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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

Fri, 16 Dec 2016 09:16:23 +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/Dec/16/t14818762055fpkic5misnpui5.htm/, Retrieved Fri, 01 Nov 2024 03:47:26 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300095, Retrieved Fri, 01 Nov 2024 03:47:26 +0000

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Original text written by user:

d=0

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

108

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

-       [(Partial) Autocorrelation Function] [autocorrelation k...] [2016-12-16 08:16:23] [d92250bd36540c2281a4ec15b45df1dd] [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=300095&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=300095&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300095&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	0.901525	4.0317	0.000327
2	0.766992	3.4301	0.001325
3	0.60878	2.7225	0.006557
4	0.445973	1.9945	0.029957
5	0.292424	1.3078	0.102894
6	0.145675	0.6515	0.261077
7	0.003813	0.0171	0.493281
8	-0.127099	-0.5684	0.288044
9	-0.241228	-1.0788	0.146757
10	-0.331355	-1.4819	0.07698
11	-0.390819	-1.7478	0.047918
12	-0.424312	-1.8976	0.036141
13	-0.436781	-1.9533	0.032456

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.901525 & 4.0317 & 0.000327 \tabularnewline
2 & 0.766992 & 3.4301 & 0.001325 \tabularnewline
3 & 0.60878 & 2.7225 & 0.006557 \tabularnewline
4 & 0.445973 & 1.9945 & 0.029957 \tabularnewline
5 & 0.292424 & 1.3078 & 0.102894 \tabularnewline
6 & 0.145675 & 0.6515 & 0.261077 \tabularnewline
7 & 0.003813 & 0.0171 & 0.493281 \tabularnewline
8 & -0.127099 & -0.5684 & 0.288044 \tabularnewline
9 & -0.241228 & -1.0788 & 0.146757 \tabularnewline
10 & -0.331355 & -1.4819 & 0.07698 \tabularnewline
11 & -0.390819 & -1.7478 & 0.047918 \tabularnewline
12 & -0.424312 & -1.8976 & 0.036141 \tabularnewline
13 & -0.436781 & -1.9533 & 0.032456 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300095&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]0.901525[/C][C]4.0317[/C][C]0.000327[/C][/ROW]
[ROW][C]2[/C][C]0.766992[/C][C]3.4301[/C][C]0.001325[/C][/ROW]
[ROW][C]3[/C][C]0.60878[/C][C]2.7225[/C][C]0.006557[/C][/ROW]
[ROW][C]4[/C][C]0.445973[/C][C]1.9945[/C][C]0.029957[/C][/ROW]
[ROW][C]5[/C][C]0.292424[/C][C]1.3078[/C][C]0.102894[/C][/ROW]
[ROW][C]6[/C][C]0.145675[/C][C]0.6515[/C][C]0.261077[/C][/ROW]
[ROW][C]7[/C][C]0.003813[/C][C]0.0171[/C][C]0.493281[/C][/ROW]
[ROW][C]8[/C][C]-0.127099[/C][C]-0.5684[/C][C]0.288044[/C][/ROW]
[ROW][C]9[/C][C]-0.241228[/C][C]-1.0788[/C][C]0.146757[/C][/ROW]
[ROW][C]10[/C][C]-0.331355[/C][C]-1.4819[/C][C]0.07698[/C][/ROW]
[ROW][C]11[/C][C]-0.390819[/C][C]-1.7478[/C][C]0.047918[/C][/ROW]
[ROW][C]12[/C][C]-0.424312[/C][C]-1.8976[/C][C]0.036141[/C][/ROW]
[ROW][C]13[/C][C]-0.436781[/C][C]-1.9533[/C][C]0.032456[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300095&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300095&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	0.901525	4.0317	0.000327
2	0.766992	3.4301	0.001325
3	0.60878	2.7225	0.006557
4	0.445973	1.9945	0.029957
5	0.292424	1.3078	0.102894
6	0.145675	0.6515	0.261077
7	0.003813	0.0171	0.493281
8	-0.127099	-0.5684	0.288044
9	-0.241228	-1.0788	0.146757
10	-0.331355	-1.4819	0.07698
11	-0.390819	-1.7478	0.047918
12	-0.424312	-1.8976	0.036141
13	-0.436781	-1.9533	0.032456

