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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 16 Dec 2010 10:18:37 +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/2010/Dec/16/t1292494600k5xiyflj8ege858.htm/, Retrieved Fri, 03 May 2024 11:23:37 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=110817, Retrieved Fri, 03 May 2024 11:23:37 +0000

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User-defined keywords

Estimated Impact

147

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

-     [Univariate Data Series] [] [2008-12-08 19:22:39] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMP   [(Partial) Autocorrelation Function] [autocorrelatie ru...] [2010-12-14 18:37:20] [d6e648f00513dd750579ba7880c5fbf5]
- R PD      [(Partial) Autocorrelation Function] [] [2010-12-16 10:18:37] [7674ee8f347756742f81ca2ada5c384c] [Current]
-   PD        [(Partial) Autocorrelation Function] [] [2010-12-16 18:23:00] [b10d6b9682dfaaa479f495240bcd67cf] 
-    D          [(Partial) Autocorrelation Function] [] [2010-12-29 09:21:36] [126c9e58bb659a0bfb4675d843c2c69e] 

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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' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110817&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110817&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110817&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' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.944403	6.2645	0
2	0.866934	5.7506	0
3	0.772799	5.1262	3e-06
4	0.681201	4.5186	2.3e-05
5	0.605725	4.0179	0.000113
6	0.50937	3.3788	0.000767
7	0.400433	2.6562	0.005484
8	0.289239	1.9186	0.030769
9	0.168804	1.1197	0.134454
10	0.054373	0.3607	0.360035
11	-0.057517	-0.3815	0.352326
12	-0.156163	-1.0359	0.152962
13	-0.217994	-1.446	0.07763
14	-0.268432	-1.7806	0.040943
15	-0.30321	-2.0113	0.025224
16	-0.350733	-2.3265	0.01233
17	-0.404515	-2.6832	0.005117

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.944403 & 6.2645 & 0 \tabularnewline
2 & 0.866934 & 5.7506 & 0 \tabularnewline
3 & 0.772799 & 5.1262 & 3e-06 \tabularnewline
4 & 0.681201 & 4.5186 & 2.3e-05 \tabularnewline
5 & 0.605725 & 4.0179 & 0.000113 \tabularnewline
6 & 0.50937 & 3.3788 & 0.000767 \tabularnewline
7 & 0.400433 & 2.6562 & 0.005484 \tabularnewline
8 & 0.289239 & 1.9186 & 0.030769 \tabularnewline
9 & 0.168804 & 1.1197 & 0.134454 \tabularnewline
10 & 0.054373 & 0.3607 & 0.360035 \tabularnewline
11 & -0.057517 & -0.3815 & 0.352326 \tabularnewline
12 & -0.156163 & -1.0359 & 0.152962 \tabularnewline
13 & -0.217994 & -1.446 & 0.07763 \tabularnewline
14 & -0.268432 & -1.7806 & 0.040943 \tabularnewline
15 & -0.30321 & -2.0113 & 0.025224 \tabularnewline
16 & -0.350733 & -2.3265 & 0.01233 \tabularnewline
17 & -0.404515 & -2.6832 & 0.005117 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110817&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]0.944403[/C][C]6.2645[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.866934[/C][C]5.7506[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.772799[/C][C]5.1262[/C][C]3e-06[/C][/ROW]
[ROW][C]4[/C][C]0.681201[/C][C]4.5186[/C][C]2.3e-05[/C][/ROW]
[ROW][C]5[/C][C]0.605725[/C][C]4.0179[/C][C]0.000113[/C][/ROW]
[ROW][C]6[/C][C]0.50937[/C][C]3.3788[/C][C]0.000767[/C][/ROW]
[ROW][C]7[/C][C]0.400433[/C][C]2.6562[/C][C]0.005484[/C][/ROW]
[ROW][C]8[/C][C]0.289239[/C][C]1.9186[/C][C]0.030769[/C][/ROW]
[ROW][C]9[/C][C]0.168804[/C][C]1.1197[/C][C]0.134454[/C][/ROW]
[ROW][C]10[/C][C]0.054373[/C][C]0.3607[/C][C]0.360035[/C][/ROW]
[ROW][C]11[/C][C]-0.057517[/C][C]-0.3815[/C][C]0.352326[/C][/ROW]
[ROW][C]12[/C][C]-0.156163[/C][C]-1.0359[/C][C]0.152962[/C][/ROW]
[ROW][C]13[/C][C]-0.217994[/C][C]-1.446[/C][C]0.07763[/C][/ROW]
[ROW][C]14[/C][C]-0.268432[/C][C]-1.7806[/C][C]0.040943[/C][/ROW]
[ROW][C]15[/C][C]-0.30321[/C][C]-2.0113[/C][C]0.025224[/C][/ROW]
[ROW][C]16[/C][C]-0.350733[/C][C]-2.3265[/C][C]0.01233[/C][/ROW]
[ROW][C]17[/C][C]-0.404515[/C][C]-2.6832[/C][C]0.005117[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110817&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110817&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	0.944403	6.2645	0
2	0.866934	5.7506	0
3	0.772799	5.1262	3e-06
4	0.681201	4.5186	2.3e-05
5	0.605725	4.0179	0.000113
6	0.50937	3.3788	0.000767
7	0.400433	2.6562	0.005484
8	0.289239	1.9186	0.030769
9	0.168804	1.1197	0.134454
10	0.054373	0.3607	0.360035
11	-0.057517	-0.3815	0.352326
12	-0.156163	-1.0359	0.152962
13	-0.217994	-1.446	0.07763
14	-0.268432	-1.7806	0.040943
15	-0.30321	-2.0113	0.025224
16	-0.350733	-2.3265	0.01233
17	-0.404515	-2.6832	0.005117

