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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

Thu, 15 Dec 2016 20:40:05 +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/15/t1481831040f237gkvd3epwooe.htm/, Retrieved Fri, 03 May 2024 12:31:54 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299983, Retrieved Fri, 03 May 2024 12:31:54 +0000

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Original text written by user:

d=0 D=0 s=6

IsPrivate?

No (this computation is public)

User-defined keywords

F1competitie d=0 D=0 s=6

Estimated Impact

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

-       [(Partial) Autocorrelation Function] [Autocorrelation f...] [2016-12-15 19:40:05] [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=299983&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=299983&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299983&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	0.803406	3.5929	0.000909
2	0.638392	2.855	0.004894
3	0.4607	2.0603	0.026309
4	0.298164	1.3334	0.09869
5	0.18807	0.8411	0.205125
6	0.09833	0.4397	0.332418
7	0.024348	0.1089	0.457188
8	-0.04595	-0.2055	0.419631
9	-0.087681	-0.3921	0.349558
10	-0.154883	-0.6927	0.248245
11	-0.212662	-0.9511	0.176465
12	-0.271125	-1.2125	0.119723
13	-0.309587	-1.3845	0.090727

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.803406 & 3.5929 & 0.000909 \tabularnewline
2 & 0.638392 & 2.855 & 0.004894 \tabularnewline
3 & 0.4607 & 2.0603 & 0.026309 \tabularnewline
4 & 0.298164 & 1.3334 & 0.09869 \tabularnewline
5 & 0.18807 & 0.8411 & 0.205125 \tabularnewline
6 & 0.09833 & 0.4397 & 0.332418 \tabularnewline
7 & 0.024348 & 0.1089 & 0.457188 \tabularnewline
8 & -0.04595 & -0.2055 & 0.419631 \tabularnewline
9 & -0.087681 & -0.3921 & 0.349558 \tabularnewline
10 & -0.154883 & -0.6927 & 0.248245 \tabularnewline
11 & -0.212662 & -0.9511 & 0.176465 \tabularnewline
12 & -0.271125 & -1.2125 & 0.119723 \tabularnewline
13 & -0.309587 & -1.3845 & 0.090727 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299983&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]0.803406[/C][C]3.5929[/C][C]0.000909[/C][/ROW]
[ROW][C]2[/C][C]0.638392[/C][C]2.855[/C][C]0.004894[/C][/ROW]
[ROW][C]3[/C][C]0.4607[/C][C]2.0603[/C][C]0.026309[/C][/ROW]
[ROW][C]4[/C][C]0.298164[/C][C]1.3334[/C][C]0.09869[/C][/ROW]
[ROW][C]5[/C][C]0.18807[/C][C]0.8411[/C][C]0.205125[/C][/ROW]
[ROW][C]6[/C][C]0.09833[/C][C]0.4397[/C][C]0.332418[/C][/ROW]
[ROW][C]7[/C][C]0.024348[/C][C]0.1089[/C][C]0.457188[/C][/ROW]
[ROW][C]8[/C][C]-0.04595[/C][C]-0.2055[/C][C]0.419631[/C][/ROW]
[ROW][C]9[/C][C]-0.087681[/C][C]-0.3921[/C][C]0.349558[/C][/ROW]
[ROW][C]10[/C][C]-0.154883[/C][C]-0.6927[/C][C]0.248245[/C][/ROW]
[ROW][C]11[/C][C]-0.212662[/C][C]-0.9511[/C][C]0.176465[/C][/ROW]
[ROW][C]12[/C][C]-0.271125[/C][C]-1.2125[/C][C]0.119723[/C][/ROW]
[ROW][C]13[/C][C]-0.309587[/C][C]-1.3845[/C][C]0.090727[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299983&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299983&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	0.803406	3.5929	0.000909
2	0.638392	2.855	0.004894
3	0.4607	2.0603	0.026309
4	0.298164	1.3334	0.09869
5	0.18807	0.8411	0.205125
6	0.09833	0.4397	0.332418
7	0.024348	0.1089	0.457188
8	-0.04595	-0.2055	0.419631
9	-0.087681	-0.3921	0.349558
10	-0.154883	-0.6927	0.248245
11	-0.212662	-0.9511	0.176465
12	-0.271125	-1.2125	0.119723
13	-0.309587	-1.3845	0.090727

