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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 22 Dec 2011 18:53:54 -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/2011/Dec/22/t13245980901qrywley2pkkdzo.htm/, Retrieved Fri, 03 May 2024 09:21:02 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160102, Retrieved Fri, 03 May 2024 09:21:02 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

134

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

-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- RMP         [(Partial) Autocorrelation Function] [Births] [2010-11-29 09:36:27] [b98453cac15ba1066b407e146608df68]
- R PD          [(Partial) Autocorrelation Function] [WS9 3.1 ACF d=0, D=0] [2010-12-07 10:00:49] [afe9379cca749d06b3d6872e02cc47ed]
- R PD            [(Partial) Autocorrelation Function] [PAPER: aantal fai...] [2011-12-22 23:47:48] [f0cb027b41af06223bae4ee77475f3bc]
-                     [(Partial) Autocorrelation Function] [PAPER: aantal fai...] [2011-12-22 23:53:54] [6baf48ba14bcb50d9e72b77bece8a45b] [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	1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160102&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]1 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=160102&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160102&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	1 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.153858	1.5075	0.067484
2	0.099997	0.9798	0.164831
3	0.067011	0.6566	0.256515
4	-0.22089	-2.1643	0.016462
5	0.04106	0.4023	0.344179
6	0.054104	0.5301	0.298629
7	0.113741	1.1144	0.133938
8	0.355729	3.4854	0.000371
9	0.111362	1.0911	0.138976
10	0.035535	0.3482	0.364238
11	0.045557	0.4464	0.32817
12	-0.461316	-4.52	9e-06
13	-0.177885	-1.7429	0.042275
14	0.022862	0.224	0.411618
15	0.065141	0.6383	0.262415
16	0.125162	1.2263	0.111537
17	0.057908	0.5674	0.285892
18	0.035544	0.3483	0.364206
19	-0.113233	-1.1095	0.135002
20	-0.150398	-1.4736	0.071932