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.901525	4.0317	0.000327
2	-0.244348	-1.0928	0.143745
3	-0.178075	-0.7964	0.217583
4	-0.092324	-0.4129	0.342041
5	-0.047517	-0.2125	0.416932
6	-0.094938	-0.4246	0.337839
7	-0.120011	-0.5367	0.298696
8	-0.088664	-0.3965	0.347961
9	-0.065652	-0.2936	0.386042
10	-0.039662	-0.1774	0.4305
11	-0.009818	-0.0439	0.482706
12	-0.03511	-0.157	0.438403
13	-0.046839	-0.2095	0.418101

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.901525 & 4.0317 & 0.000327 \tabularnewline
2 & -0.244348 & -1.0928 & 0.143745 \tabularnewline
3 & -0.178075 & -0.7964 & 0.217583 \tabularnewline
4 & -0.092324 & -0.4129 & 0.342041 \tabularnewline
5 & -0.047517 & -0.2125 & 0.416932 \tabularnewline
6 & -0.094938 & -0.4246 & 0.337839 \tabularnewline
7 & -0.120011 & -0.5367 & 0.298696 \tabularnewline
8 & -0.088664 & -0.3965 & 0.347961 \tabularnewline
9 & -0.065652 & -0.2936 & 0.386042 \tabularnewline
10 & -0.039662 & -0.1774 & 0.4305 \tabularnewline
11 & -0.009818 & -0.0439 & 0.482706 \tabularnewline
12 & -0.03511 & -0.157 & 0.438403 \tabularnewline
13 & -0.046839 & -0.2095 & 0.418101 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300095&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]0.901525[/C][C]4.0317[/C][C]0.000327[/C][/ROW]
[ROW][C]2[/C][C]-0.244348[/C][C]-1.0928[/C][C]0.143745[/C][/ROW]
[ROW][C]3[/C][C]-0.178075[/C][C]-0.7964[/C][C]0.217583[/C][/ROW]
[ROW][C]4[/C][C]-0.092324[/C][C]-0.4129[/C][C]0.342041[/C][/ROW]
[ROW][C]5[/C][C]-0.047517[/C][C]-0.2125[/C][C]0.416932[/C][/ROW]
[ROW][C]6[/C][C]-0.094938[/C][C]-0.4246[/C][C]0.337839[/C][/ROW]
[ROW][C]7[/C][C]-0.120011[/C][C]-0.5367[/C][C]0.298696[/C][/ROW]
[ROW][C]8[/C][C]-0.088664[/C][C]-0.3965[/C][C]0.347961[/C][/ROW]
[ROW][C]9[/C][C]-0.065652[/C][C]-0.2936[/C][C]0.386042[/C][/ROW]
[ROW][C]10[/C][C]-0.039662[/C][C]-0.1774[/C][C]0.4305[/C][/ROW]
[ROW][C]11[/C][C]-0.009818[/C][C]-0.0439[/C][C]0.482706[/C][/ROW]
[ROW][C]12[/C][C]-0.03511[/C][C]-0.157[/C][C]0.438403[/C][/ROW]
[ROW][C]13[/C][C]-0.046839[/C][C]-0.2095[/C][C]0.418101[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300095&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300095&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	0.901525	4.0317	0.000327
2	-0.244348	-1.0928	0.143745
3	-0.178075	-0.7964	0.217583
4	-0.092324	-0.4129	0.342041
5	-0.047517	-0.2125	0.416932
6	-0.094938	-0.4246	0.337839
7	-0.120011	-0.5367	0.298696
8	-0.088664	-0.3965	0.347961
9	-0.065652	-0.2936	0.386042
10	-0.039662	-0.1774	0.4305
11	-0.009818	-0.0439	0.482706
12	-0.03511	-0.157	0.438403
13	-0.046839	-0.2095	0.418101

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):

par4 = 12 ;

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')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code