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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 22 Dec 2015 14:20:54 +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/2015/Dec/22/t1450794098guwmyshe5lwsh51.htm/, Retrieved Sun, 19 May 2024 00:38:53 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=287027, Retrieved Sun, 19 May 2024 00:38:53 +0000

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User-defined keywords

Estimated Impact

121

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [(Partial) Autocorrelation Function] [Koffie indexprijz...] [2015-12-22 14:20:54] [91f26e786dd8a1c147ebc049dd81fbad] [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	'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287027&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' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287027&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287027&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' @ yule.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.402057	4.1589	3.2e-05
2	0.115249	1.1921	0.117921
3	0.011178	0.1156	0.454084
4	0.152509	1.5776	0.058809
5	0.173814	1.798	0.037502
6	0.09179	0.9495	0.172257
7	-0.040995	-0.4241	0.336189
8	-0.067593	-0.6992	0.242977
9	0.154899	1.6023	0.05602
10	0.188387	1.9487	0.026976
11	0.023431	0.2424	0.404479
12	-0.086789	-0.8978	0.185667
13	-0.111975	-1.1583	0.124665
14	0.004694	0.0486	0.48068
15	-0.030164	-0.312	0.377818
16	-0.071394	-0.7385	0.230911
17	-0.159666	-1.6516	0.050775
18	-0.134518	-1.3915	0.083485
19	-0.047578	-0.4921	0.311812
20	-0.102898	-1.0644	0.144776

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.402057 & 4.1589 & 3.2e-05 \tabularnewline
2 & 0.115249 & 1.1921 & 0.117921 \tabularnewline
3 & 0.011178 & 0.1156 & 0.454084 \tabularnewline
4 & 0.152509 & 1.5776 & 0.058809 \tabularnewline
5 & 0.173814 & 1.798 & 0.037502 \tabularnewline
6 & 0.09179 & 0.9495 & 0.172257 \tabularnewline
7 & -0.040995 & -0.4241 & 0.336189 \tabularnewline
8 & -0.067593 & -0.6992 & 0.242977 \tabularnewline
9 & 0.154899 & 1.6023 & 0.05602 \tabularnewline
10 & 0.188387 & 1.9487 & 0.026976 \tabularnewline
11 & 0.023431 & 0.2424 & 0.404479 \tabularnewline
12 & -0.086789 & -0.8978 & 0.185667 \tabularnewline
13 & -0.111975 & -1.1583 & 0.124665 \tabularnewline
14 & 0.004694 & 0.0486 & 0.48068 \tabularnewline
15 & -0.030164 & -0.312 & 0.377818 \tabularnewline
