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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 26 Dec 2010 10:33:38 +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/2010/Dec/26/t1293359531tbg22qnj458u446.htm/, Retrieved Mon, 06 May 2024 13:27:49 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115500, Retrieved Mon, 06 May 2024 13:27:49 +0000

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145

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-       [(Partial) Autocorrelation Function] [] [2010-12-26 10:33:38] [1e640daebbc6b5a89eef23229b5a56d5] [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	6 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 6 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115500&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]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115500&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115500&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	6 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.637674	4.8143	6e-06
2	0.544825	4.1133	6.3e-05
3	0.604576	4.5644	1.4e-05
4	0.420114	3.1718	0.00122
5	0.356986	2.6952	0.004615
6	0.321752	2.4292	0.009154
7	0.089478	0.6755	0.25103
8	0.020882	0.1577	0.437643
9	-0.096828	-0.731	0.233876
10	-0.264102	-1.9939	0.025476
11	-0.259141	-1.9565	0.027658
12	-0.154568	-1.167	0.124042
13	-0.3723	-2.8108	0.003381
14	-0.418693	-3.1611	0.001259
15	-0.3596	-2.7149	0.004378
16	-0.374724	-2.8291	0.003217
17	-0.33189	-2.5057	0.00755

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.637674 & 4.8143 & 6e-06 \tabularnewline
2 & 0.544825 & 4.1133 & 6.3e-05 \tabularnewline
3 & 0.604576 & 4.5644 & 1.4e-05 \tabularnewline
4 & 0.420114 & 3.1718 & 0.00122 \tabularnewline
5 & 0.356986 & 2.6952 & 0.004615 \tabularnewline
6 & 0.321752 & 2.4292 & 0.009154 \tabularnewline
7 & 0.089478 & 0.6755 & 0.25103 \tabularnewline
8 & 0.020882 & 0.1577 & 0.437643 \tabularnewline
9 & -0.096828 & -0.731 & 0.233876 \tabularnewline
10 & -0.264102 & -1.9939 & 0.025476 \tabularnewline
11 & -0.259141 & -1.9565 & 0.027658 \tabularnewline
12 & -0.154568 & -1.167 & 0.124042 \tabularnewline
13 & -0.3723 & -2.8108 & 0.003381 \tabularnewline
14 & -0.418693 & -3.1611 & 0.001259 \tabularnewline
15 & -0.3596 & -2.7149 & 0.004378 \tabularnewline
16 & -0.374724 & -2.8291 & 0.003217 \tabularnewline
17 & -0.33189 & -2.5057 & 0.00755 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115500&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]0.637674[/C][C]4.8143[/C][C]6e-06[/C][/ROW]
[ROW][C]2[/C][C]0.544825[/C][C]4.1133[/C][C]6.3e-05[/C][/ROW]
[ROW][C]3[/C][C]0.604576[/C][C]4.5644[/C][C]1.4e-05[/C][/ROW]
[ROW][C]4[/C][C]0.420114[/C][C]3.1718[/C][C]0.00122[/C][/ROW]
[ROW][C]5[/C][C]0.356986[/C][C]2.6952[/C][C]0.004615[/C][/ROW]
[ROW][C]6[/C][C]0.321752[/C][C]2.4292[/C][C]0.009154[/C][/ROW]
[ROW][C]7[/C][C]0.089478[/C][C]0.6755[/C][C]0.25103[/C][/ROW]
[ROW][C]8[/C][C]0.020882[/C][C]0.1577[/C][C]0.437643[/C][/ROW]
[ROW][C]9[/C][C]-0.096828[/C][C]-0.731[/C][C]0.233876[/C][/ROW]
[ROW][C]10[/C][C]-0.264102[/C][C]-1.9939[/C][C]0.025476[/C][/ROW]
[ROW][C]11[/C][C]-0.259141[/C][C]-1.9565[/C][C]0.027658[/C][/ROW]
[ROW][C]12[/C][C]-0.154568[/C][C]-1.167[/C][C]0.124042[/C][/ROW]
[ROW][C]13[/C][C]-0.3723[/C][C]-2.8108[/C][C]0.003381[/C][/ROW]
[ROW][C]14[/C][C]-0.418693[/C][C]-3.1611[/C][C]0.001259[/C][/ROW]
[ROW][C]15[/C][C]-0.3596[/C][C]-2.7149[/C][C]0.004378[/C][/ROW]
[ROW][C]16[/C][C]-0.374724[/C][C]-2.8291[/C][C]0.003217[/C][/ROW]
[ROW][C]17[/C][C]-0.33189[/C][C]-2.5057[/C][C]0.00755[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115500&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115500&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	0.637674	4.8143	6e-06
2	0.544825	4.1133	6.3e-05
3	0.604576	4.5644	1.4e-05
4	0.420114	3.1718	0.00122
5	0.356986	2.6952	0.004615
6	0.321752	2.4292	0.009154
7	0.089478	0.6755	0.25103
8	0.020882	0.1577	0.437643
9	-0.096828	-0.731	0.233876
10	-0.264102	-1.9939	0.025476
11	-0.259141	-1.9565	0.027658
12	-0.154568	-1.167	0.124042
13	-0.3723	-2.8108	0.003381
14	-0.418693	-3.1611	0.001259
15	-0.3596	-2.7149	0.004378
16	-0.374724	-2.8291	0.003217
17	-0.33189	-2.5057	0.00755

