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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 01 Apr 2012 12:13:00 -0400

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/Apr/01/t1333296862gqjplx97cwbnfax.htm/, Retrieved Wed, 01 May 2024 02:00:19 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=164251, Retrieved Wed, 01 May 2024 02:00:19 +0000

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No (this computation is public)

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Estimated Impact

228

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

-       [(Partial) Autocorrelation Function] [Kleding en kledin...] [2012-04-01 16:13:00] [675223405f94cd8491f4a89fc80aa26c] [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	'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164251&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164251&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164251&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	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.108885	0.8364	0.203164
2	-0.245371	-1.8847	0.032197
3	-0.488711	-3.7539	2e-04
4	-0.341795	-2.6254	0.005503
5	0.253059	1.9438	0.028348
6	0.409136	3.1426	0.00131
7	0.253729	1.9489	0.028032
8	-0.265559	-2.0398	0.022928
9	-0.408402	-3.137	0.001331
10	-0.305319	-2.3452	0.0112
11	0.230639	1.7716	0.040815
12	0.616648	4.7366	7e-06
13	0.148429	1.1401	0.129425
14	-0.146317	-1.1239	0.132807
15	-0.459696	-3.531	0.000405
16	-0.20218	-1.553	0.062888
17	0.182375	1.4008	0.083249

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.108885 & 0.8364 & 0.203164 \tabularnewline
2 & -0.245371 & -1.8847 & 0.032197 \tabularnewline
3 & -0.488711 & -3.7539 & 2e-04 \tabularnewline
4 & -0.341795 & -2.6254 & 0.005503 \tabularnewline
5 & 0.253059 & 1.9438 & 0.028348 \tabularnewline
6 & 0.409136 & 3.1426 & 0.00131 \tabularnewline
7 & 0.253729 & 1.9489 & 0.028032 \tabularnewline
8 & -0.265559 & -2.0398 & 0.022928 \tabularnewline
9 & -0.408402 & -3.137 & 0.001331 \tabularnewline
10 & -0.305319 & -2.3452 & 0.0112 \tabularnewline
11 & 0.230639 & 1.7716 & 0.040815 \tabularnewline
12 & 0.616648 & 4.7366 & 7e-06 \tabularnewline
13 & 0.148429 & 1.1401 & 0.129425 \tabularnewline
14 & -0.146317 & -1.1239 & 0.132807 \tabularnewline
15 & -0.459696 & -3.531 & 0.000405 \tabularnewline
16 & -0.20218 & -1.553 & 0.062888 \tabularnewline
17 & 0.182375 & 1.4008 & 0.083249 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164251&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]0.108885[/C][C]0.8364[/C][C]0.203164[/C][/ROW]
[ROW][C]2[/C][C]-0.245371[/C][C]-1.8847[/C][C]0.032197[/C][/ROW]
[ROW][C]3[/C][C]-0.488711[/C][C]-3.7539[/C][C]2e-04[/C][/ROW]
[ROW][C]4[/C][C]-0.341795[/C][C]-2.6254[/C][C]0.005503[/C][/ROW]
[ROW][C]5[/C][C]0.253059[/C][C]1.9438[/C][C]0.028348[/C][/ROW]
[ROW][C]6[/C][C]0.409136[/C][C]3.1426[/C][C]0.00131[/C][/ROW]
[ROW][C]7[/C][C]0.253729[/C][C]1.9489[/C][C]0.028032[/C][/ROW]
[ROW][C]8[/C][C]-0.265559[/C][C]-2.0398[/C][C]0.022928[/C][/ROW]
[ROW][C]9[/C][C]-0.408402[/C][C]-3.137[/C][C]0.001331[/C][/ROW]
[ROW][C]10[/C][C]-0.305319[/C][C]-2.3452[/C][C]0.0112[/C][/ROW]
[ROW][C]11[/C][C]0.230639[/C][C]1.7716[/C][C]0.040815[/C][/ROW]
[ROW][C]12[/C][C]0.616648[/C][C]4.7366[/C][C]7e-06[/C][/ROW]
[ROW][C]13[/C][C]0.148429[/C][C]1.1401[/C][C]0.129425[/C][/ROW]
[ROW][C]14[/C][C]-0.146317[/C][C]-1.1239[/C][C]0.132807[/C][/ROW]
[ROW][C]15[/C][C]-0.459696[/C][C]-3.531[/C][C]0.000405[/C][/ROW]
[ROW][C]16[/C][C]-0.20218[/C][C]-1.553[/C][C]0.062888[/C][/ROW]
[ROW][C]17[/C][C]0.182375[/C][C]1.4008[/C][C]0.083249[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164251&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164251&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	0.108885	0.8364	0.203164
2	-0.245371	-1.8847	0.032197
3	-0.488711	-3.7539	2e-04
4	-0.341795	-2.6254	0.005503
5	0.253059	1.9438	0.028348
6	0.409136	3.1426	0.00131
7	0.253729	1.9489	0.028032
8	-0.265559	-2.0398	0.022928
9	-0.408402	-3.137	0.001331
10	-0.305319	-2.3452	0.0112
11	0.230639	1.7716	0.040815
12	0.616648	4.7366	7e-06
13	0.148429	1.1401	0.129425
14	-0.146317	-1.1239	0.132807
15	-0.459696	-3.531	0.000405
16	-0.20218	-1.553	0.062888
17	0.182375	1.4008	0.083249

