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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 29 Dec 2012 04:50:22 -0500

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/2012/Dec/29/t1356774691ii3j8u2onl59h2s.htm/, Retrieved Thu, 02 May 2024 02:28:26 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=204857, Retrieved Thu, 02 May 2024 02:28:26 +0000

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User-defined keywords

Omdat er ook hier bij het overlopen van mijn paper geen link te vinden was, het ik opnieuw dit geblogt.

Estimated Impact

125

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-       [(Partial) Autocorrelation Function] [Autocorrelatie me...] [2012-12-29 09:50:22] [0bad526123a64cc9f33318d2fc48f385] [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	3 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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204857&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]3 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=204857&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204857&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	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.148693	-1.2529	0.107175
2	-0.102038	-0.8598	0.1964
3	-0.11999	-1.0111	0.157713
4	-0.133962	-1.1288	0.131394
5	0.305925	2.5778	0.00601
6	-0.066193	-0.5578	0.289383
7	-0.073211	-0.6169	0.269641
8	-0.074614	-0.6287	0.265778
9	-0.085458	-0.7201	0.236919
10	0.036224	0.3052	0.380542
11	0.180609	1.5218	0.066246
12	0.104999	0.8847	0.189642
13	-0.017656	-0.1488	0.441079
14	-0.121608	-1.0247	0.154495
15	0.025767	0.2171	0.41437
16	0.076274	0.6427	0.261245
17	0.047608	0.4012	0.344756
18	-0.06902	-0.5816	0.281347

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.148693 & -1.2529 & 0.107175 \tabularnewline
2 & -0.102038 & -0.8598 & 0.1964 \tabularnewline
3 & -0.11999 & -1.0111 & 0.157713 \tabularnewline
4 & -0.133962 & -1.1288 & 0.131394 \tabularnewline
5 & 0.305925 & 2.5778 & 0.00601 \tabularnewline
6 & -0.066193 & -0.5578 & 0.289383 \tabularnewline
7 & -0.073211 & -0.6169 & 0.269641 \tabularnewline
8 & -0.074614 & -0.6287 & 0.265778 \tabularnewline
9 & -0.085458 & -0.7201 & 0.236919 \tabularnewline
10 & 0.036224 & 0.3052 & 0.380542 \tabularnewline
11 & 0.180609 & 1.5218 & 0.066246 \tabularnewline
12 & 0.104999 & 0.8847 & 0.189642 \tabularnewline
13 & -0.017656 & -0.1488 & 0.441079 \tabularnewline
14 & -0.121608 & -1.0247 & 0.154495 \tabularnewline
15 & 0.025767 & 0.2171 & 0.41437 \tabularnewline
16 & 0.076274 & 0.6427 & 0.261245 \tabularnewline
17 & 0.047608 & 0.4012 & 0.344756 \tabularnewline
18 & -0.06902 & -0.5816 & 0.281347 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204857&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]-0.148693[/C][C]-1.2529[/C][C]0.107175[/C][/ROW]
[ROW][C]2[/C][C]-0.102038[/C][C]-0.8598[/C][C]0.1964[/C][/ROW]
[ROW][C]3[/C][C]-0.11999[/C][C]-1.0111[/C][C]0.157713[/C][/ROW]
[ROW][C]4[/C][C]-0.133962[/C][C]-1.1288[/C][C]0.131394[/C][/ROW]
[ROW][C]5[/C][C]0.305925[/C][C]2.5778[/C][C]0.00601[/C][/ROW]
[ROW][C]6[/C][C]-0.066193[/C][C]-0.5578[/C][C]0.289383[/C][/ROW]
[ROW][C]7[/C][C]-0.073211[/C][C]-0.6169[/C][C]0.269641[/C][/ROW]
[ROW][C]8[/C][C]-0.074614[/C][C]-0.6287[/C][C]0.265778[/C][/ROW]
[ROW][C]9[/C][C]-0.085458[/C][C]-0.7201[/C][C]0.236919[/C][/ROW]
[ROW][C]10[/C][C]0.036224[/C][C]0.3052[/C][C]0.380542[/C][/ROW]
[ROW][C]11[/C][C]0.180609[/C][C]1.5218[/C][C]0.066246[/C][/ROW]
[ROW][C]12[/C][C]0.104999[/C][C]0.8847[/C][C]0.189642[/C][/ROW]
[ROW][C]13[/C][C]-0.017656[/C][C]-0.1488[/C][C]0.441079[/C][/ROW]
[ROW][C]14[/C][C]-0.121608[/C][C]-1.0247[/C][C]0.154495[/C][/ROW]
[ROW][C]15[/C][C]0.025767[/C][C]0.2171[/C][C]0.41437[/C][/ROW]
[ROW][C]16[/C][C]0.076274[/C][C]0.6427[/C][C]0.261245[/C][/ROW]
[ROW][C]17[/C][C]0.047608[/C][C]0.4012[/C][C]0.344756[/C][/ROW]
[ROW][C]18[/C][C]-0.06902[/C][C]-0.5816[/C][C]0.281347[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204857&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204857&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	-0.148693	-1.2529	0.107175
2	-0.102038	-0.8598	0.1964
3	-0.11999	-1.0111	0.157713
4	-0.133962	-1.1288	0.131394
5	0.305925	2.5778	0.00601
6	-0.066193	-0.5578	0.289383
7	-0.073211	-0.6169	0.269641
8	-0.074614	-0.6287	0.265778
9	-0.085458	-0.7201	0.236919
10	0.036224	0.3052	0.380542
11	0.180609	1.5218	0.066246
12	0.104999	0.8847	0.189642
13	-0.017656	-0.1488	0.441079
14	-0.121608	-1.0247	0.154495
15	0.025767	0.2171	0.41437
16	0.076274	0.6427	0.261245
17	0.047608	0.4012	0.344756
18	-0.06902	-0.5816	0.281347

