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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 19 May 2016 18:16:36 +0100

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/2016/May/19/t1463678230c02ameb5ost1bfq.htm/, Retrieved Sat, 27 Apr 2024 07:23:24 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=295405, Retrieved Sat, 27 Apr 2024 07:23:24 +0000

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No (this computation is public)

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Estimated Impact

127

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

-       [(Partial) Autocorrelation Function] [] [2016-05-19 17:16:36] [c9bda892eb41b28d549a884a1978c032] [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	'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295405&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295405&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295405&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	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.236984	-2.159	0.016868
2	0.008983	0.0818	0.467485
3	-0.028572	-0.2603	0.397636
4	-0.207805	-1.8932	0.030908
5	0.217257	1.9793	0.025549
6	-0.088091	-0.8025	0.212265
7	-0.019442	-0.1771	0.42992
8	-0.15278	-1.3919	0.083837
9	-0.076854	-0.7002	0.24289
10	0.150941	1.3751	0.086394
11	-0.17509	-1.5951	0.057241
12	0.299917	2.7324	0.003841
13	-0.257915	-2.3497	0.010581
14	0.106003	0.9657	0.168492
15	0.103703	0.9448	0.173756
16	-0.10959	-0.9984	0.16049
17	0.214315	1.9525	0.027125
18	-0.138855	-1.265	0.104701
19	0.028844	0.2628	0.396685

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.236984 & -2.159 & 0.016868 \tabularnewline
2 & 0.008983 & 0.0818 & 0.467485 \tabularnewline
3 & -0.028572 & -0.2603 & 0.397636 \tabularnewline
4 & -0.207805 & -1.8932 & 0.030908 \tabularnewline
5 & 0.217257 & 1.9793 & 0.025549 \tabularnewline
6 & -0.088091 & -0.8025 & 0.212265 \tabularnewline
7 & -0.019442 & -0.1771 & 0.42992 \tabularnewline
8 & -0.15278 & -1.3919 & 0.083837 \tabularnewline
9 & -0.076854 & -0.7002 & 0.24289 \tabularnewline
10 & 0.150941 & 1.3751 & 0.086394 \tabularnewline
11 & -0.17509 & -1.5951 & 0.057241 \tabularnewline
12 & 0.299917 & 2.7324 & 0.003841 \tabularnewline
13 & -0.257915 & -2.3497 & 0.010581 \tabularnewline
14 & 0.106003 & 0.9657 & 0.168492 \tabularnewline
15 & 0.103703 & 0.9448 & 0.173756 \tabularnewline
16 & -0.10959 & -0.9984 & 0.16049 \tabularnewline
17 & 0.214315 & 1.9525 & 0.027125 \tabularnewline
18 & -0.138855 & -1.265 & 0.104701 \tabularnewline
19 & 0.028844 & 0.2628 & 0.396685 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295405&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]-0.236984[/C][C]-2.159[/C][C]0.016868[/C][/ROW]
[ROW][C]2[/C][C]0.008983[/C][C]0.0818[/C][C]0.467485[/C][/ROW]
[ROW][C]3[/C][C]-0.028572[/C][C]-0.2603[/C][C]0.397636[/C][/ROW]
[ROW][C]4[/C][C]-0.207805[/C][C]-1.8932[/C][C]0.030908[/C][/ROW]
[ROW][C]5[/C][C]0.217257[/C][C]1.9793[/C][C]0.025549[/C][/ROW]
[ROW][C]6[/C][C]-0.088091[/C][C]-0.8025[/C][C]0.212265[/C][/ROW]
[ROW][C]7[/C][C]-0.019442[/C][C]-0.1771[/C][C]0.42992[/C][/ROW]
[ROW][C]8[/C][C]-0.15278[/C][C]-1.3919[/C][C]0.083837[/C][/ROW]
[ROW][C]9[/C][C]-0.076854[/C][C]-0.7002[/C][C]0.24289[/C][/ROW]
[ROW][C]10[/C][C]0.150941[/C][C]1.3751[/C][C]0.086394[/C][/ROW]
[ROW][C]11[/C][C]-0.17509[/C][C]-1.5951[/C][C]0.057241[/C][/ROW]
[ROW][C]12[/C][C]0.299917[/C][C]2.7324[/C][C]0.003841[/C][/ROW]
[ROW][C]13[/C][C]-0.257915[/C][C]-2.3497[/C][C]0.010581[/C][/ROW]
[ROW][C]14[/C][C]0.106003[/C][C]0.9657[/C][C]0.168492[/C][/ROW]
[ROW][C]15[/C][C]0.103703[/C][C]0.9448[/C][C]0.173756[/C][/ROW]
[ROW][C]16[/C][C]-0.10959[/C][C]-0.9984[/C][C]0.16049[/C][/ROW]
[ROW][C]17[/C][C]0.214315[/C][C]1.9525[/C][C]0.027125[/C][/ROW]
[ROW][C]18[/C][C]-0.138855[/C][C]-1.265[/C][C]0.104701[/C][/ROW]
[ROW][C]19[/C][C]0.028844[/C][C]0.2628[/C][C]0.396685[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295405&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295405&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	-0.236984	-2.159	0.016868
2	0.008983	0.0818	0.467485
3	-0.028572	-0.2603	0.397636
4	-0.207805	-1.8932	0.030908
5	0.217257	1.9793	0.025549
6	-0.088091	-0.8025	0.212265
7	-0.019442	-0.1771	0.42992
8	-0.15278	-1.3919	0.083837
9	-0.076854	-0.7002	0.24289
10	0.150941	1.3751	0.086394
11	-0.17509	-1.5951	0.057241
12	0.299917	2.7324	0.003841
13	-0.257915	-2.3497	0.010581
14	0.106003	0.9657	0.168492
15	0.103703	0.9448	0.173756
16	-0.10959	-0.9984	0.16049
17	0.214315	1.9525	0.027125
18	-0.138855	-1.265	0.104701
19	0.028844	0.2628	0.396685