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.637674	4.8143	6e-06
2	0.232902	1.7584	0.042026
3	0.337775	2.5501	0.00674
4	-0.161558	-1.2197	0.113794
5	-0.006313	-0.0477	0.481075
6	-0.06642	-0.5015	0.308989
7	-0.299831	-2.2637	0.013709
8	-0.108229	-0.8171	0.208633
9	-0.25092	-1.8944	0.031624
10	-0.159398	-1.2034	0.116892
11	0.013149	0.0993	0.460635
12	0.428188	3.2327	0.00102
13	-0.183977	-1.389	0.085119
14	-0.136257	-1.0287	0.153979
15	-0.123898	-0.9354	0.176762
16	0.09922	0.7491	0.228441
17	-0.037753	-0.285	0.388328

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.637674 & 4.8143 & 6e-06 \tabularnewline
2 & 0.232902 & 1.7584 & 0.042026 \tabularnewline
3 & 0.337775 & 2.5501 & 0.00674 \tabularnewline
4 & -0.161558 & -1.2197 & 0.113794 \tabularnewline
5 & -0.006313 & -0.0477 & 0.481075 \tabularnewline
6 & -0.06642 & -0.5015 & 0.308989 \tabularnewline
7 & -0.299831 & -2.2637 & 0.013709 \tabularnewline
8 & -0.108229 & -0.8171 & 0.208633 \tabularnewline
9 & -0.25092 & -1.8944 & 0.031624 \tabularnewline
10 & -0.159398 & -1.2034 & 0.116892 \tabularnewline
11 & 0.013149 & 0.0993 & 0.460635 \tabularnewline
12 & 0.428188 & 3.2327 & 0.00102 \tabularnewline
13 & -0.183977 & -1.389 & 0.085119 \tabularnewline
14 & -0.136257 & -1.0287 & 0.153979 \tabularnewline
15 & -0.123898 & -0.9354 & 0.176762 \tabularnewline
16 & 0.09922 & 0.7491 & 0.228441 \tabularnewline
17 & -0.037753 & -0.285 & 0.388328 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115500&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]0.637674[/C][C]4.8143[/C][C]6e-06[/C][/ROW]
[ROW][C]2[/C][C]0.232902[/C][C]1.7584[/C][C]0.042026[/C][/ROW]
[ROW][C]3[/C][C]0.337775[/C][C]2.5501[/C][C]0.00674[/C][/ROW]
[ROW][C]4[/C][C]-0.161558[/C][C]-1.2197[/C][C]0.113794[/C][/ROW]
[ROW][C]5[/C][C]-0.006313[/C][C]-0.0477[/C][C]0.481075[/C][/ROW]
[ROW][C]6[/C][C]-0.06642[/C][C]-0.5015[/C][C]0.308989[/C][/ROW]
[ROW][C]7[/C][C]-0.299831[/C][C]-2.2637[/C][C]0.013709[/C][/ROW]
[ROW][C]8[/C][C]-0.108229[/C][C]-0.8171[/C][C]0.208633[/C][/ROW]
[ROW][C]9[/C][C]-0.25092[/C][C]-1.8944[/C][C]0.031624[/C][/ROW]
[ROW][C]10[/C][C]-0.159398[/C][C]-1.2034[/C][C]0.116892[/C][/ROW]
[ROW][C]11[/C][C]0.013149[/C][C]0.0993[/C][C]0.460635[/C][/ROW]
[ROW][C]12[/C][C]0.428188[/C][C]3.2327[/C][C]0.00102[/C][/ROW]
[ROW][C]13[/C][C]-0.183977[/C][C]-1.389[/C][C]0.085119[/C][/ROW]
[ROW][C]14[/C][C]-0.136257[/C][C]-1.0287[/C][C]0.153979[/C][/ROW]
[ROW][C]15[/C][C]-0.123898[/C][C]-0.9354[/C][C]0.176762[/C][/ROW]
[ROW][C]16[/C][C]0.09922[/C][C]0.7491[/C][C]0.228441[/C][/ROW]
[ROW][C]17[/C][C]-0.037753[/C][C]-0.285[/C][C]0.388328[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115500&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115500&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	0.637674	4.8143	6e-06
2	0.232902	1.7584	0.042026
3	0.337775	2.5501	0.00674
4	-0.161558	-1.2197	0.113794
5	-0.006313	-0.0477	0.481075
6	-0.06642	-0.5015	0.308989
7	-0.299831	-2.2637	0.013709
8	-0.108229	-0.8171	0.208633
9	-0.25092	-1.8944	0.031624
10	-0.159398	-1.2034	0.116892
11	0.013149	0.0993	0.460635
12	0.428188	3.2327	0.00102
13	-0.183977	-1.389	0.085119
14	-0.136257	-1.0287	0.153979
15	-0.123898	-0.9354	0.176762
16	0.09922	0.7491	0.228441
17	-0.037753	-0.285	0.388328

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):

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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Input Parameters & R Code