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Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 04 Dec 2013 07:22:58 -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/2013/Dec/04/t13861598644x3ed8qh9hel3hk.htm/, Retrieved Thu, 25 Apr 2024 23:35:46 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=230565, Retrieved Thu, 25 Apr 2024 23:35:46 +0000

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

-       [(Partial) Autocorrelation Function] [d=1] [2013-12-04 12:22:58] [b86744663ec671173a5f381479557f00] [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	4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230565&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]4 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=230565&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230565&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	4 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.458827	-5.2113	0
2	0.056099	0.6372	0.262573
3	-0.085027	-0.9657	0.167995
4	0.025353	0.288	0.386921
5	-0.009211	-0.1046	0.458419
6	-0.011606	-0.1318	0.447668
7	-0.020011	-0.2273	0.410281
8	-0.018448	-0.2095	0.417185
9	-0.128234	-1.4565	0.073847
10	0.119854	1.3613	0.0879
11	0.061042	0.6933	0.244683
12	0.010295	0.1169	0.45355
13	0.055854	0.6344	0.263478
14	-0.192153	-2.1824	0.015444
15	0.210454	2.3903	0.00914
16	-0.097331	-1.1055	0.135508
17	-0.042654	-0.4845	0.314442
18	0.077785	0.8835	0.189315
19	-0.124831	-1.4178	0.079329
20	-0.046137	-0.524	0.300585
21	0.085017	0.9656	0.168024

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.458827 & -5.2113 & 0 \tabularnewline
2 & 0.056099 & 0.6372 & 0.262573 \tabularnewline
3 & -0.085027 & -0.9657 & 0.167995 \tabularnewline
4 & 0.025353 & 0.288 & 0.386921 \tabularnewline
5 & -0.009211 & -0.1046 & 0.458419 \tabularnewline
6 & -0.011606 & -0.1318 & 0.447668 \tabularnewline
7 & -0.020011 & -0.2273 & 0.410281 \tabularnewline
8 & -0.018448 & -0.2095 & 0.417185 \tabularnewline
9 & -0.128234 & -1.4565 & 0.073847 \tabularnewline
10 & 0.119854 & 1.3613 & 0.0879 \tabularnewline
11 & 0.061042 & 0.6933 & 0.244683 \tabularnewline
12 & 0.010295 & 0.1169 & 0.45355 \tabularnewline
13 & 0.055854 & 0.6344 & 0.263478 \tabularnewline
14 & -0.192153 & -2.1824 & 0.015444 \tabularnewline
15 & 0.210454 & 2.3903 & 0.00914 \tabularnewline
16 & -0.097331 & -1.1055 & 0.135508 \tabularnewline
17 & -0.042654 & -0.4845 & 0.314442 \tabularnewline