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.108885	0.8364	0.203164
2	-0.260313	-1.9995	0.025083
3	-0.463202	-3.5579	0.000373
4	-0.458162	-3.5192	0.00042
5	-0.027796	-0.2135	0.415834
6	0.038858	0.2985	0.383196
7	0.048277	0.3708	0.356049
8	-0.235242	-1.8069	0.037937
9	-0.192144	-1.4759	0.072646
10	-0.375656	-2.8855	0.002725
11	-0.173345	-1.3315	0.094075
12	0.232395	1.7851	0.039696
13	-0.064347	-0.4943	0.31148
14	-0.004053	-0.0311	0.487634
15	0.007479	0.0574	0.477192
16	0.167655	1.2878	0.101425
17	0.062333	0.4788	0.31693

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.108885 & 0.8364 & 0.203164 \tabularnewline
2 & -0.260313 & -1.9995 & 0.025083 \tabularnewline
3 & -0.463202 & -3.5579 & 0.000373 \tabularnewline
4 & -0.458162 & -3.5192 & 0.00042 \tabularnewline
5 & -0.027796 & -0.2135 & 0.415834 \tabularnewline
6 & 0.038858 & 0.2985 & 0.383196 \tabularnewline
7 & 0.048277 & 0.3708 & 0.356049 \tabularnewline
8 & -0.235242 & -1.8069 & 0.037937 \tabularnewline
9 & -0.192144 & -1.4759 & 0.072646 \tabularnewline
10 & -0.375656 & -2.8855 & 0.002725 \tabularnewline
11 & -0.173345 & -1.3315 & 0.094075 \tabularnewline
12 & 0.232395 & 1.7851 & 0.039696 \tabularnewline
13 & -0.064347 & -0.4943 & 0.31148 \tabularnewline
14 & -0.004053 & -0.0311 & 0.487634 \tabularnewline
15 & 0.007479 & 0.0574 & 0.477192 \tabularnewline
16 & 0.167655 & 1.2878 & 0.101425 \tabularnewline
17 & 0.062333 & 0.4788 & 0.31693 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164251&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]0.108885[/C][C]0.8364[/C][C]0.203164[/C][/ROW]
[ROW][C]2[/C][C]-0.260313[/C][C]-1.9995[/C][C]0.025083[/C][/ROW]
[ROW][C]3[/C][C]-0.463202[/C][C]-3.5579[/C][C]0.000373[/C][/ROW]
[ROW][C]4[/C][C]-0.458162[/C][C]-3.5192[/C][C]0.00042[/C][/ROW]
[ROW][C]5[/C][C]-0.027796[/C][C]-0.2135[/C][C]0.415834[/C][/ROW]
[ROW][C]6[/C][C]0.038858[/C][C]0.2985[/C][C]0.383196[/C][/ROW]
[ROW][C]7[/C][C]0.048277[/C][C]0.3708[/C][C]0.356049[/C][/ROW]
[ROW][C]8[/C][C]-0.235242[/C][C]-1.8069[/C][C]0.037937[/C][/ROW]
[ROW][C]9[/C][C]-0.192144[/C][C]-1.4759[/C][C]0.072646[/C][/ROW]
[ROW][C]10[/C][C]-0.375656[/C][C]-2.8855[/C][C]0.002725[/C][/ROW]
[ROW][C]11[/C][C]-0.173345[/C][C]-1.3315[/C][C]0.094075[/C][/ROW]
[ROW][C]12[/C][C]0.232395[/C][C]1.7851[/C][C]0.039696[/C][/ROW]
[ROW][C]13[/C][C]-0.064347[/C][C]-0.4943[/C][C]0.31148[/C][/ROW]
[ROW][C]14[/C][C]-0.004053[/C][C]-0.0311[/C][C]0.487634[/C][/ROW]
[ROW][C]15[/C][C]0.007479[/C][C]0.0574[/C][C]0.477192[/C][/ROW]
[ROW][C]16[/C][C]0.167655[/C][C]1.2878[/C][C]0.101425[/C][/ROW]
[ROW][C]17[/C][C]0.062333[/C][C]0.4788[/C][C]0.31693[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164251&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164251&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	0.108885	0.8364	0.203164
2	-0.260313	-1.9995	0.025083
3	-0.463202	-3.5579	0.000373
4	-0.458162	-3.5192	0.00042
5	-0.027796	-0.2135	0.415834
6	0.038858	0.2985	0.383196
7	0.048277	0.3708	0.356049
8	-0.235242	-1.8069	0.037937
9	-0.192144	-1.4759	0.072646
10	-0.375656	-2.8855	0.002725
11	-0.173345	-1.3315	0.094075
12	0.232395	1.7851	0.039696
13	-0.064347	-0.4943	0.31148
14	-0.004053	-0.0311	0.487634
15	0.007479	0.0574	0.477192
16	0.167655	1.2878	0.101425
17	0.062333	0.4788	0.31693

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)
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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