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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 09 Dec 2017 14:27:12 +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/2017/Dec/09/t15128260535rg6x4d4qdlwucx.htm/, Retrieved Tue, 14 May 2024 10:02:40 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308852, Retrieved Tue, 14 May 2024 10:02:40 +0000

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User-defined keywords

Estimated Impact

105

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

-       [(Partial) Autocorrelation Function] [] [2017-12-09 13:27:12] [20141777ecd6b11d9726230b5f8289b4] [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	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308852&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=308852&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308852&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	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.809522	11.7868	0
2	0.74193	10.8027	0
3	0.813409	11.8434	0
4	0.743377	10.8237	0
5	0.766565	11.1614	0
6	0.811687	11.8183	0
7	0.709638	10.3325	0
8	0.684253	9.9629	0
9	0.700764	10.2033	0
10	0.607175	8.8406	0
11	0.668783	9.7376	0
12	0.770601	11.2201	0
13	0.625722	9.1106	0
14	0.573372	8.3484	0
15	0.616723	8.9796	0
16	0.572115	8.3301	0
17	0.596979	8.6921	0
18	0.630823	9.1849	0
19	0.54701	7.9646	0
20	0.536321	7.809	0
21	0.540275	7.8665	0
22	0.464485	6.763	0
23	0.532485	7.7531	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.809522 & 11.7868 & 0 \tabularnewline
2 & 0.74193 & 10.8027 & 0 \tabularnewline
3 & 0.813409 & 11.8434 & 0 \tabularnewline
4 & 0.743377 & 10.8237 & 0 \tabularnewline
5 & 0.766565 & 11.1614 & 0 \tabularnewline
6 & 0.811687 & 11.8183 & 0 \tabularnewline
7 & 0.709638 & 10.3325 & 0 \tabularnewline
8 & 0.684253 & 9.9629 & 0 \tabularnewline
9 & 0.700764 & 10.2033 & 0 \tabularnewline
10 & 0.607175 & 8.8406 & 0 \tabularnewline
11 & 0.668783 & 9.7376 & 0 \tabularnewline
12 & 0.770601 & 11.2201 & 0 \tabularnewline
13 & 0.625722 & 9.1106 & 0 \tabularnewline
14 & 0.573372 & 8.3484 & 0 \tabularnewline
15 & 0.616723 & 8.9796 & 0 \tabularnewline
16 & 0.572115 & 8.3301 & 0 \tabularnewline
17 & 0.596979 & 8.6921 & 0 \tabularnewline
18 & 0.630823 & 9.1849 & 0 \tabularnewline
19 & 0.54701 & 7.9646 & 0 \tabularnewline
20 & 0.536321 & 7.809 & 0 \tabularnewline
21 & 0.540275 & 7.8665 & 0 \tabularnewline
22 & 0.464485 & 6.763 & 0 \tabularnewline
23 & 0.532485 & 7.7531 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308852&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]0.809522[/C][C]11.7868[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.74193[/C][C]10.8027[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.813409[/C][C]11.8434[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.743377[/C][C]10.8237[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.766565[/C][C]11.1614[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.811687[/C][C]11.8183[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.709638[/C][C]10.3325[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.684253[/C][C]9.9629[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.700764[/C][C]10.2033[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.607175[/C][C]8.8406[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.668783[/C][C]9.7376[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.770601[/C][C]11.2201[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.625722[/C][C]9.1106[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.573372[/C][C]8.3484[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.616723[/C][C]8.9796[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.572115[/C][C]8.3301[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.596979[/C][C]8.6921[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.630823[/C][C]9.1849[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.54701[/C][C]7.9646[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.536321[/C][C]7.809[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.540275[/C][C]7.8665[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]0.464485[/C][C]6.763[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]0.532485[/C][C]7.7531[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308852&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308852&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	0.809522	11.7868	0
2	0.74193	10.8027	0
3	0.813409	11.8434	0
4	0.743377	10.8237	0
5	0.766565	11.1614	0
6	0.811687	11.8183	0
7	0.709638	10.3325	0
8	0.684253	9.9629	0
9	0.700764	10.2033	0
10	0.607175	8.8406	0
11	0.668783	9.7376	0
12	0.770601	11.2201	0
13	0.625722	9.1106	0
14	0.573372	8.3484	0
15	0.616723	8.9796	0
16	0.572115	8.3301	0
17	0.596979	8.6921	0
18	0.630823	9.1849	0
19	0.54701	7.9646	0
20	0.536321	7.809	0
21	0.540275	7.8665	0
22	0.464485	6.763	0
23	0.532485	7.7531	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.809522	11.7868	0
2	0.251264	3.6585	0.00016
3	0.496442	7.2283	0
4	-0.05439	-0.7919	0.214643
5	0.36065	5.2511	0
6	0.141833	2.0651	0.020064
7	-0.122512	-1.7838	0.037943
8	-0.07886	-1.1482	0.126085
9	-0.086879	-1.265	0.103634
10	-0.267576	-3.896	6.6e-05
11	0.269449	3.9232	5.9e-05
12	0.419289	6.1049	0
13	-0.18912	-2.7536	0.003203
14	-0.207518	-3.0215	0.001412
15	-0.082323	-1.1986	0.116002
16	0.088796	1.2929	0.098729
17	-0.053629	-0.7808	0.217882
18	0.055241	0.8043	0.211057
19	0.043926	0.6396	0.261573
20	0.038674	0.5631	0.286982
21	-0.046603	-0.6786	0.249081
22	-0.029719	-0.4327	0.33283
23	0.061391	0.8939	0.186205