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.148693	-1.2529	0.107175
2	-0.126954	-1.0697	0.144181
3	-0.162104	-1.3659	0.088138
4	-0.209605	-1.7662	0.040833
5	0.225601	1.9009	0.030684
6	-0.039352	-0.3316	0.37059
7	-0.076224	-0.6423	0.261382
8	-0.067087	-0.5653	0.28683
9	-0.072791	-0.6134	0.270802
10	-0.131036	-1.1041	0.136632
11	0.162264	1.3673	0.087929
12	0.180915	1.5244	0.065924
13	0.079721	0.6717	0.251963
14	-0.028807	-0.2427	0.404457
15	0.106531	0.8976	0.186204
16	0.008822	0.0743	0.470475
17	0.001946	0.0164	0.493481
18	-0.027594	-0.2325	0.408406

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.148693 & -1.2529 & 0.107175 \tabularnewline
2 & -0.126954 & -1.0697 & 0.144181 \tabularnewline
3 & -0.162104 & -1.3659 & 0.088138 \tabularnewline
4 & -0.209605 & -1.7662 & 0.040833 \tabularnewline
5 & 0.225601 & 1.9009 & 0.030684 \tabularnewline
6 & -0.039352 & -0.3316 & 0.37059 \tabularnewline
7 & -0.076224 & -0.6423 & 0.261382 \tabularnewline
8 & -0.067087 & -0.5653 & 0.28683 \tabularnewline
9 & -0.072791 & -0.6134 & 0.270802 \tabularnewline
10 & -0.131036 & -1.1041 & 0.136632 \tabularnewline
11 & 0.162264 & 1.3673 & 0.087929 \tabularnewline
12 & 0.180915 & 1.5244 & 0.065924 \tabularnewline
13 & 0.079721 & 0.6717 & 0.251963 \tabularnewline
14 & -0.028807 & -0.2427 & 0.404457 \tabularnewline
15 & 0.106531 & 0.8976 & 0.186204 \tabularnewline
16 & 0.008822 & 0.0743 & 0.470475 \tabularnewline
17 & 0.001946 & 0.0164 & 0.493481 \tabularnewline
18 & -0.027594 & -0.2325 & 0.408406 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204857&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]-0.148693[/C][C]-1.2529[/C][C]0.107175[/C][/ROW]
[ROW][C]2[/C][C]-0.126954[/C][C]-1.0697[/C][C]0.144181[/C][/ROW]
[ROW][C]3[/C][C]-0.162104[/C][C]-1.3659[/C][C]0.088138[/C][/ROW]
[ROW][C]4[/C][C]-0.209605[/C][C]-1.7662[/C][C]0.040833[/C][/ROW]
[ROW][C]5[/C][C]0.225601[/C][C]1.9009[/C][C]0.030684[/C][/ROW]
[ROW][C]6[/C][C]-0.039352[/C][C]-0.3316[/C][C]0.37059[/C][/ROW]
[ROW][C]7[/C][C]-0.076224[/C][C]-0.6423[/C][C]0.261382[/C][/ROW]
[ROW][C]8[/C][C]-0.067087[/C][C]-0.5653[/C][C]0.28683[/C][/ROW]
[ROW][C]9[/C][C]-0.072791[/C][C]-0.6134[/C][C]0.270802[/C][/ROW]
[ROW][C]10[/C][C]-0.131036[/C][C]-1.1041[/C][C]0.136632[/C][/ROW]
[ROW][C]11[/C][C]0.162264[/C][C]1.3673[/C][C]0.087929[/C][/ROW]
[ROW][C]12[/C][C]0.180915[/C][C]1.5244[/C][C]0.065924[/C][/ROW]
[ROW][C]13[/C][C]0.079721[/C][C]0.6717[/C][C]0.251963[/C][/ROW]
[ROW][C]14[/C][C]-0.028807[/C][C]-0.2427[/C][C]0.404457[/C][/ROW]
[ROW][C]15[/C][C]0.106531[/C][C]0.8976[/C][C]0.186204[/C][/ROW]
[ROW][C]16[/C][C]0.008822[/C][C]0.0743[/C][C]0.470475[/C][/ROW]
[ROW][C]17[/C][C]0.001946[/C][C]0.0164[/C][C]0.493481[/C][/ROW]
[ROW][C]18[/C][C]-0.027594[/C][C]-0.2325[/C][C]0.408406[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204857&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204857&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	-0.148693	-1.2529	0.107175
2	-0.126954	-1.0697	0.144181
3	-0.162104	-1.3659	0.088138
4	-0.209605	-1.7662	0.040833
5	0.225601	1.9009	0.030684
6	-0.039352	-0.3316	0.37059
7	-0.076224	-0.6423	0.261382
8	-0.067087	-0.5653	0.28683
9	-0.072791	-0.6134	0.270802
10	-0.131036	-1.1041	0.136632
11	0.162264	1.3673	0.087929
12	0.180915	1.5244	0.065924
13	0.079721	0.6717	0.251963
14	-0.028807	-0.2427	0.404457
15	0.106531	0.8976	0.186204
16	0.008822	0.0743	0.470475
17	0.001946	0.0164	0.493481
18	-0.027594	-0.2325	0.408406

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 <- '0'
par3 <- '1'
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

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code