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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 26 Nov 2015 19:18:56 +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/Nov/26/t1448565604ugtbp5bbwcpwy6f.htm/, Retrieved Tue, 21 May 2024 17:18:20 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284271, Retrieved Tue, 21 May 2024 17:18:20 +0000

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No (this computation is public)

User-defined keywords

d = 1 D = 0

Estimated Impact

128

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-       [(Partial) Autocorrelation Function] [Partial Autocorre...] [2015-11-26 19:18:56] [60fe8c82fc27b8a1ae22563c57c4f789] [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=284271&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=284271&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284271&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	0.18793	1.4435	0.077082
2	0.038962	0.2993	0.382893
3	0.058917	0.4526	0.326265
4	-0.221742	-1.7032	0.046893
5	-0.388615	-2.985	0.002061
6	-0.173788	-1.3349	0.09352
7	-0.32473	-2.4943	0.007721
8	-0.277451	-2.1311	0.018627
9	0.049044	0.3767	0.353868
10	0.03989	0.3064	0.38019
11	0.149878	1.1512	0.127139
12	0.733603	5.6349	0
13	0.178526	1.3713	0.08774
14	0.000644	0.0049	0.498034
15	0.053783	0.4131	0.34051
16	-0.15379	-1.1813	0.121115
17	-0.317144	-2.436	0.008944

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.18793 & 1.4435 & 0.077082 \tabularnewline
2 & 0.038962 & 0.2993 & 0.382893 \tabularnewline
3 & 0.058917 & 0.4526 & 0.326265 \tabularnewline
4 & -0.221742 & -1.7032 & 0.046893 \tabularnewline
5 & -0.388615 & -2.985 & 0.002061 \tabularnewline
6 & -0.173788 & -1.3349 & 0.09352 \tabularnewline
7 & -0.32473 & -2.4943 & 0.007721 \tabularnewline
8 & -0.277451 & -2.1311 & 0.018627 \tabularnewline
9 & 0.049044 & 0.3767 & 0.353868 \tabularnewline
10 & 0.03989 & 0.3064 & 0.38019 \tabularnewline
11 & 0.149878 & 1.1512 & 0.127139 \tabularnewline
12 & 0.733603 & 5.6349 & 0 \tabularnewline
13 & 0.178526 & 1.3713 & 0.08774 \tabularnewline
14 & 0.000644 & 0.0049 & 0.498034 \tabularnewline
15 & 0.053783 & 0.4131 & 0.34051 \tabularnewline
16 & -0.15379 & -1.1813 & 0.121115 \tabularnewline
17 & -0.317144 & -2.436 & 0.008944 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284271&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]0.18793[/C][C]1.4435[/C][C]0.077082[/C][/ROW]
[ROW][C]2[/C][C]0.038962[/C][C]0.2993[/C][C]0.382893[/C][/ROW]
[ROW][C]3[/C][C]0.058917[/C][C]0.4526[/C][C]0.326265[/C][/ROW]
[ROW][C]4[/C][C]-0.221742[/C][C]-1.7032[/C][C]0.046893[/C][/ROW]
[ROW][C]5[/C][C]-0.388615[/C][C]-2.985[/C][C]0.002061[/C][/ROW]
[ROW][C]6[/C][C]-0.173788[/C][C]-1.3349[/C][C]0.09352[/C][/ROW]
[ROW][C]7[/C][C]-0.32473[/C][C]-2.4943[/C][C]0.007721[/C][/ROW]
[ROW][C]8[/C][C]-0.277451[/C][C]-2.1311[/C][C]0.018627[/C][/ROW]
[ROW][C]9[/C][C]0.049044[/C][C]0.3767[/C][C]0.353868[/C][/ROW]
[ROW][C]10[/C][C]0.03989[/C][C]0.3064[/C][C]0.38019[/C][/ROW]
[ROW][C]11[/C][C]0.149878[/C][C]1.1512[/C][C]0.127139[/C][/ROW]
[ROW][C]12[/C][C]0.733603[/C][C]5.6349[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.178526[/C][C]1.3713[/C][C]0.08774[/C][/ROW]
[ROW][C]14[/C][C]0.000644[/C][C]0.0049[/C][C]0.498034[/C][/ROW]
[ROW][C]15[/C][C]0.053783[/C][C]0.4131[/C][C]0.34051[/C][/ROW]
[ROW][C]16[/C][C]-0.15379[/C][C]-1.1813[/C][C]0.121115[/C][/ROW]
[ROW][C]17[/C][C]-0.317144[/C][C]-2.436[/C][C]0.008944[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284271&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284271&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	0.18793	1.4435	0.077082
2	0.038962	0.2993	0.382893
3	0.058917	0.4526	0.326265
4	-0.221742	-1.7032	0.046893
5	-0.388615	-2.985	0.002061
6	-0.173788	-1.3349	0.09352
7	-0.32473	-2.4943	0.007721
8	-0.277451	-2.1311	0.018627
9	0.049044	0.3767	0.353868
10	0.03989	0.3064	0.38019
11	0.149878	1.1512	0.127139
12	0.733603	5.6349	0
13	0.178526	1.3713	0.08774
14	0.000644	0.0049	0.498034
15	0.053783	0.4131	0.34051
16	-0.15379	-1.1813	0.121115
17	-0.317144	-2.436	0.008944