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.944403	6.2645	0
2	-0.230922	-1.5318	0.06637
3	-0.165309	-1.0965	0.139405
4	0.020559	0.1364	0.446074
5	0.10848	0.7196	0.237797
6	-0.327629	-2.1732	0.017594
7	-0.167305	-1.1098	0.136562
8	0.037144	0.2464	0.403264
9	-0.161136	-1.0689	0.145482
10	-0.148042	-0.982	0.165735
11	-0.046842	-0.3107	0.378742
12	0.079374	0.5265	0.30059
13	0.212145	1.4072	0.083195
14	-0.096807	-0.6421	0.262055
15	-0.0069	-0.0458	0.481851
16	-0.186688	-1.2383	0.111077
17	-0.073869	-0.49	0.313287

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.944403 & 6.2645 & 0 \tabularnewline
2 & -0.230922 & -1.5318 & 0.06637 \tabularnewline
3 & -0.165309 & -1.0965 & 0.139405 \tabularnewline
4 & 0.020559 & 0.1364 & 0.446074 \tabularnewline
5 & 0.10848 & 0.7196 & 0.237797 \tabularnewline
6 & -0.327629 & -2.1732 & 0.017594 \tabularnewline
7 & -0.167305 & -1.1098 & 0.136562 \tabularnewline
8 & 0.037144 & 0.2464 & 0.403264 \tabularnewline
9 & -0.161136 & -1.0689 & 0.145482 \tabularnewline
10 & -0.148042 & -0.982 & 0.165735 \tabularnewline
11 & -0.046842 & -0.3107 & 0.378742 \tabularnewline
12 & 0.079374 & 0.5265 & 0.30059 \tabularnewline
13 & 0.212145 & 1.4072 & 0.083195 \tabularnewline
14 & -0.096807 & -0.6421 & 0.262055 \tabularnewline
15 & -0.0069 & -0.0458 & 0.481851 \tabularnewline
16 & -0.186688 & -1.2383 & 0.111077 \tabularnewline
17 & -0.073869 & -0.49 & 0.313287 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110817&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]0.944403[/C][C]6.2645[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.230922[/C][C]-1.5318[/C][C]0.06637[/C][/ROW]
[ROW][C]3[/C][C]-0.165309[/C][C]-1.0965[/C][C]0.139405[/C][/ROW]
[ROW][C]4[/C][C]0.020559[/C][C]0.1364[/C][C]0.446074[/C][/ROW]
[ROW][C]5[/C][C]0.10848[/C][C]0.7196[/C][C]0.237797[/C][/ROW]
[ROW][C]6[/C][C]-0.327629[/C][C]-2.1732[/C][C]0.017594[/C][/ROW]
[ROW][C]7[/C][C]-0.167305[/C][C]-1.1098[/C][C]0.136562[/C][/ROW]
[ROW][C]8[/C][C]0.037144[/C][C]0.2464[/C][C]0.403264[/C][/ROW]
[ROW][C]9[/C][C]-0.161136[/C][C]-1.0689[/C][C]0.145482[/C][/ROW]
[ROW][C]10[/C][C]-0.148042[/C][C]-0.982[/C][C]0.165735[/C][/ROW]
[ROW][C]11[/C][C]-0.046842[/C][C]-0.3107[/C][C]0.378742[/C][/ROW]
[ROW][C]12[/C][C]0.079374[/C][C]0.5265[/C][C]0.30059[/C][/ROW]
[ROW][C]13[/C][C]0.212145[/C][C]1.4072[/C][C]0.083195[/C][/ROW]
[ROW][C]14[/C][C]-0.096807[/C][C]-0.6421[/C][C]0.262055[/C][/ROW]
[ROW][C]15[/C][C]-0.0069[/C][C]-0.0458[/C][C]0.481851[/C][/ROW]
[ROW][C]16[/C][C]-0.186688[/C][C]-1.2383[/C][C]0.111077[/C][/ROW]
[ROW][C]17[/C][C]-0.073869[/C][C]-0.49[/C][C]0.313287[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110817&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110817&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	0.944403	6.2645	0
2	-0.230922	-1.5318	0.06637
3	-0.165309	-1.0965	0.139405
4	0.020559	0.1364	0.446074
5	0.10848	0.7196	0.237797
6	-0.327629	-2.1732	0.017594
7	-0.167305	-1.1098	0.136562
8	0.037144	0.2464	0.403264
9	-0.161136	-1.0689	0.145482
10	-0.148042	-0.982	0.165735
11	-0.046842	-0.3107	0.378742
12	0.079374	0.5265	0.30059
13	0.212145	1.4072	0.083195
14	-0.096807	-0.6421	0.262055
15	-0.0069	-0.0458	0.481851
16	-0.186688	-1.2383	0.111077
17	-0.073869	-0.49	0.313287

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 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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