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.236984	-2.159	0.016868
2	-0.049985	-0.4554	0.32501
3	-0.040556	-0.3695	0.356354
4	-0.238362	-2.1716	0.016371
5	0.118898	1.0832	0.140926
6	-0.026548	-0.2419	0.404741
7	-0.066005	-0.6013	0.274628
8	-0.225509	-2.0545	0.021537
9	-0.123938	-1.1291	0.131048
10	0.046084	0.4198	0.337841
11	-0.200647	-1.828	0.035573
12	0.18505	1.6859	0.047787
13	-0.189269	-1.7243	0.044186
14	0.082824	0.7546	0.226324
15	0.014123	0.1287	0.448967
16	0.004422	0.0403	0.483981
17	0.061367	0.5591	0.288807
18	0.01293	0.1178	0.453257
19	0.032432	0.2955	0.384185

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.236984 & -2.159 & 0.016868 \tabularnewline
2 & -0.049985 & -0.4554 & 0.32501 \tabularnewline
3 & -0.040556 & -0.3695 & 0.356354 \tabularnewline
4 & -0.238362 & -2.1716 & 0.016371 \tabularnewline
5 & 0.118898 & 1.0832 & 0.140926 \tabularnewline
6 & -0.026548 & -0.2419 & 0.404741 \tabularnewline
7 & -0.066005 & -0.6013 & 0.274628 \tabularnewline
8 & -0.225509 & -2.0545 & 0.021537 \tabularnewline
9 & -0.123938 & -1.1291 & 0.131048 \tabularnewline
10 & 0.046084 & 0.4198 & 0.337841 \tabularnewline
11 & -0.200647 & -1.828 & 0.035573 \tabularnewline
12 & 0.18505 & 1.6859 & 0.047787 \tabularnewline
13 & -0.189269 & -1.7243 & 0.044186 \tabularnewline
14 & 0.082824 & 0.7546 & 0.226324 \tabularnewline
15 & 0.014123 & 0.1287 & 0.448967 \tabularnewline
16 & 0.004422 & 0.0403 & 0.483981 \tabularnewline
17 & 0.061367 & 0.5591 & 0.288807 \tabularnewline
18 & 0.01293 & 0.1178 & 0.453257 \tabularnewline
19 & 0.032432 & 0.2955 & 0.384185 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295405&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]-0.236984[/C][C]-2.159[/C][C]0.016868[/C][/ROW]
[ROW][C]2[/C][C]-0.049985[/C][C]-0.4554[/C][C]0.32501[/C][/ROW]
[ROW][C]3[/C][C]-0.040556[/C][C]-0.3695[/C][C]0.356354[/C][/ROW]
[ROW][C]4[/C][C]-0.238362[/C][C]-2.1716[/C][C]0.016371[/C][/ROW]
[ROW][C]5[/C][C]0.118898[/C][C]1.0832[/C][C]0.140926[/C][/ROW]
[ROW][C]6[/C][C]-0.026548[/C][C]-0.2419[/C][C]0.404741[/C][/ROW]
[ROW][C]7[/C][C]-0.066005[/C][C]-0.6013[/C][C]0.274628[/C][/ROW]
[ROW][C]8[/C][C]-0.225509[/C][C]-2.0545[/C][C]0.021537[/C][/ROW]
[ROW][C]9[/C][C]-0.123938[/C][C]-1.1291[/C][C]0.131048[/C][/ROW]
[ROW][C]10[/C][C]0.046084[/C][C]0.4198[/C][C]0.337841[/C][/ROW]
[ROW][C]11[/C][C]-0.200647[/C][C]-1.828[/C][C]0.035573[/C][/ROW]
[ROW][C]12[/C][C]0.18505[/C][C]1.6859[/C][C]0.047787[/C][/ROW]
[ROW][C]13[/C][C]-0.189269[/C][C]-1.7243[/C][C]0.044186[/C][/ROW]
[ROW][C]14[/C][C]0.082824[/C][C]0.7546[/C][C]0.226324[/C][/ROW]
[ROW][C]15[/C][C]0.014123[/C][C]0.1287[/C][C]0.448967[/C][/ROW]
[ROW][C]16[/C][C]0.004422[/C][C]0.0403[/C][C]0.483981[/C][/ROW]
[ROW][C]17[/C][C]0.061367[/C][C]0.5591[/C][C]0.288807[/C][/ROW]
[ROW][C]18[/C][C]0.01293[/C][C]0.1178[/C][C]0.453257[/C][/ROW]
[ROW][C]19[/C][C]0.032432[/C][C]0.2955[/C][C]0.384185[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295405&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295405&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	-0.236984	-2.159	0.016868
2	-0.049985	-0.4554	0.32501
3	-0.040556	-0.3695	0.356354
4	-0.238362	-2.1716	0.016371
5	0.118898	1.0832	0.140926
6	-0.026548	-0.2419	0.404741
7	-0.066005	-0.6013	0.274628
8	-0.225509	-2.0545	0.021537
9	-0.123938	-1.1291	0.131048
10	0.046084	0.4198	0.337841
11	-0.200647	-1.828	0.035573
12	0.18505	1.6859	0.047787
13	-0.189269	-1.7243	0.044186
14	0.082824	0.7546	0.226324
15	0.014123	0.1287	0.448967
16	0.004422	0.0403	0.483981
17	0.061367	0.5591	0.288807
18	0.01293	0.1178	0.453257
19	0.032432	0.2955	0.384185

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)
x <- na.omit(x)
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