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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 04 Apr 2012 16:46:03 -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/Apr/04/t1333572412ryqhhkhvd0uksqa.htm/, Retrieved Mon, 29 Apr 2024 03:46:40 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=164316, Retrieved Mon, 29 Apr 2024 03:46:40 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W12

Estimated Impact

156

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

-       [(Partial) Autocorrelation Function] [Opgave6bisoef2Stap1] [2012-04-04 20:46:03] [08dcc0ed4004cc7fccfdee3f5920290a] [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	'AstonUniversity' @ aston.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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164316&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164316&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164316&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	'AstonUniversity' @ aston.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.840598	6.5112	0
2	0.767323	5.9437	0
3	0.700491	5.426	1e-06
4	0.643648	4.9857	3e-06
5	0.599475	4.6435	1e-05
6	0.554987	4.2989	3.2e-05
7	0.503389	3.8992	0.000123
8	0.479097	3.7111	0.000227
9	0.449826	3.4843	0.000464
10	0.428267	3.3173	0.000774
11	0.40229	3.1161	0.001405
12	0.375455	2.9083	0.002544
13	0.341298	2.6437	0.005224
14	0.283515	2.1961	0.015981
15	0.224386	1.7381	0.043663
16	0.168602	1.306	0.098271
17	0.119854	0.9284	0.178464

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.840598 & 6.5112 & 0 \tabularnewline
2 & 0.767323 & 5.9437 & 0 \tabularnewline
3 & 0.700491 & 5.426 & 1e-06 \tabularnewline
4 & 0.643648 & 4.9857 & 3e-06 \tabularnewline
5 & 0.599475 & 4.6435 & 1e-05 \tabularnewline
6 & 0.554987 & 4.2989 & 3.2e-05 \tabularnewline
7 & 0.503389 & 3.8992 & 0.000123 \tabularnewline
8 & 0.479097 & 3.7111 & 0.000227 \tabularnewline
9 & 0.449826 & 3.4843 & 0.000464 \tabularnewline
10 & 0.428267 & 3.3173 & 0.000774 \tabularnewline
11 & 0.40229 & 3.1161 & 0.001405 \tabularnewline
12 & 0.375455 & 2.9083 & 0.002544 \tabularnewline
13 & 0.341298 & 2.6437 & 0.005224 \tabularnewline
14 & 0.283515 & 2.1961 & 0.015981 \tabularnewline
15 & 0.224386 & 1.7381 & 0.043663 \tabularnewline
16 & 0.168602 & 1.306 & 0.098271 \tabularnewline
17 & 0.119854 & 0.9284 & 0.178464 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164316&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]0.840598[/C][C]6.5112[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.767323[/C][C]5.9437[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.700491[/C][C]5.426[/C][C]1e-06[/C][/ROW]
[ROW][C]4[/C][C]0.643648[/C][C]4.9857[/C][C]3e-06[/C][/ROW]
[ROW][C]5[/C][C]0.599475[/C][C]4.6435[/C][C]1e-05[/C][/ROW]
[ROW][C]6[/C][C]0.554987[/C][C]4.2989[/C][C]3.2e-05[/C][/ROW]
[ROW][C]7[/C][C]0.503389[/C][C]3.8992[/C][C]0.000123[/C][/ROW]
[ROW][C]8[/C][C]0.479097[/C][C]3.7111[/C][C]0.000227[/C][/ROW]
[ROW][C]9[/C][C]0.449826[/C][C]3.4843[/C][C]0.000464[/C][/ROW]
[ROW][C]10[/C][C]0.428267[/C][C]3.3173[/C][C]0.000774[/C][/ROW]
[ROW][C]11[/C][C]0.40229[/C][C]3.1161[/C][C]0.001405[/C][/ROW]
[ROW][C]12[/C][C]0.375455[/C][C]2.9083[/C][C]0.002544[/C][/ROW]
[ROW][C]13[/C][C]0.341298[/C][C]2.6437[/C][C]0.005224[/C][/ROW]
[ROW][C]14[/C][C]0.283515[/C][C]2.1961[/C][C]0.015981[/C][/ROW]
[ROW][C]15[/C][C]0.224386[/C][C]1.7381[/C][C]0.043663[/C][/ROW]
[ROW][C]16[/C][C]0.168602[/C][C]1.306[/C][C]0.098271[/C][/ROW]
[ROW][C]17[/C][C]0.119854[/C][C]0.9284[/C][C]0.178464[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164316&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164316&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	0.840598	6.5112	0
2	0.767323	5.9437	0
3	0.700491	5.426	1e-06
4	0.643648	4.9857	3e-06
5	0.599475	4.6435	1e-05
6	0.554987	4.2989	3.2e-05
7	0.503389	3.8992	0.000123
8	0.479097	3.7111	0.000227
9	0.449826	3.4843	0.000464
10	0.428267	3.3173	0.000774
11	0.40229	3.1161	0.001405
12	0.375455	2.9083	0.002544
13	0.341298	2.6437	0.005224
14	0.283515	2.1961	0.015981
15	0.224386	1.7381	0.043663
16	0.168602	1.306	0.098271
17	0.119854	0.9284	0.178464