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.153858 & 1.5075 & 0.067484 \tabularnewline
2 & 0.099997 & 0.9798 & 0.164831 \tabularnewline
3 & 0.067011 & 0.6566 & 0.256515 \tabularnewline
4 & -0.22089 & -2.1643 & 0.016462 \tabularnewline
5 & 0.04106 & 0.4023 & 0.344179 \tabularnewline
6 & 0.054104 & 0.5301 & 0.298629 \tabularnewline
7 & 0.113741 & 1.1144 & 0.133938 \tabularnewline
8 & 0.355729 & 3.4854 & 0.000371 \tabularnewline
9 & 0.111362 & 1.0911 & 0.138976 \tabularnewline
10 & 0.035535 & 0.3482 & 0.364238 \tabularnewline
11 & 0.045557 & 0.4464 & 0.32817 \tabularnewline
12 & -0.461316 & -4.52 & 9e-06 \tabularnewline
13 & -0.177885 & -1.7429 & 0.042275 \tabularnewline
14 & 0.022862 & 0.224 & 0.411618 \tabularnewline
15 & 0.065141 & 0.6383 & 0.262415 \tabularnewline
16 & 0.125162 & 1.2263 & 0.111537 \tabularnewline
17 & 0.057908 & 0.5674 & 0.285892 \tabularnewline
18 & 0.035544 & 0.3483 & 0.364206 \tabularnewline
19 & -0.113233 & -1.1095 & 0.135002 \tabularnewline
20 & -0.150398 & -1.4736 & 0.071932 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160102&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]0.153858[/C][C]1.5075[/C][C]0.067484[/C][/ROW]
[ROW][C]2[/C][C]0.099997[/C][C]0.9798[/C][C]0.164831[/C][/ROW]
[ROW][C]3[/C][C]0.067011[/C][C]0.6566[/C][C]0.256515[/C][/ROW]
[ROW][C]4[/C][C]-0.22089[/C][C]-2.1643[/C][C]0.016462[/C][/ROW]
[ROW][C]5[/C][C]0.04106[/C][C]0.4023[/C][C]0.344179[/C][/ROW]
[ROW][C]6[/C][C]0.054104[/C][C]0.5301[/C][C]0.298629[/C][/ROW]
[ROW][C]7[/C][C]0.113741[/C][C]1.1144[/C][C]0.133938[/C][/ROW]
[ROW][C]8[/C][C]0.355729[/C][C]3.4854[/C][C]0.000371[/C][/ROW]
[ROW][C]9[/C][C]0.111362[/C][C]1.0911[/C][C]0.138976[/C][/ROW]
[ROW][C]10[/C][C]0.035535[/C][C]0.3482[/C][C]0.364238[/C][/ROW]
[ROW][C]11[/C][C]0.045557[/C][C]0.4464[/C][C]0.32817[/C][/ROW]
[ROW][C]12[/C][C]-0.461316[/C][C]-4.52[/C][C]9e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.177885[/C][C]-1.7429[/C][C]0.042275[/C][/ROW]
[ROW][C]14[/C][C]0.022862[/C][C]0.224[/C][C]0.411618[/C][/ROW]
[ROW][C]15[/C][C]0.065141[/C][C]0.6383[/C][C]0.262415[/C][/ROW]
[ROW][C]16[/C][C]0.125162[/C][C]1.2263[/C][C]0.111537[/C][/ROW]
[ROW][C]17[/C][C]0.057908[/C][C]0.5674[/C][C]0.285892[/C][/ROW]
[ROW][C]18[/C][C]0.035544[/C][C]0.3483[/C][C]0.364206[/C][/ROW]
[ROW][C]19[/C][C]-0.113233[/C][C]-1.1095[/C][C]0.135002[/C][/ROW]
[ROW][C]20[/C][C]-0.150398[/C][C]-1.4736[/C][C]0.071932[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160102&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160102&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	0.153858	1.5075	0.067484
2	0.099997	0.9798	0.164831
3	0.067011	0.6566	0.256515
4	-0.22089	-2.1643	0.016462
5	0.04106	0.4023	0.344179
6	0.054104	0.5301	0.298629
7	0.113741	1.1144	0.133938
8	0.355729	3.4854	0.000371
9	0.111362	1.0911	0.138976
10	0.035535	0.3482	0.364238
11	0.045557	0.4464	0.32817
12	-0.461316	-4.52	9e-06
13	-0.177885	-1.7429	0.042275
14	0.022862	0.224	0.411618
15	0.065141	0.6383	0.262415
16	0.125162	1.2263	0.111537
17	0.057908	0.5674	0.285892
18	0.035544	0.3483	0.364206
19	-0.113233	-1.1095	0.135002
20	-0.150398	-1.4736	0.071932

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.153858	1.5075	0.067484
2	0.078176	0.766	0.222789
3	0.042046	0.412	0.340641
4	-0.251758	-2.4667	0.007704
5	0.109105	1.069	0.143873
6	0.07863	0.7704	0.221474
7	0.124413	1.219	0.112917
8	0.269169	2.6373	0.004874
9	0.028923	0.2834	0.388746
10	-0.04018	-0.3937	0.347345
11	0.033369	0.3269	0.37221
12	-0.442629	-4.3369	1.8e-05
13	-0.141118	-1.3827	0.084987
14	0.112095	1.0983	0.13741
15	0.154488	1.5137	0.066698
16	-0.170139	-1.667	0.049386
17	0.011343	0.1111	0.45587
18	0.125026	1.225	0.111785
19	-0.079599	-0.7799	0.218683
20	0.117842	1.1546	0.125558