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.803406	3.5929	0.000909
2	-0.019939	-0.0892	0.464916
3	-0.13091	-0.5854	0.282397
4	-0.082455	-0.3687	0.358095
5	0.031833	0.1424	0.444109
6	-0.024389	-0.1091	0.457117
7	-0.049707	-0.2223	0.413169
8	-0.072097	-0.3224	0.375237
9	0.007334	0.0328	0.487081
10	-0.125372	-0.5607	0.290621
11	-0.076087	-0.3403	0.3686
12	-0.087277	-0.3903	0.350215
13	-0.033167	-0.1483	0.441786

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.803406 & 3.5929 & 0.000909 \tabularnewline
2 & -0.019939 & -0.0892 & 0.464916 \tabularnewline
3 & -0.13091 & -0.5854 & 0.282397 \tabularnewline
4 & -0.082455 & -0.3687 & 0.358095 \tabularnewline
5 & 0.031833 & 0.1424 & 0.444109 \tabularnewline
6 & -0.024389 & -0.1091 & 0.457117 \tabularnewline
7 & -0.049707 & -0.2223 & 0.413169 \tabularnewline
8 & -0.072097 & -0.3224 & 0.375237 \tabularnewline
9 & 0.007334 & 0.0328 & 0.487081 \tabularnewline
10 & -0.125372 & -0.5607 & 0.290621 \tabularnewline
11 & -0.076087 & -0.3403 & 0.3686 \tabularnewline
12 & -0.087277 & -0.3903 & 0.350215 \tabularnewline
13 & -0.033167 & -0.1483 & 0.441786 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299983&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]0.803406[/C][C]3.5929[/C][C]0.000909[/C][/ROW]
[ROW][C]2[/C][C]-0.019939[/C][C]-0.0892[/C][C]0.464916[/C][/ROW]
[ROW][C]3[/C][C]-0.13091[/C][C]-0.5854[/C][C]0.282397[/C][/ROW]
[ROW][C]4[/C][C]-0.082455[/C][C]-0.3687[/C][C]0.358095[/C][/ROW]
[ROW][C]5[/C][C]0.031833[/C][C]0.1424[/C][C]0.444109[/C][/ROW]
[ROW][C]6[/C][C]-0.024389[/C][C]-0.1091[/C][C]0.457117[/C][/ROW]
[ROW][C]7[/C][C]-0.049707[/C][C]-0.2223[/C][C]0.413169[/C][/ROW]
[ROW][C]8[/C][C]-0.072097[/C][C]-0.3224[/C][C]0.375237[/C][/ROW]
[ROW][C]9[/C][C]0.007334[/C][C]0.0328[/C][C]0.487081[/C][/ROW]
[ROW][C]10[/C][C]-0.125372[/C][C]-0.5607[/C][C]0.290621[/C][/ROW]
[ROW][C]11[/C][C]-0.076087[/C][C]-0.3403[/C][C]0.3686[/C][/ROW]
[ROW][C]12[/C][C]-0.087277[/C][C]-0.3903[/C][C]0.350215[/C][/ROW]
[ROW][C]13[/C][C]-0.033167[/C][C]-0.1483[/C][C]0.441786[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299983&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299983&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	0.803406	3.5929	0.000909
2	-0.019939	-0.0892	0.464916
3	-0.13091	-0.5854	0.282397
4	-0.082455	-0.3687	0.358095
5	0.031833	0.1424	0.444109
6	-0.024389	-0.1091	0.457117
7	-0.049707	-0.2223	0.413169
8	-0.072097	-0.3224	0.375237
9	0.007334	0.0328	0.487081
10	-0.125372	-0.5607	0.290621
11	-0.076087	-0.3403	0.3686
12	-0.087277	-0.3903	0.350215
13	-0.033167	-0.1483	0.441786

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 = 6 ; 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