18 & 0.077785 & 0.8835 & 0.189315 \tabularnewline
19 & -0.124831 & -1.4178 & 0.079329 \tabularnewline
20 & -0.046137 & -0.524 & 0.300585 \tabularnewline
21 & 0.085017 & 0.9656 & 0.168024 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230565&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]-0.458827[/C][C]-5.2113[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.056099[/C][C]0.6372[/C][C]0.262573[/C][/ROW]
[ROW][C]3[/C][C]-0.085027[/C][C]-0.9657[/C][C]0.167995[/C][/ROW]
[ROW][C]4[/C][C]0.025353[/C][C]0.288[/C][C]0.386921[/C][/ROW]
[ROW][C]5[/C][C]-0.009211[/C][C]-0.1046[/C][C]0.458419[/C][/ROW]
[ROW][C]6[/C][C]-0.011606[/C][C]-0.1318[/C][C]0.447668[/C][/ROW]
[ROW][C]7[/C][C]-0.020011[/C][C]-0.2273[/C][C]0.410281[/C][/ROW]
[ROW][C]8[/C][C]-0.018448[/C][C]-0.2095[/C][C]0.417185[/C][/ROW]
[ROW][C]9[/C][C]-0.128234[/C][C]-1.4565[/C][C]0.073847[/C][/ROW]
[ROW][C]10[/C][C]0.119854[/C][C]1.3613[/C][C]0.0879[/C][/ROW]
[ROW][C]11[/C][C]0.061042[/C][C]0.6933[/C][C]0.244683[/C][/ROW]
[ROW][C]12[/C][C]0.010295[/C][C]0.1169[/C][C]0.45355[/C][/ROW]
[ROW][C]13[/C][C]0.055854[/C][C]0.6344[/C][C]0.263478[/C][/ROW]
[ROW][C]14[/C][C]-0.192153[/C][C]-2.1824[/C][C]0.015444[/C][/ROW]
[ROW][C]15[/C][C]0.210454[/C][C]2.3903[/C][C]0.00914[/C][/ROW]
[ROW][C]16[/C][C]-0.097331[/C][C]-1.1055[/C][C]0.135508[/C][/ROW]
[ROW][C]17[/C][C]-0.042654[/C][C]-0.4845[/C][C]0.314442[/C][/ROW]
[ROW][C]18[/C][C]0.077785[/C][C]0.8835[/C][C]0.189315[/C][/ROW]
[ROW][C]19[/C][C]-0.124831[/C][C]-1.4178[/C][C]0.079329[/C][/ROW]
[ROW][C]20[/C][C]-0.046137[/C][C]-0.524[/C][C]0.300585[/C][/ROW]
[ROW][C]21[/C][C]0.085017[/C][C]0.9656[/C][C]0.168024[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230565&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230565&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	-0.458827	-5.2113	0
2	0.056099	0.6372	0.262573
3	-0.085027	-0.9657	0.167995
4	0.025353	0.288	0.386921
5	-0.009211	-0.1046	0.458419
6	-0.011606	-0.1318	0.447668
7	-0.020011	-0.2273	0.410281
8	-0.018448	-0.2095	0.417185
9	-0.128234	-1.4565	0.073847
10	0.119854	1.3613	0.0879
11	0.061042	0.6933	0.244683
12	0.010295	0.1169	0.45355
13	0.055854	0.6344	0.263478
14	-0.192153	-2.1824	0.015444
15	0.210454	2.3903	0.00914
16	-0.097331	-1.1055	0.135508
17	-0.042654	-0.4845	0.314442
18	0.077785	0.8835	0.189315
19	-0.124831	-1.4178	0.079329
20	-0.046137	-0.524	0.300585
21	0.085017	0.9656	0.168024

