]17[/C][C]-0.137028[/C][C]-0.9592[/C][C]0.171084[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115896&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115896&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	0.233141	1.632	0.054547
2	0.318446	2.2291	0.015212
3	0.375289	2.627	0.005733
4	0.360441	2.5231	0.007464
5	0.264775	1.8534	0.034923
6	0.166513	1.1656	0.124712
7	0.115603	0.8092	0.21115
8	0.053174	0.3722	0.355668
9	0.027798	0.1946	0.423261
10	0.024891	0.1742	0.431199
11	0.056371	0.3946	0.347427
12	-0.366004	-2.562	0.006766
13	-0.01554	-0.1088	0.456911
14	-0.074231	-0.5196	0.302834
15	-0.151336	-1.0594	0.147317
16	-0.177373	-1.2416	0.110146
17	-0.137028	-0.9592	0.171084

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.233141	1.632	0.054547
2	0.279271	1.9549	0.028156
3	0.294383	2.0607	0.022331
4	0.234099	1.6387	0.053842
5	0.067363	0.4715	0.319675
6	-0.105365	-0.7376	0.23215
7	-0.174258	-1.2198	0.114189
8	-0.191987	-1.3439	0.092584
9	-0.11034	-0.7724	0.221799
10	0.028773	0.2014	0.420607
11	0.193708	1.356	0.090664
12	-0.388555	-2.7199	0.004505
13	0.023624	0.1654	0.434668
14	0.051107	0.3578	0.361033
15	0.05371	0.376	0.35428
16	0.047839	0.3349	0.369576
17	0.031985	0.2239	0.411885

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.233141 & 1.632 & 0.054547 \tabularnewline
2 & 0.279271 & 1.9549 & 0.028156 \tabularnewline
3 & 0.294383 & 2.0607 & 0.022331 \tabularnewline
4 & 0.234099 & 1.6387 & 0.053842 \tabularnewline
5 & 0.067363 & 0.4715 & 0.319675 \tabularnewline
6 & -0.105365 & -0.7376 & 0.23215 \tabularnewline
7 & -0.174258 & -1.2198 & 0.114189 \tabularnewline
8 & -0.191987 & -1.3439 & 0.092584 \tabularnewline
9 & -0.11034 & -0.7724 & 0.221799 \tabularnewline
10 & 0.028773 & 0.2014 & 0.420607 \tabularnewline
11 & 0.193708 & 1.356 & 0.090664 \tabularnewline
12 & -0.388555 & -2.7199 & 0.004505 \tabularnewline
13 & 0.023624 & 0.1654 & 0.434668 \tabularnewline
14 & 0.051107 & 0.3578 & 0.361033 \tabularnewline
15 & 0.05371 & 0.376 & 0.35428 \tabularnewline
16 & 0.047839 & 0.3349 & 0.369576 \tabularnewline
17 & 0.031985 & 0.2239 & 0.411885 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115896&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]0.233141[/C][C]1.632[/C][C]0.054547[/C][/ROW]
[ROW][C]2[/C][C]0.279271[/C][C]1.9549[/C][C]0.028156[/C][/ROW]
[ROW][C]3[/C][C]0.294383[/C][C]2.0607[/C][C]0.022331[/C][/ROW]
[ROW][C]4[/C][C]0.234099[/C][C]1.6387[/C][C]0.053842[/C][/ROW]
[ROW][C]5[/C][C]0.067363[/C][C]0.4715[/C][C]0.319675[/C][/ROW]
[ROW][C]6[/C][C]-0.105365[/C][C]-0.7376[/C][C]0.23215[/C][/ROW]
[ROW][C]7[/C][C]-0.174258[/C][C]-1.2198[/C][C]0.114189[/C][/ROW]
[ROW][C]8[/C][C]-0.191987[/C][C]-1.3439[/C][C]0.092584[/C][/ROW]
[ROW][C]9[/C][C]-0.11034[/C][C]-0.7724[/C][C]0.221799[/C][/ROW]
[ROW][C]10[/C][C]0.028773[/C][C]0.2014[/C][C]0.420607[/C][/ROW]
[ROW][C]11[/C][C]0.193708[/C][C]1.356[/C][C]0.090664[/C][/ROW]
[ROW][C]12[/C][C]-0.388555[/C][C]-2.7199[/C][C]0.004505[/C][/ROW]
[ROW][C]13[/C][C]0.023624[/C][C]0.1654[/C][C]0.434668[/C][/ROW]
[ROW][C]14[/C][C]0.051107[/C][C]0.3578[/C][C]0.361033[/C][/ROW]
[ROW][C]15[/C][C]0.05371[/C][C]0.376[/C][C]0.35428[/C][/ROW]
[ROW][C]16[/C][C]0.047839[/C][C]0.3349[/C][C]0.369576[/C][/ROW]
[ROW][C]17[/C][C]0.031985[/C][C]0.2239[/C][C]0.411885[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115896&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115896&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	0.233141	1.632	0.054547
2	0.279271	1.9549	0.028156
3	0.294383	2.0607	0.022331
4	0.234099	1.6387	0.053842
5	0.067363	0.4715	0.319675
6	-0.105365	-0.7376	0.23215
7	-0.174258	-1.2198	0.114189
8	-0.191987	-1.3439	0.092584
9	-0.11034	-0.7724	0.221799
10	0.028773	0.2014	0.420607
11	0.193708	1.356	0.090664
12	-0.388555	-2.7199	0.004505
13	0.023624	0.1654	0.434668
14	0.051107	0.3578	0.361033
15	0.05371	0.376	0.35428
16	0.047839	0.3349	0.369576
17	0.031985	0.2239	0.411885

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 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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