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.809522 & 11.7868 & 0 \tabularnewline
2 & 0.251264 & 3.6585 & 0.00016 \tabularnewline
3 & 0.496442 & 7.2283 & 0 \tabularnewline
4 & -0.05439 & -0.7919 & 0.214643 \tabularnewline
5 & 0.36065 & 5.2511 & 0 \tabularnewline
6 & 0.141833 & 2.0651 & 0.020064 \tabularnewline
7 & -0.122512 & -1.7838 & 0.037943 \tabularnewline
8 & -0.07886 & -1.1482 & 0.126085 \tabularnewline
9 & -0.086879 & -1.265 & 0.103634 \tabularnewline
10 & -0.267576 & -3.896 & 6.6e-05 \tabularnewline
11 & 0.269449 & 3.9232 & 5.9e-05 \tabularnewline
12 & 0.419289 & 6.1049 & 0 \tabularnewline
13 & -0.18912 & -2.7536 & 0.003203 \tabularnewline
14 & -0.207518 & -3.0215 & 0.001412 \tabularnewline
15 & -0.082323 & -1.1986 & 0.116002 \tabularnewline
16 & 0.088796 & 1.2929 & 0.098729 \tabularnewline
17 & -0.053629 & -0.7808 & 0.217882 \tabularnewline
18 & 0.055241 & 0.8043 & 0.211057 \tabularnewline
19 & 0.043926 & 0.6396 & 0.261573 \tabularnewline
20 & 0.038674 & 0.5631 & 0.286982 \tabularnewline
21 & -0.046603 & -0.6786 & 0.249081 \tabularnewline
22 & -0.029719 & -0.4327 & 0.33283 \tabularnewline
23 & 0.061391 & 0.8939 & 0.186205 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308852&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]0.809522[/C][C]11.7868[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.251264[/C][C]3.6585[/C][C]0.00016[/C][/ROW]
[ROW][C]3[/C][C]0.496442[/C][C]7.2283[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]-0.05439[/C][C]-0.7919[/C][C]0.214643[/C][/ROW]
[ROW][C]5[/C][C]0.36065[/C][C]5.2511[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.141833[/C][C]2.0651[/C][C]0.020064[/C][/ROW]
[ROW][C]7[/C][C]-0.122512[/C][C]-1.7838[/C][C]0.037943[/C][/ROW]
[ROW][C]8[/C][C]-0.07886[/C][C]-1.1482[/C][C]0.126085[/C][/ROW]
[ROW][C]9[/C][C]-0.086879[/C][C]-1.265[/C][C]0.103634[/C][/ROW]
[ROW][C]10[/C][C]-0.267576[/C][C]-3.896[/C][C]6.6e-05[/C][/ROW]
[ROW][C]11[/C][C]0.269449[/C][C]3.9232[/C][C]5.9e-05[/C][/ROW]
[ROW][C]12[/C][C]0.419289[/C][C]6.1049[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.18912[/C][C]-2.7536[/C][C]0.003203[/C][/ROW]
[ROW][C]14[/C][C]-0.207518[/C][C]-3.0215[/C][C]0.001412[/C][/ROW]
[ROW][C]15[/C][C]-0.082323[/C][C]-1.1986[/C][C]0.116002[/C][/ROW]
[ROW][C]16[/C][C]0.088796[/C][C]1.2929[/C][C]0.098729[/C][/ROW]
[ROW][C]17[/C][C]-0.053629[/C][C]-0.7808[/C][C]0.217882[/C][/ROW]
[ROW][C]18[/C][C]0.055241[/C][C]0.8043[/C][C]0.211057[/C][/ROW]
[ROW][C]19[/C][C]0.043926[/C][C]0.6396[/C][C]0.261573[/C][/ROW]
[ROW][C]20[/C][C]0.038674[/C][C]0.5631[/C][C]0.286982[/C][/ROW]
[ROW][C]21[/C][C]-0.046603[/C][C]-0.6786[/C][C]0.249081[/C][/ROW]
[ROW][C]22[/C][C]-0.029719[/C][C]-0.4327[/C][C]0.33283[/C][/ROW]
[ROW][C]23[/C][C]0.061391[/C][C]0.8939[/C][C]0.186205[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308852&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308852&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	0.809522	11.7868	0
2	0.251264	3.6585	0.00016
3	0.496442	7.2283	0
4	-0.05439	-0.7919	0.214643
5	0.36065	5.2511	0
6	0.141833	2.0651	0.020064
7	-0.122512	-1.7838	0.037943
8	-0.07886	-1.1482	0.126085
9	-0.086879	-1.265	0.103634
10	-0.267576	-3.896	6.6e-05
11	0.269449	3.9232	5.9e-05
12	0.419289	6.1049	0
13	-0.18912	-2.7536	0.003203
14	-0.207518	-3.0215	0.001412
15	-0.082323	-1.1986	0.116002
16	0.088796	1.2929	0.098729
17	-0.053629	-0.7808	0.217882
18	0.055241	0.8043	0.211057
19	0.043926	0.6396	0.261573
20	0.038674	0.5631	0.286982
21	-0.046603	-0.6786	0.249081
22	-0.029719	-0.4327	0.33283
23	0.061391	0.8939	0.186205

Figure 1

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Postscript link

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Figure 2

PNG link

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Figure 3

PNG link

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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)
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,'ACF(k)',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,'PACF(k)',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