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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 24 May 2012 07:57:51 -0400

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/May/24/t13378607311g4s3g9p663owhj.htm/, Retrieved Sun, 05 May 2024 10:59:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167306, Retrieved Sun, 05 May 2024 10:59:10 +0000

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-       [(Partial) Autocorrelation Function] [] [2012-05-24 11:57:51] [f26bc165187ae19198203e315c1ca52f] [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=167306&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=167306&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167306&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	0.965098	7.4756	0
2	0.922996	7.1495	0
3	0.87805	6.8013	0
4	0.833345	6.4551	0
5	0.788617	6.1086	0
6	0.741959	5.7472	0
7	0.693331	5.3705	1e-06
8	0.637387	4.9372	3e-06
9	0.577699	4.4748	1.7e-05
10	0.513387	3.9767	9.5e-05
11	0.450276	3.4878	0.000459
12	0.384528	2.9785	0.002087
13	0.320533	2.4828	0.007924
14	0.251601	1.9489	0.027994
15	0.183748	1.4233	0.079913
16	0.123242	0.9546	0.171798
17	0.065669	0.5087	0.306424

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.965098 & 7.4756 & 0 \tabularnewline
2 & 0.922996 & 7.1495 & 0 \tabularnewline
3 & 0.87805 & 6.8013 & 0 \tabularnewline
4 & 0.833345 & 6.4551 & 0 \tabularnewline
5 & 0.788617 & 6.1086 & 0 \tabularnewline
6 & 0.741959 & 5.7472 & 0 \tabularnewline
7 & 0.693331 & 5.3705 & 1e-06 \tabularnewline
8 & 0.637387 & 4.9372 & 3e-06 \tabularnewline
9 & 0.577699 & 4.4748 & 1.7e-05 \tabularnewline
10 & 0.513387 & 3.9767 & 9.5e-05 \tabularnewline
11 & 0.450276 & 3.4878 & 0.000459 \tabularnewline
12 & 0.384528 & 2.9785 & 0.002087 \tabularnewline
13 & 0.320533 & 2.4828 & 0.007924 \tabularnewline
14 & 0.251601 & 1.9489 & 0.027994 \tabularnewline
15 & 0.183748 & 1.4233 & 0.079913 \tabularnewline
16 & 0.123242 & 0.9546 & 0.171798 \tabularnewline
17 & 0.065669 & 0.5087 & 0.306424 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167306&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]0.965098[/C][C]7.4756[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.922996[/C][C]7.1495[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.87805[/C][C]6.8013[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.833345[/C][C]6.4551[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.788617[/C][C]6.1086[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.741959[/C][C]5.7472[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.693331[/C][C]5.3705[/C][C]1e-06[/C][/ROW]
[ROW][C]8[/C][C]0.637387[/C][C]4.9372[/C][C]3e-06[/C][/ROW]
[ROW][C]9[/C][C]0.577699[/C][C]4.4748[/C][C]1.7e-05[/C][/ROW]
[ROW][C]10[/C][C]0.513387[/C][C]3.9767[/C][C]9.5e-05[/C][/ROW]
[ROW][C]11[/C][C]0.450276[/C][C]3.4878[/C][C]0.000459[/C][/ROW]
[ROW][C]12[/C][C]0.384528[/C][C]2.9785[/C][C]0.002087[/C][/ROW]
[ROW][C]13[/C][C]0.320533[/C][C]2.4828[/C][C]0.007924[/C][/ROW]
[ROW][C]14[/C][C]0.251601[/C][C]1.9489[/C][C]0.027994[/C][/ROW]
[ROW][C]15[/C][C]0.183748[/C][C]1.4233[/C][C]0.079913[/C][/ROW]
[ROW][C]16[/C][C]0.123242[/C][C]0.9546[/C][C]0.171798[/C][/ROW]
[ROW][C]17[/C][C]0.065669[/C][C]0.5087[/C][C]0.306424[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167306&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167306&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	0.965098	7.4756	0
2	0.922996	7.1495	0
3	0.87805	6.8013	0
4	0.833345	6.4551	0
5	0.788617	6.1086	0
6	0.741959	5.7472	0
7	0.693331	5.3705	1e-06
8	0.637387	4.9372	3e-06
9	0.577699	4.4748	1.7e-05
10	0.513387	3.9767	9.5e-05
11	0.450276	3.4878	0.000459
12	0.384528	2.9785	0.002087
13	0.320533	2.4828	0.007924
14	0.251601	1.9489	0.027994
15	0.183748	1.4233	0.079913
16	0.123242	0.9546	0.171798
17	0.065669	0.5087	0.306424