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.18793	1.4435	0.077082
2	0.003777	0.029	0.488476
3	0.052778	0.4054	0.343327
4	-0.252024	-1.9358	0.028842
5	-0.333312	-2.5602	0.006521
6	-0.073394	-0.5638	0.28753
7	-0.305913	-2.3498	0.011076
8	-0.286265	-2.1988	0.015911
9	-0.106871	-0.8209	0.207506
10	-0.221957	-1.7049	0.046739
11	-0.114205	-0.8772	0.191961
12	0.580338	4.4577	1.9e-05
13	-0.14248	-1.0944	0.139111
14	-0.13605	-1.045	0.150139
15	-0.082956	-0.6372	0.263232
16	-0.034763	-0.267	0.395191
17	0.099111	0.7613	0.22476

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.18793 & 1.4435 & 0.077082 \tabularnewline
2 & 0.003777 & 0.029 & 0.488476 \tabularnewline
3 & 0.052778 & 0.4054 & 0.343327 \tabularnewline
4 & -0.252024 & -1.9358 & 0.028842 \tabularnewline
5 & -0.333312 & -2.5602 & 0.006521 \tabularnewline
6 & -0.073394 & -0.5638 & 0.28753 \tabularnewline
7 & -0.305913 & -2.3498 & 0.011076 \tabularnewline
8 & -0.286265 & -2.1988 & 0.015911 \tabularnewline
9 & -0.106871 & -0.8209 & 0.207506 \tabularnewline
10 & -0.221957 & -1.7049 & 0.046739 \tabularnewline
11 & -0.114205 & -0.8772 & 0.191961 \tabularnewline
12 & 0.580338 & 4.4577 & 1.9e-05 \tabularnewline
13 & -0.14248 & -1.0944 & 0.139111 \tabularnewline
14 & -0.13605 & -1.045 & 0.150139 \tabularnewline
15 & -0.082956 & -0.6372 & 0.263232 \tabularnewline
16 & -0.034763 & -0.267 & 0.395191 \tabularnewline
17 & 0.099111 & 0.7613 & 0.22476 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284271&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]0.18793[/C][C]1.4435[/C][C]0.077082[/C][/ROW]
[ROW][C]2[/C][C]0.003777[/C][C]0.029[/C][C]0.488476[/C][/ROW]
[ROW][C]3[/C][C]0.052778[/C][C]0.4054[/C][C]0.343327[/C][/ROW]
[ROW][C]4[/C][C]-0.252024[/C][C]-1.9358[/C][C]0.028842[/C][/ROW]
[ROW][C]5[/C][C]-0.333312[/C][C]-2.5602[/C][C]0.006521[/C][/ROW]
[ROW][C]6[/C][C]-0.073394[/C][C]-0.5638[/C][C]0.28753[/C][/ROW]
[ROW][C]7[/C][C]-0.305913[/C][C]-2.3498[/C][C]0.011076[/C][/ROW]
[ROW][C]8[/C][C]-0.286265[/C][C]-2.1988[/C][C]0.015911[/C][/ROW]
[ROW][C]9[/C][C]-0.106871[/C][C]-0.8209[/C][C]0.207506[/C][/ROW]
[ROW][C]10[/C][C]-0.221957[/C][C]-1.7049[/C][C]0.046739[/C][/ROW]
[ROW][C]11[/C][C]-0.114205[/C][C]-0.8772[/C][C]0.191961[/C][/ROW]
[ROW][C]12[/C][C]0.580338[/C][C]4.4577[/C][C]1.9e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.14248[/C][C]-1.0944[/C][C]0.139111[/C][/ROW]
[ROW][C]14[/C][C]-0.13605[/C][C]-1.045[/C][C]0.150139[/C][/ROW]
[ROW][C]15[/C][C]-0.082956[/C][C]-0.6372[/C][C]0.263232[/C][/ROW]
[ROW][C]16[/C][C]-0.034763[/C][C]-0.267[/C][C]0.395191[/C][/ROW]
[ROW][C]17[/C][C]0.099111[/C][C]0.7613[/C][C]0.22476[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284271&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284271&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	0.18793	1.4435	0.077082
2	0.003777	0.029	0.488476
3	0.052778	0.4054	0.343327
4	-0.252024	-1.9358	0.028842
5	-0.333312	-2.5602	0.006521
6	-0.073394	-0.5638	0.28753
7	-0.305913	-2.3498	0.011076
8	-0.286265	-2.1988	0.015911
9	-0.106871	-0.8209	0.207506
10	-0.221957	-1.7049	0.046739
11	-0.114205	-0.8772	0.191961
12	0.580338	4.4577	1.9e-05
13	-0.14248	-1.0944	0.139111
14	-0.13605	-1.045	0.150139
15	-0.082956	-0.6372	0.263232
16	-0.034763	-0.267	0.395191
17	0.099111	0.7613	0.22476

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 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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 <- '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)
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