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.153858 & 1.5075 & 0.067484 \tabularnewline
2 & 0.078176 & 0.766 & 0.222789 \tabularnewline
3 & 0.042046 & 0.412 & 0.340641 \tabularnewline
4 & -0.251758 & -2.4667 & 0.007704 \tabularnewline
5 & 0.109105 & 1.069 & 0.143873 \tabularnewline
6 & 0.07863 & 0.7704 & 0.221474 \tabularnewline
7 & 0.124413 & 1.219 & 0.112917 \tabularnewline
8 & 0.269169 & 2.6373 & 0.004874 \tabularnewline
9 & 0.028923 & 0.2834 & 0.388746 \tabularnewline
10 & -0.04018 & -0.3937 & 0.347345 \tabularnewline
11 & 0.033369 & 0.3269 & 0.37221 \tabularnewline
12 & -0.442629 & -4.3369 & 1.8e-05 \tabularnewline
13 & -0.141118 & -1.3827 & 0.084987 \tabularnewline
14 & 0.112095 & 1.0983 & 0.13741 \tabularnewline
15 & 0.154488 & 1.5137 & 0.066698 \tabularnewline
16 & -0.170139 & -1.667 & 0.049386 \tabularnewline
17 & 0.011343 & 0.1111 & 0.45587 \tabularnewline
18 & 0.125026 & 1.225 & 0.111785 \tabularnewline
19 & -0.079599 & -0.7799 & 0.218683 \tabularnewline
20 & 0.117842 & 1.1546 & 0.125558 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160102&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]0.153858[/C][C]1.5075[/C][C]0.067484[/C][/ROW]
[ROW][C]2[/C][C]0.078176[/C][C]0.766[/C][C]0.222789[/C][/ROW]
[ROW][C]3[/C][C]0.042046[/C][C]0.412[/C][C]0.340641[/C][/ROW]
[ROW][C]4[/C][C]-0.251758[/C][C]-2.4667[/C][C]0.007704[/C][/ROW]
[ROW][C]5[/C][C]0.109105[/C][C]1.069[/C][C]0.143873[/C][/ROW]
[ROW][C]6[/C][C]0.07863[/C][C]0.7704[/C][C]0.221474[/C][/ROW]
[ROW][C]7[/C][C]0.124413[/C][C]1.219[/C][C]0.112917[/C][/ROW]
[ROW][C]8[/C][C]0.269169[/C][C]2.6373[/C][C]0.004874[/C][/ROW]
[ROW][C]9[/C][C]0.028923[/C][C]0.2834[/C][C]0.388746[/C][/ROW]
[ROW][C]10[/C][C]-0.04018[/C][C]-0.3937[/C][C]0.347345[/C][/ROW]
[ROW][C]11[/C][C]0.033369[/C][C]0.3269[/C][C]0.37221[/C][/ROW]
[ROW][C]12[/C][C]-0.442629[/C][C]-4.3369[/C][C]1.8e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.141118[/C][C]-1.3827[/C][C]0.084987[/C][/ROW]
[ROW][C]14[/C][C]0.112095[/C][C]1.0983[/C][C]0.13741[/C][/ROW]
[ROW][C]15[/C][C]0.154488[/C][C]1.5137[/C][C]0.066698[/C][/ROW]
[ROW][C]16[/C][C]-0.170139[/C][C]-1.667[/C][C]0.049386[/C][/ROW]
[ROW][C]17[/C][C]0.011343[/C][C]0.1111[/C][C]0.45587[/C][/ROW]
[ROW][C]18[/C][C]0.125026[/C][C]1.225[/C][C]0.111785[/C][/ROW]
[ROW][C]19[/C][C]-0.079599[/C][C]-0.7799[/C][C]0.218683[/C][/ROW]
[ROW][C]20[/C][C]0.117842[/C][C]1.1546[/C][C]0.125558[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160102&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160102&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	0.153858	1.5075	0.067484
2	0.078176	0.766	0.222789
3	0.042046	0.412	0.340641
4	-0.251758	-2.4667	0.007704
5	0.109105	1.069	0.143873
6	0.07863	0.7704	0.221474
7	0.124413	1.219	0.112917
8	0.269169	2.6373	0.004874
9	0.028923	0.2834	0.388746
10	-0.04018	-0.3937	0.347345
11	0.033369	0.3269	0.37221
12	-0.442629	-4.3369	1.8e-05
13	-0.141118	-1.3827	0.084987
14	0.112095	1.0983	0.13741
15	0.154488	1.5137	0.066698
16	-0.170139	-1.667	0.049386
17	0.011343	0.1111	0.45587
18	0.125026	1.225	0.111785
19	-0.079599	-0.7799	0.218683
20	0.117842	1.1546	0.125558

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 = multiplicative ; par2 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 2 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code