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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 07 Dec 2011 05:55:32 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/07/t1323255372iqm22v9tnbxogfo.htm/, Retrieved Thu, 02 May 2024 15:59:56 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=152175, Retrieved Thu, 02 May 2024 15:59:56 +0000

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-       [(Partial) Autocorrelation Function] [Autocorrelatie fu...] [2011-12-07 10:55:32] [f15d0acd791188344a5291b640d5aaed] [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	'Gertrude Mary Cox' @ cox.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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152175&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152175&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152175&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	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.796636	7.2577	0
2	0.472554	4.3052	2.3e-05
3	0.063841	0.5816	0.2812
4	-0.325233	-2.963	0.001987
5	-0.584038	-5.3208	0
6	-0.676418	-6.1625	0
7	-0.559745	-5.0995	1e-06
8	-0.287153	-2.6161	0.005282
9	0.071826	0.6544	0.257342
10	0.433068	3.9454	8.3e-05
11	0.671036	6.1134	0
12	0.741277	6.7534	0
13	0.569916	5.1922	1e-06
14	0.276202	2.5163	0.006892
15	-0.063263	-0.5764	0.282969
16	-0.378759	-3.4507	0.000441
17	-0.566252	-5.1588	1e-06
18	-0.612138	-5.5768	0
19	-0.489882	-4.463	1.3e-05

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.796636 & 7.2577 & 0 \tabularnewline
2 & 0.472554 & 4.3052 & 2.3e-05 \tabularnewline
3 & 0.063841 & 0.5816 & 0.2812 \tabularnewline
4 & -0.325233 & -2.963 & 0.001987 \tabularnewline
5 & -0.584038 & -5.3208 & 0 \tabularnewline
6 & -0.676418 & -6.1625 & 0 \tabularnewline
7 & -0.559745 & -5.0995 & 1e-06 \tabularnewline
8 & -0.287153 & -2.6161 & 0.005282 \tabularnewline
9 & 0.071826 & 0.6544 & 0.257342 \tabularnewline
10 & 0.433068 & 3.9454 & 8.3e-05 \tabularnewline
11 & 0.671036 & 6.1134 & 0 \tabularnewline
12 & 0.741277 & 6.7534 & 0 \tabularnewline
13 & 0.569916 & 5.1922 & 1e-06 \tabularnewline
14 & 0.276202 & 2.5163 & 0.006892 \tabularnewline
15 & -0.063263 & -0.5764 & 0.282969 \tabularnewline
16 & -0.378759 & -3.4507 & 0.000441 \tabularnewline
17 & -0.566252 & -5.1588 & 1e-06 \tabularnewline
18 & -0.612138 & -5.5768 & 0 \tabularnewline
19 & -0.489882 & -4.463 & 1.3e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152175&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]0.796636[/C][C]7.2577[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.472554[/C][C]4.3052[/C][C]2.3e-05[/C][/ROW]
[ROW][C]3[/C][C]0.063841[/C][C]0.5816[/C][C]0.2812[/C][/ROW]
[ROW][C]4[/C][C]-0.325233[/C][C]-2.963[/C][C]0.001987[/C][/ROW]
[ROW][C]5[/C][C]-0.584038[/C][C]-5.3208[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]-0.676418[/C][C]-6.1625[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]-0.559745[/C][C]-5.0995[/C][C]1e-06[/C][/ROW]
[ROW][C]8[/C][C]-0.287153[/C][C]-2.6161[/C][C]0.005282[/C][/ROW]
[ROW][C]9[/C][C]0.071826[/C][C]0.6544[/C][C]0.257342[/C][/ROW]
[ROW][C]10[/C][C]0.433068[/C][C]3.9454[/C][C]8.3e-05[/C][/ROW]
[ROW][C]11[/C][C]0.671036[/C][C]6.1134[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.741277[/C][C]6.7534[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.569916[/C][C]5.1922[/C][C]1e-06[/C][/ROW]
[ROW][C]14[/C][C]0.276202[/C][C]2.5163[/C][C]0.006892[/C][/ROW]
[ROW][C]15[/C][C]-0.063263[/C][C]-0.5764[/C][C]0.282969[/C][/ROW]
[ROW][C]16[/C][C]-0.378759[/C][C]-3.4507[/C][C]0.000441[/C][/ROW]
[ROW][C]17[/C][C]-0.566252[/C][C]-5.1588[/C][C]1e-06[/C][/ROW]
[ROW][C]18[/C][C]-0.612138[/C][C]-5.5768[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]-0.489882[/C][C]-4.463[/C][C]1.3e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152175&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152175&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	0.796636	7.2577	0
2	0.472554	4.3052	2.3e-05
3	0.063841	0.5816	0.2812
4	-0.325233	-2.963	0.001987
5	-0.584038	-5.3208	0
6	-0.676418	-6.1625	0
7	-0.559745	-5.0995	1e-06
8	-0.287153	-2.6161	0.005282
9	0.071826	0.6544	0.257342
10	0.433068	3.9454	8.3e-05
11	0.671036	6.1134	0
12	0.741277	6.7534	0
13	0.569916	5.1922	1e-06
14	0.276202	2.5163	0.006892
15	-0.063263	-0.5764	0.282969
16	-0.378759	-3.4507	0.000441
17	-0.566252	-5.1588	1e-06
18	-0.612138	-5.5768	0
19	-0.489882	-4.463	1.3e-05

