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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 17 Oct 2014 09:40:26 +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/2014/Oct/17/t14135355130trmlxl3y988513.htm/, Retrieved Thu, 09 May 2024 20:31:53 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=243187, Retrieved Thu, 09 May 2024 20:31:53 +0000

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Estimated Impact

122

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-       [(Partial) Autocorrelation Function] [] [2014-10-17 08:40:26] [e5757b82694375e1f239be852782e5f7] [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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243187&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243187&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243187&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	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.862465	7.3183	0
2	0.721639	6.1233	0
3	0.589404	5.0013	2e-06
4	0.468084	3.9718	8.4e-05
5	0.39618	3.3617	0.000621
6	0.311069	2.6395	0.005086
7	0.221772	1.8818	0.031953
8	0.133773	1.1351	0.130048
9	0.000796	0.0068	0.497315
10	-0.094891	-0.8052	0.211684
11	-0.200943	-1.7051	0.046248
12	-0.30198	-2.5624	0.006244
13	-0.298297	-2.5311	0.006777
14	-0.307713	-2.611	0.005489
15	-0.300204	-2.5473	0.006496
16	-0.283935	-2.4093	0.009272
17	-0.279652	-2.3729	0.01016
18	-0.266497	-2.2613	0.013381

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.862465 & 7.3183 & 0 \tabularnewline
2 & 0.721639 & 6.1233 & 0 \tabularnewline
3 & 0.589404 & 5.0013 & 2e-06 \tabularnewline
4 & 0.468084 & 3.9718 & 8.4e-05 \tabularnewline
5 & 0.39618 & 3.3617 & 0.000621 \tabularnewline
6 & 0.311069 & 2.6395 & 0.005086 \tabularnewline
7 & 0.221772 & 1.8818 & 0.031953 \tabularnewline
8 & 0.133773 & 1.1351 & 0.130048 \tabularnewline
9 & 0.000796 & 0.0068 & 0.497315 \tabularnewline
10 & -0.094891 & -0.8052 & 0.211684 \tabularnewline
11 & -0.200943 & -1.7051 & 0.046248 \tabularnewline
12 & -0.30198 & -2.5624 & 0.006244 \tabularnewline
13 & -0.298297 & -2.5311 & 0.006777 \tabularnewline
14 & -0.307713 & -2.611 & 0.005489 \tabularnewline
15 & -0.300204 & -2.5473 & 0.006496 \tabularnewline
16 & -0.283935 & -2.4093 & 0.009272 \tabularnewline
17 & -0.279652 & -2.3729 & 0.01016 \tabularnewline
18 & -0.266497 & -2.2613 & 0.013381 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243187&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]0.862465[/C][C]7.3183[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.721639[/C][C]6.1233[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.589404[/C][C]5.0013[/C][C]2e-06[/C][/ROW]
[ROW][C]4[/C][C]0.468084[/C][C]3.9718[/C][C]8.4e-05[/C][/ROW]
[ROW][C]5[/C][C]0.39618[/C][C]3.3617[/C][C]0.000621[/C][/ROW]
[ROW][C]6[/C][C]0.311069[/C][C]2.6395[/C][C]0.005086[/C][/ROW]
[ROW][C]7[/C][C]0.221772[/C][C]1.8818[/C][C]0.031953[/C][/ROW]
[ROW][C]8[/C][C]0.133773[/C][C]1.1351[/C][C]0.130048[/C][/ROW]
[ROW][C]9[/C][C]0.000796[/C][C]0.0068[/C][C]0.497315[/C][/ROW]
[ROW][C]10[/C][C]-0.094891[/C][C]-0.8052[/C][C]0.211684[/C][/ROW]
[ROW][C]11[/C][C]-0.200943[/C][C]-1.7051[/C][C]0.046248[/C][/ROW]
[ROW][C]12[/C][C]-0.30198[/C][C]-2.5624[/C][C]0.006244[/C][/ROW]
[ROW][C]13[/C][C]-0.298297[/C][C]-2.5311[/C][C]0.006777[/C][/ROW]
[ROW][C]14[/C][C]-0.307713[/C][C]-2.611[/C][C]0.005489[/C][/ROW]
[ROW][C]15[/C][C]-0.300204[/C][C]-2.5473[/C][C]0.006496[/C][/ROW]
[ROW][C]16[/C][C]-0.283935[/C][C]-2.4093[/C][C]0.009272[/C][/ROW]
[ROW][C]17[/C][C]-0.279652[/C][C]-2.3729[/C][C]0.01016[/C][/ROW]
[ROW][C]18[/C][C]-0.266497[/C][C]-2.2613[/C][C]0.013381[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243187&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243187&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	0.862465	7.3183	0
2	0.721639	6.1233	0
3	0.589404	5.0013	2e-06
4	0.468084	3.9718	8.4e-05
5	0.39618	3.3617	0.000621
6	0.311069	2.6395	0.005086
7	0.221772	1.8818	0.031953
8	0.133773	1.1351	0.130048
9	0.000796	0.0068	0.497315
10	-0.094891	-0.8052	0.211684
11	-0.200943	-1.7051	0.046248
12	-0.30198	-2.5624	0.006244
13	-0.298297	-2.5311	0.006777
14	-0.307713	-2.611	0.005489
15	-0.300204	-2.5473	0.006496
16	-0.283935	-2.4093	0.009272
17	-0.279652	-2.3729	0.01016
18	-0.266497	-2.2613	0.013381