16 & -0.071394 & -0.7385 & 0.230911 \tabularnewline
17 & -0.159666 & -1.6516 & 0.050775 \tabularnewline
18 & -0.134518 & -1.3915 & 0.083485 \tabularnewline
19 & -0.047578 & -0.4921 & 0.311812 \tabularnewline
20 & -0.102898 & -1.0644 & 0.144776 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287027&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]0.402057[/C][C]4.1589[/C][C]3.2e-05[/C][/ROW]
[ROW][C]2[/C][C]0.115249[/C][C]1.1921[/C][C]0.117921[/C][/ROW]
[ROW][C]3[/C][C]0.011178[/C][C]0.1156[/C][C]0.454084[/C][/ROW]
[ROW][C]4[/C][C]0.152509[/C][C]1.5776[/C][C]0.058809[/C][/ROW]
[ROW][C]5[/C][C]0.173814[/C][C]1.798[/C][C]0.037502[/C][/ROW]
[ROW][C]6[/C][C]0.09179[/C][C]0.9495[/C][C]0.172257[/C][/ROW]
[ROW][C]7[/C][C]-0.040995[/C][C]-0.4241[/C][C]0.336189[/C][/ROW]
[ROW][C]8[/C][C]-0.067593[/C][C]-0.6992[/C][C]0.242977[/C][/ROW]
[ROW][C]9[/C][C]0.154899[/C][C]1.6023[/C][C]0.05602[/C][/ROW]
[ROW][C]10[/C][C]0.188387[/C][C]1.9487[/C][C]0.026976[/C][/ROW]
[ROW][C]11[/C][C]0.023431[/C][C]0.2424[/C][C]0.404479[/C][/ROW]
[ROW][C]12[/C][C]-0.086789[/C][C]-0.8978[/C][C]0.185667[/C][/ROW]
[ROW][C]13[/C][C]-0.111975[/C][C]-1.1583[/C][C]0.124665[/C][/ROW]
[ROW][C]14[/C][C]0.004694[/C][C]0.0486[/C][C]0.48068[/C][/ROW]
[ROW][C]15[/C][C]-0.030164[/C][C]-0.312[/C][C]0.377818[/C][/ROW]
[ROW][C]16[/C][C]-0.071394[/C][C]-0.7385[/C][C]0.230911[/C][/ROW]
[ROW][C]17[/C][C]-0.159666[/C][C]-1.6516[/C][C]0.050775[/C][/ROW]
[ROW][C]18[/C][C]-0.134518[/C][C]-1.3915[/C][C]0.083485[/C][/ROW]
[ROW][C]19[/C][C]-0.047578[/C][C]-0.4921[/C][C]0.311812[/C][/ROW]
[ROW][C]20[/C][C]-0.102898[/C][C]-1.0644[/C][C]0.144776[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287027&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287027&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	0.402057	4.1589	3.2e-05
2	0.115249	1.1921	0.117921
3	0.011178	0.1156	0.454084
4	0.152509	1.5776	0.058809
5	0.173814	1.798	0.037502
6	0.09179	0.9495	0.172257
7	-0.040995	-0.4241	0.336189
8	-0.067593	-0.6992	0.242977
9	0.154899	1.6023	0.05602
10	0.188387	1.9487	0.026976
11	0.023431	0.2424	0.404479
12	-0.086789	-0.8978	0.185667
13	-0.111975	-1.1583	0.124665
14	0.004694	0.0486	0.48068
15	-0.030164	-0.312	0.377818
16	-0.071394	-0.7385	0.230911
17	-0.159666	-1.6516	0.050775
18	-0.134518	-1.3915	0.083485
19	-0.047578	-0.4921	0.311812
20	-0.102898	-1.0644	0.144776