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.458827	-5.2113	0
2	-0.195601	-2.2216	0.014027
3	-0.189654	-2.1541	0.016547
4	-0.129315	-1.4687	0.07217
5	-0.093033	-1.0567	0.146323
6	-0.091971	-1.0446	0.149082
7	-0.106079	-1.2048	0.115239
8	-0.12665	-1.4385	0.076362
9	-0.312391	-3.5481	0.000271
10	-0.22095	-2.5095	0.006664
11	-0.077756	-0.8831	0.189402
12	-0.032098	-0.3646	0.358018
13	0.097964	1.1127	0.133963
14	-0.15527	-1.7635	0.04009
15	0.04623	0.5251	0.300219
16	0.024206	0.2749	0.391906
17	-0.118155	-1.342	0.09098
18	0.021715	0.2466	0.40279
19	-0.074921	-0.8509	0.198191
20	-0.202352	-2.2983	0.011578
21	-0.110506	-1.2551	0.105854

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.458827 & -5.2113 & 0 \tabularnewline
2 & -0.195601 & -2.2216 & 0.014027 \tabularnewline
3 & -0.189654 & -2.1541 & 0.016547 \tabularnewline
4 & -0.129315 & -1.4687 & 0.07217 \tabularnewline
5 & -0.093033 & -1.0567 & 0.146323 \tabularnewline
6 & -0.091971 & -1.0446 & 0.149082 \tabularnewline
7 & -0.106079 & -1.2048 & 0.115239 \tabularnewline
8 & -0.12665 & -1.4385 & 0.076362 \tabularnewline
9 & -0.312391 & -3.5481 & 0.000271 \tabularnewline
10 & -0.22095 & -2.5095 & 0.006664 \tabularnewline
11 & -0.077756 & -0.8831 & 0.189402 \tabularnewline
12 & -0.032098 & -0.3646 & 0.358018 \tabularnewline
13 & 0.097964 & 1.1127 & 0.133963 \tabularnewline
14 & -0.15527 & -1.7635 & 0.04009 \tabularnewline
15 & 0.04623 & 0.5251 & 0.300219 \tabularnewline
16 & 0.024206 & 0.2749 & 0.391906 \tabularnewline
17 & -0.118155 & -1.342 & 0.09098 \tabularnewline
18 & 0.021715 & 0.2466 & 0.40279 \tabularnewline
19 & -0.074921 & -0.8509 & 0.198191 \tabularnewline
20 & -0.202352 & -2.2983 & 0.011578 \tabularnewline
21 & -0.110506 & -1.2551 & 0.105854 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230565&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]-0.458827[/C][C]-5.2113[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.195601[/C][C]-2.2216[/C][C]0.014027[/C][/ROW]
[ROW][C]3[/C][C]-0.189654[/C][C]-2.1541[/C][C]0.016547[/C][/ROW]
[ROW][C]4[/C][C]-0.129315[/C][C]-1.4687[/C][C]0.07217[/C][/ROW]
[ROW][C]5[/C][C]-0.093033[/C][C]-1.0567[/C][C]0.146323[/C][/ROW]
[ROW][C]6[/C][C]-0.091971[/C][C]-1.0446[/C][C]0.149082[/C][/ROW]
[ROW][C]7[/C][C]-0.106079[/C][C]-1.2048[/C][C]0.115239[/C][/ROW]
[ROW][C]8[/C][C]-0.12665[/C][C]-1.4385[/C][C]0.076362[/C][/ROW]
[ROW][C]9[/C][C]-0.312391[/C][C]-3.5481[/C][C]0.000271[/C][/ROW]
[ROW][C]10[/C][C]-0.22095[/C][C]-2.5095[/C][C]0.006664[/C][/ROW]
[ROW][C]11[/C][C]-0.077756[/C][C]-0.8831[/C][C]0.189402[/C][/ROW]
[ROW][C]12[/C][C]-0.032098[/C][C]-0.3646[/C][C]0.358018[/C][/ROW]
[ROW][C]13[/C][C]0.097964[/C][C]1.1127[/C][C]0.133963[/C][/ROW]
[ROW][C]14[/C][C]-0.15527[/C][C]-1.7635[/C][C]0.04009[/C][/ROW]
[ROW][C]15[/C][C]0.04623[/C][C]0.5251[/C][C]0.300219[/C][/ROW]
[ROW][C]16[/C][C]0.024206[/C][C]0.2749[/C][C]0.391906[/C][/ROW]
[ROW][C]17[/C][C]-0.118155[/C][C]-1.342[/C][C]0.09098[/C][/ROW]
[ROW][C]18[/C][C]0.021715[/C][C]0.2466[/C][C]0.40279[/C][/ROW]
[ROW][C]19[/C][C]-0.074921[/C][C]-0.8509[/C][C]0.198191[/C][/ROW]
[ROW][C]20[/C][C]-0.202352[/C][C]-2.2983[/C][C]0.011578[/C][/ROW]
[ROW][C]21[/C][C]-0.110506[/C][C]-1.2551[/C][C]0.105854[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230565&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230565&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	-0.458827	-5.2113	0
2	-0.195601	-2.2216	0.014027
3	-0.189654	-2.1541	0.016547
4	-0.129315	-1.4687	0.07217
5	-0.093033	-1.0567	0.146323
6	-0.091971	-1.0446	0.149082
7	-0.106079	-1.2048	0.115239
8	-0.12665	-1.4385	0.076362
9	-0.312391	-3.5481	0.000271
10	-0.22095	-2.5095	0.006664
11	-0.077756	-0.8831	0.189402
12	-0.032098	-0.3646	0.358018
13	0.097964	1.1127	0.133963
14	-0.15527	-1.7635	0.04009
15	0.04623	0.5251	0.300219
16	0.024206	0.2749	0.391906
17	-0.118155	-1.342	0.09098
18	0.021715	0.2466	0.40279
19	-0.074921	-0.8509	0.198191
20	-0.202352	-2.2983	0.011578
21	-0.110506	-1.2551	0.105854

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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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code