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.840598	6.5112	0
2	0.206949	1.603	0.057091
3	0.053428	0.4139	0.340228
4	0.028714	0.2224	0.412372
5	0.040172	0.3112	0.378374
6	0.007806	0.0605	0.475993
7	-0.035125	-0.2721	0.393247
8	0.062799	0.4864	0.314214
9	0.015618	0.121	0.452056
10	0.024805	0.1921	0.424142
11	-0.004207	-0.0326	0.487056
12	-0.007318	-0.0567	0.477491
13	-0.037227	-0.2884	0.387033
14	-0.119306	-0.9241	0.179558
15	-0.089399	-0.6925	0.245654
16	-0.063433	-0.4914	0.312486
17	-0.035167	-0.2724	0.393125

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.840598 & 6.5112 & 0 \tabularnewline
2 & 0.206949 & 1.603 & 0.057091 \tabularnewline
3 & 0.053428 & 0.4139 & 0.340228 \tabularnewline
4 & 0.028714 & 0.2224 & 0.412372 \tabularnewline
5 & 0.040172 & 0.3112 & 0.378374 \tabularnewline
6 & 0.007806 & 0.0605 & 0.475993 \tabularnewline
7 & -0.035125 & -0.2721 & 0.393247 \tabularnewline
8 & 0.062799 & 0.4864 & 0.314214 \tabularnewline
9 & 0.015618 & 0.121 & 0.452056 \tabularnewline
10 & 0.024805 & 0.1921 & 0.424142 \tabularnewline
11 & -0.004207 & -0.0326 & 0.487056 \tabularnewline
12 & -0.007318 & -0.0567 & 0.477491 \tabularnewline
13 & -0.037227 & -0.2884 & 0.387033 \tabularnewline
14 & -0.119306 & -0.9241 & 0.179558 \tabularnewline
15 & -0.089399 & -0.6925 & 0.245654 \tabularnewline
16 & -0.063433 & -0.4914 & 0.312486 \tabularnewline
17 & -0.035167 & -0.2724 & 0.393125 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164316&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]0.840598[/C][C]6.5112[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.206949[/C][C]1.603[/C][C]0.057091[/C][/ROW]
[ROW][C]3[/C][C]0.053428[/C][C]0.4139[/C][C]0.340228[/C][/ROW]
[ROW][C]4[/C][C]0.028714[/C][C]0.2224[/C][C]0.412372[/C][/ROW]
[ROW][C]5[/C][C]0.040172[/C][C]0.3112[/C][C]0.378374[/C][/ROW]
[ROW][C]6[/C][C]0.007806[/C][C]0.0605[/C][C]0.475993[/C][/ROW]
[ROW][C]7[/C][C]-0.035125[/C][C]-0.2721[/C][C]0.393247[/C][/ROW]
[ROW][C]8[/C][C]0.062799[/C][C]0.4864[/C][C]0.314214[/C][/ROW]
[ROW][C]9[/C][C]0.015618[/C][C]0.121[/C][C]0.452056[/C][/ROW]
[ROW][C]10[/C][C]0.024805[/C][C]0.1921[/C][C]0.424142[/C][/ROW]
[ROW][C]11[/C][C]-0.004207[/C][C]-0.0326[/C][C]0.487056[/C][/ROW]
[ROW][C]12[/C][C]-0.007318[/C][C]-0.0567[/C][C]0.477491[/C][/ROW]
[ROW][C]13[/C][C]-0.037227[/C][C]-0.2884[/C][C]0.387033[/C][/ROW]
[ROW][C]14[/C][C]-0.119306[/C][C]-0.9241[/C][C]0.179558[/C][/ROW]
[ROW][C]15[/C][C]-0.089399[/C][C]-0.6925[/C][C]0.245654[/C][/ROW]
[ROW][C]16[/C][C]-0.063433[/C][C]-0.4914[/C][C]0.312486[/C][/ROW]
[ROW][C]17[/C][C]-0.035167[/C][C]-0.2724[/C][C]0.393125[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164316&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164316&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	0.840598	6.5112	0
2	0.206949	1.603	0.057091
3	0.053428	0.4139	0.340228
4	0.028714	0.2224	0.412372
5	0.040172	0.3112	0.378374
6	0.007806	0.0605	0.475993
7	-0.035125	-0.2721	0.393247
8	0.062799	0.4864	0.314214
9	0.015618	0.121	0.452056
10	0.024805	0.1921	0.424142
11	-0.004207	-0.0326	0.487056
12	-0.007318	-0.0567	0.477491
13	-0.037227	-0.2884	0.387033
14	-0.119306	-0.9241	0.179558
15	-0.089399	-0.6925	0.245654
16	-0.063433	-0.4914	0.312486
17	-0.035167	-0.2724	0.393125

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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code