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.965098	7.4756	0
2	-0.122742	-0.9508	0.172771
3	-0.053436	-0.4139	0.340205
4	-0.013254	-0.1027	0.459285
5	-0.024915	-0.193	0.423808
6	-0.05415	-0.4194	0.338195
7	-0.050662	-0.3924	0.348067
8	-0.131184	-1.0161	0.156819
9	-0.071263	-0.552	0.2915
10	-0.095917	-0.743	0.230199
11	-0.015611	-0.1209	0.452079
12	-0.088726	-0.6873	0.24728
13	-0.015743	-0.1219	0.451676
14	-0.126795	-0.9822	0.164985
15	-0.019097	-0.1479	0.44145
16	0.060524	0.4688	0.320449
17	-0.016151	-0.1251	0.45043

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.965098 & 7.4756 & 0 \tabularnewline
2 & -0.122742 & -0.9508 & 0.172771 \tabularnewline
3 & -0.053436 & -0.4139 & 0.340205 \tabularnewline
4 & -0.013254 & -0.1027 & 0.459285 \tabularnewline
5 & -0.024915 & -0.193 & 0.423808 \tabularnewline
6 & -0.05415 & -0.4194 & 0.338195 \tabularnewline
7 & -0.050662 & -0.3924 & 0.348067 \tabularnewline
8 & -0.131184 & -1.0161 & 0.156819 \tabularnewline
9 & -0.071263 & -0.552 & 0.2915 \tabularnewline
10 & -0.095917 & -0.743 & 0.230199 \tabularnewline
11 & -0.015611 & -0.1209 & 0.452079 \tabularnewline
12 & -0.088726 & -0.6873 & 0.24728 \tabularnewline
13 & -0.015743 & -0.1219 & 0.451676 \tabularnewline
14 & -0.126795 & -0.9822 & 0.164985 \tabularnewline
15 & -0.019097 & -0.1479 & 0.44145 \tabularnewline
16 & 0.060524 & 0.4688 & 0.320449 \tabularnewline
17 & -0.016151 & -0.1251 & 0.45043 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167306&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]0.965098[/C][C]7.4756[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.122742[/C][C]-0.9508[/C][C]0.172771[/C][/ROW]
[ROW][C]3[/C][C]-0.053436[/C][C]-0.4139[/C][C]0.340205[/C][/ROW]
[ROW][C]4[/C][C]-0.013254[/C][C]-0.1027[/C][C]0.459285[/C][/ROW]
[ROW][C]5[/C][C]-0.024915[/C][C]-0.193[/C][C]0.423808[/C][/ROW]
[ROW][C]6[/C][C]-0.05415[/C][C]-0.4194[/C][C]0.338195[/C][/ROW]
[ROW][C]7[/C][C]-0.050662[/C][C]-0.3924[/C][C]0.348067[/C][/ROW]
[ROW][C]8[/C][C]-0.131184[/C][C]-1.0161[/C][C]0.156819[/C][/ROW]
[ROW][C]9[/C][C]-0.071263[/C][C]-0.552[/C][C]0.2915[/C][/ROW]
[ROW][C]10[/C][C]-0.095917[/C][C]-0.743[/C][C]0.230199[/C][/ROW]
[ROW][C]11[/C][C]-0.015611[/C][C]-0.1209[/C][C]0.452079[/C][/ROW]
[ROW][C]12[/C][C]-0.088726[/C][C]-0.6873[/C][C]0.24728[/C][/ROW]
[ROW][C]13[/C][C]-0.015743[/C][C]-0.1219[/C][C]0.451676[/C][/ROW]
[ROW][C]14[/C][C]-0.126795[/C][C]-0.9822[/C][C]0.164985[/C][/ROW]
[ROW][C]15[/C][C]-0.019097[/C][C]-0.1479[/C][C]0.44145[/C][/ROW]
[ROW][C]16[/C][C]0.060524[/C][C]0.4688[/C][C]0.320449[/C][/ROW]
[ROW][C]17[/C][C]-0.016151[/C][C]-0.1251[/C][C]0.45043[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167306&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167306&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	0.965098	7.4756	0
2	-0.122742	-0.9508	0.172771
3	-0.053436	-0.4139	0.340205
4	-0.013254	-0.1027	0.459285
5	-0.024915	-0.193	0.423808
6	-0.05415	-0.4194	0.338195
7	-0.050662	-0.3924	0.348067
8	-0.131184	-1.0161	0.156819
9	-0.071263	-0.552	0.2915
10	-0.095917	-0.743	0.230199
11	-0.015611	-0.1209	0.452079
12	-0.088726	-0.6873	0.24728
13	-0.015743	-0.1219	0.451676
14	-0.126795	-0.9822	0.164985
15	-0.019097	-0.1479	0.44145
16	0.060524	0.4688	0.320449
17	-0.016151	-0.1251	0.45043

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