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.796636	7.2577	0
2	-0.443592	-4.0413	5.9e-05
3	-0.430096	-3.9184	9.1e-05
4	-0.2841	-2.5883	0.005693
5	-0.069124	-0.6297	0.265295
6	-0.043454	-0.3959	0.346603
7	0.138005	1.2573	0.106088
8	0.144108	1.3129	0.09642
9	0.177082	1.6133	0.055238
10	0.230905	2.1036	0.019218
11	0.087084	0.7934	0.214912
12	0.07034	0.6408	0.261701
13	-0.243321	-2.2168	0.014687
14	0.006461	0.0589	0.476601
15	0.083465	0.7604	0.224584
16	-0.005978	-0.0545	0.478348
17	0.010756	0.098	0.461087
18	-0.08694	-0.7921	0.215292
19	-0.069226	-0.6307	0.264992

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.796636 & 7.2577 & 0 \tabularnewline
2 & -0.443592 & -4.0413 & 5.9e-05 \tabularnewline
3 & -0.430096 & -3.9184 & 9.1e-05 \tabularnewline
4 & -0.2841 & -2.5883 & 0.005693 \tabularnewline
5 & -0.069124 & -0.6297 & 0.265295 \tabularnewline
6 & -0.043454 & -0.3959 & 0.346603 \tabularnewline
7 & 0.138005 & 1.2573 & 0.106088 \tabularnewline
8 & 0.144108 & 1.3129 & 0.09642 \tabularnewline
9 & 0.177082 & 1.6133 & 0.055238 \tabularnewline
10 & 0.230905 & 2.1036 & 0.019218 \tabularnewline
11 & 0.087084 & 0.7934 & 0.214912 \tabularnewline
12 & 0.07034 & 0.6408 & 0.261701 \tabularnewline
13 & -0.243321 & -2.2168 & 0.014687 \tabularnewline
14 & 0.006461 & 0.0589 & 0.476601 \tabularnewline
15 & 0.083465 & 0.7604 & 0.224584 \tabularnewline
16 & -0.005978 & -0.0545 & 0.478348 \tabularnewline
17 & 0.010756 & 0.098 & 0.461087 \tabularnewline
18 & -0.08694 & -0.7921 & 0.215292 \tabularnewline
19 & -0.069226 & -0.6307 & 0.264992 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152175&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]0.796636[/C][C]7.2577[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.443592[/C][C]-4.0413[/C][C]5.9e-05[/C][/ROW]
[ROW][C]3[/C][C]-0.430096[/C][C]-3.9184[/C][C]9.1e-05[/C][/ROW]
[ROW][C]4[/C][C]-0.2841[/C][C]-2.5883[/C][C]0.005693[/C][/ROW]
[ROW][C]5[/C][C]-0.069124[/C][C]-0.6297[/C][C]0.265295[/C][/ROW]
[ROW][C]6[/C][C]-0.043454[/C][C]-0.3959[/C][C]0.346603[/C][/ROW]
[ROW][C]7[/C][C]0.138005[/C][C]1.2573[/C][C]0.106088[/C][/ROW]
[ROW][C]8[/C][C]0.144108[/C][C]1.3129[/C][C]0.09642[/C][/ROW]
[ROW][C]9[/C][C]0.177082[/C][C]1.6133[/C][C]0.055238[/C][/ROW]
[ROW][C]10[/C][C]0.230905[/C][C]2.1036[/C][C]0.019218[/C][/ROW]
[ROW][C]11[/C][C]0.087084[/C][C]0.7934[/C][C]0.214912[/C][/ROW]
[ROW][C]12[/C][C]0.07034[/C][C]0.6408[/C][C]0.261701[/C][/ROW]
[ROW][C]13[/C][C]-0.243321[/C][C]-2.2168[/C][C]0.014687[/C][/ROW]
[ROW][C]14[/C][C]0.006461[/C][C]0.0589[/C][C]0.476601[/C][/ROW]
[ROW][C]15[/C][C]0.083465[/C][C]0.7604[/C][C]0.224584[/C][/ROW]
[ROW][C]16[/C][C]-0.005978[/C][C]-0.0545[/C][C]0.478348[/C][/ROW]
[ROW][C]17[/C][C]0.010756[/C][C]0.098[/C][C]0.461087[/C][/ROW]
[ROW][C]18[/C][C]-0.08694[/C][C]-0.7921[/C][C]0.215292[/C][/ROW]
[ROW][C]19[/C][C]-0.069226[/C][C]-0.6307[/C][C]0.264992[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152175&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152175&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	0.796636	7.2577	0
2	-0.443592	-4.0413	5.9e-05
3	-0.430096	-3.9184	9.1e-05
4	-0.2841	-2.5883	0.005693
5	-0.069124	-0.6297	0.265295
6	-0.043454	-0.3959	0.346603
7	0.138005	1.2573	0.106088
8	0.144108	1.3129	0.09642
9	0.177082	1.6133	0.055238
10	0.230905	2.1036	0.019218
11	0.087084	0.7934	0.214912
12	0.07034	0.6408	0.261701
13	-0.243321	-2.2168	0.014687
14	0.006461	0.0589	0.476601
15	0.083465	0.7604	0.224584
16	-0.005978	-0.0545	0.478348
17	0.010756	0.098	0.461087
18	-0.08694	-0.7921	0.215292
19	-0.069226	-0.6307	0.264992

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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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code