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.862465	7.3183	0
2	-0.086691	-0.7356	0.232183
3	-0.047879	-0.4063	0.342876
4	-0.041031	-0.3482	0.364368
5	0.111792	0.9486	0.173001
6	-0.114645	-0.9728	0.166956
7	-0.073786	-0.6261	0.266617
8	-0.061821	-0.5246	0.300747
9	-0.235256	-1.9962	0.024847
10	0.022211	0.1885	0.425519
11	-0.168969	-1.4337	0.077986
12	-0.105615	-0.8962	0.186572
13	0.270102	2.2919	0.012419
14	-0.101647	-0.8625	0.195636
15	0.010202	0.0866	0.465628
16	0.021878	0.1856	0.426624
17	0.027668	0.2348	0.407526
18	-0.087262	-0.7404	0.23072

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.862465 & 7.3183 & 0 \tabularnewline
2 & -0.086691 & -0.7356 & 0.232183 \tabularnewline
3 & -0.047879 & -0.4063 & 0.342876 \tabularnewline
4 & -0.041031 & -0.3482 & 0.364368 \tabularnewline
5 & 0.111792 & 0.9486 & 0.173001 \tabularnewline
6 & -0.114645 & -0.9728 & 0.166956 \tabularnewline
7 & -0.073786 & -0.6261 & 0.266617 \tabularnewline
8 & -0.061821 & -0.5246 & 0.300747 \tabularnewline
9 & -0.235256 & -1.9962 & 0.024847 \tabularnewline
10 & 0.022211 & 0.1885 & 0.425519 \tabularnewline
11 & -0.168969 & -1.4337 & 0.077986 \tabularnewline
12 & -0.105615 & -0.8962 & 0.186572 \tabularnewline
13 & 0.270102 & 2.2919 & 0.012419 \tabularnewline
14 & -0.101647 & -0.8625 & 0.195636 \tabularnewline
15 & 0.010202 & 0.0866 & 0.465628 \tabularnewline
16 & 0.021878 & 0.1856 & 0.426624 \tabularnewline
17 & 0.027668 & 0.2348 & 0.407526 \tabularnewline
18 & -0.087262 & -0.7404 & 0.23072 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243187&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]0.862465[/C][C]7.3183[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.086691[/C][C]-0.7356[/C][C]0.232183[/C][/ROW]
[ROW][C]3[/C][C]-0.047879[/C][C]-0.4063[/C][C]0.342876[/C][/ROW]
[ROW][C]4[/C][C]-0.041031[/C][C]-0.3482[/C][C]0.364368[/C][/ROW]
[ROW][C]5[/C][C]0.111792[/C][C]0.9486[/C][C]0.173001[/C][/ROW]
[ROW][C]6[/C][C]-0.114645[/C][C]-0.9728[/C][C]0.166956[/C][/ROW]
[ROW][C]7[/C][C]-0.073786[/C][C]-0.6261[/C][C]0.266617[/C][/ROW]
[ROW][C]8[/C][C]-0.061821[/C][C]-0.5246[/C][C]0.300747[/C][/ROW]
[ROW][C]9[/C][C]-0.235256[/C][C]-1.9962[/C][C]0.024847[/C][/ROW]
[ROW][C]10[/C][C]0.022211[/C][C]0.1885[/C][C]0.425519[/C][/ROW]
[ROW][C]11[/C][C]-0.168969[/C][C]-1.4337[/C][C]0.077986[/C][/ROW]
[ROW][C]12[/C][C]-0.105615[/C][C]-0.8962[/C][C]0.186572[/C][/ROW]
[ROW][C]13[/C][C]0.270102[/C][C]2.2919[/C][C]0.012419[/C][/ROW]
[ROW][C]14[/C][C]-0.101647[/C][C]-0.8625[/C][C]0.195636[/C][/ROW]
[ROW][C]15[/C][C]0.010202[/C][C]0.0866[/C][C]0.465628[/C][/ROW]
[ROW][C]16[/C][C]0.021878[/C][C]0.1856[/C][C]0.426624[/C][/ROW]
[ROW][C]17[/C][C]0.027668[/C][C]0.2348[/C][C]0.407526[/C][/ROW]
[ROW][C]18[/C][C]-0.087262[/C][C]-0.7404[/C][C]0.23072[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243187&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243187&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	0.862465	7.3183	0
2	-0.086691	-0.7356	0.232183
3	-0.047879	-0.4063	0.342876
4	-0.041031	-0.3482	0.364368
5	0.111792	0.9486	0.173001
6	-0.114645	-0.9728	0.166956
7	-0.073786	-0.6261	0.266617
8	-0.061821	-0.5246	0.300747
9	-0.235256	-1.9962	0.024847
10	0.022211	0.1885	0.425519
11	-0.168969	-1.4337	0.077986
12	-0.105615	-0.8962	0.186572
13	0.270102	2.2919	0.012419
14	-0.101647	-0.8625	0.195636
15	0.010202	0.0866	0.465628
16	0.021878	0.1856	0.426624
17	0.027668	0.2348	0.407526
18	-0.087262	-0.7404	0.23072

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):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
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)
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')

Free Statistics

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code