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.402057	4.1589	3.2e-05
2	-0.055348	-0.5725	0.284083
3	-0.01851	-0.1915	0.424261
4	0.192333	1.9895	0.024599
5	0.053857	0.5571	0.289312
6	-0.019506	-0.2018	0.420241
7	-0.074985	-0.7757	0.219833
8	-0.037074	-0.3835	0.351057
9	0.217979	2.2548	0.013091
10	0.031888	0.3299	0.371077
11	-0.113643	-1.1755	0.121195
12	-0.019462	-0.2013	0.420419
13	-0.084972	-0.879	0.190698
14	0.026368	0.2728	0.392785
15	-0.09521	-0.9849	0.163458
16	-0.025395	-0.2627	0.396647
17	-0.036835	-0.381	0.351972
18	-0.068621	-0.7098	0.239681
19	-0.011206	-0.1159	0.453968
20	-0.118603	-1.2268	0.111288

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.402057 & 4.1589 & 3.2e-05 \tabularnewline
2 & -0.055348 & -0.5725 & 0.284083 \tabularnewline
3 & -0.01851 & -0.1915 & 0.424261 \tabularnewline
4 & 0.192333 & 1.9895 & 0.024599 \tabularnewline
5 & 0.053857 & 0.5571 & 0.289312 \tabularnewline
6 & -0.019506 & -0.2018 & 0.420241 \tabularnewline
7 & -0.074985 & -0.7757 & 0.219833 \tabularnewline
8 & -0.037074 & -0.3835 & 0.351057 \tabularnewline
9 & 0.217979 & 2.2548 & 0.013091 \tabularnewline
10 & 0.031888 & 0.3299 & 0.371077 \tabularnewline
11 & -0.113643 & -1.1755 & 0.121195 \tabularnewline
12 & -0.019462 & -0.2013 & 0.420419 \tabularnewline
13 & -0.084972 & -0.879 & 0.190698 \tabularnewline
14 & 0.026368 & 0.2728 & 0.392785 \tabularnewline
15 & -0.09521 & -0.9849 & 0.163458 \tabularnewline
16 & -0.025395 & -0.2627 & 0.396647 \tabularnewline
17 & -0.036835 & -0.381 & 0.351972 \tabularnewline
18 & -0.068621 & -0.7098 & 0.239681 \tabularnewline
19 & -0.011206 & -0.1159 & 0.453968 \tabularnewline
20 & -0.118603 & -1.2268 & 0.111288 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287027&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]0.402057[/C][C]4.1589[/C][C]3.2e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.055348[/C][C]-0.5725[/C][C]0.284083[/C][/ROW]
[ROW][C]3[/C][C]-0.01851[/C][C]-0.1915[/C][C]0.424261[/C][/ROW]
[ROW][C]4[/C][C]0.192333[/C][C]1.9895[/C][C]0.024599[/C][/ROW]
[ROW][C]5[/C][C]0.053857[/C][C]0.5571[/C][C]0.289312[/C][/ROW]
[ROW][C]6[/C][C]-0.019506[/C][C]-0.2018[/C][C]0.420241[/C][/ROW]
[ROW][C]7[/C][C]-0.074985[/C][C]-0.7757[/C][C]0.219833[/C][/ROW]
[ROW][C]8[/C][C]-0.037074[/C][C]-0.3835[/C][C]0.351057[/C][/ROW]
[ROW][C]9[/C][C]0.217979[/C][C]2.2548[/C][C]0.013091[/C][/ROW]
[ROW][C]10[/C][C]0.031888[/C][C]0.3299[/C][C]0.371077[/C][/ROW]
[ROW][C]11[/C][C]-0.113643[/C][C]-1.1755[/C][C]0.121195[/C][/ROW]
[ROW][C]12[/C][C]-0.019462[/C][C]-0.2013[/C][C]0.420419[/C][/ROW]
[ROW][C]13[/C][C]-0.084972[/C][C]-0.879[/C][C]0.190698[/C][/ROW]
[ROW][C]14[/C][C]0.026368[/C][C]0.2728[/C][C]0.392785[/C][/ROW]
[ROW][C]15[/C][C]-0.09521[/C][C]-0.9849[/C][C]0.163458[/C][/ROW]
[ROW][C]16[/C][C]-0.025395[/C][C]-0.2627[/C][C]0.396647[/C][/ROW]
[ROW][C]17[/C][C]-0.036835[/C][C]-0.381[/C][C]0.351972[/C][/ROW]
[ROW][C]18[/C][C]-0.068621[/C][C]-0.7098[/C][C]0.239681[/C][/ROW]
[ROW][C]19[/C][C]-0.011206[/C][C]-0.1159[/C][C]0.453968[/C][/ROW]
[ROW][C]20[/C][C]-0.118603[/C][C]-1.2268[/C][C]0.111288[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287027&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287027&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	0.402057	4.1589	3.2e-05
2	-0.055348	-0.5725	0.284083
3	-0.01851	-0.1915	0.424261
4	0.192333	1.9895	0.024599
5	0.053857	0.5571	0.289312
6	-0.019506	-0.2018	0.420241
7	-0.074985	-0.7757	0.219833
8	-0.037074	-0.3835	0.351057
9	0.217979	2.2548	0.013091
10	0.031888	0.3299	0.371077
11	-0.113643	-1.1755	0.121195
12	-0.019462	-0.2013	0.420419
13	-0.084972	-0.879	0.190698
14	0.026368	0.2728	0.392785
15	-0.09521	-0.9849	0.163458
16	-0.025395	-0.2627	0.396647
17	-0.036835	-0.381	0.351972
18	-0.068621	-0.7098	0.239681
19	-0.011206	-0.1159	0.453968
20	-0.118603	-1.2268	0.111288

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):

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)
x <- na.omit(x)
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

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code