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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

Sat, 28 Nov 2015 11:11:44 +0000

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/2015/Nov/28/t1448709120f0b6xyi6fxyx3nw.htm/, Retrieved Tue, 14 May 2024 00:57:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284369, Retrieved Tue, 14 May 2024 00:57:10 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

117

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

-       [(Partial) Autocorrelation Function] [Autocorrelation v...] [2015-11-28 11:11:44] [8acc4c3875a0c63009483cc7dfb4f316] [Current]

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Boxplots

7.1
6.8
6.5
6.1
5.7
5.6
5.7
5.8
5.9
6.3
6.5
6.3
6.4
6.3
6.3
6.2
6.2
6.2
6.4
6.5
6.5
6.7
6.7
6.3
6.2
6.3
6.5
6.9
7
7
6.9
6.7
6.7
7.1
7.1
6.9
7
6.9
6.9
6.8
6.5
6.2
5.9
5.8
6.1
7
7.4
7.3
7.2
7.1
7.1
7.1
7.1
6.9
6.6
6.4
6.5
6.9
6.9
6.7

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	'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284369&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284369&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284369&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	'George Udny Yule' @ yule.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.844534	6.5417	0
2	0.561764	4.3514	2.7e-05
3	0.301996	2.3392	0.011335
4	0.12482	0.9668	0.168751
5	0.053754	0.4164	0.339309
6	0.043656	0.3382	0.368211
7	0.037062	0.2871	0.38752
8	0.03331	0.258	0.398637
9	0.056927	0.441	0.330416
10	0.0918	0.7111	0.239895
11	0.151256	1.1716	0.12299
12	0.177313	1.3735	0.08736
13	0.09097	0.7047	0.241876
14	0.001181	0.0091	0.496365
15	-0.019743	-0.1529	0.439483
16	0.025095	0.1944	0.423265
17	0.104136	0.8066	0.211531

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.844534 & 6.5417 & 0 \tabularnewline
2 & 0.561764 & 4.3514 & 2.7e-05 \tabularnewline
3 & 0.301996 & 2.3392 & 0.011335 \tabularnewline
4 & 0.12482 & 0.9668 & 0.168751 \tabularnewline
5 & 0.053754 & 0.4164 & 0.339309 \tabularnewline
6 & 0.043656 & 0.3382 & 0.368211 \tabularnewline
7 & 0.037062 & 0.2871 & 0.38752 \tabularnewline
8 & 0.03331 & 0.258 & 0.398637 \tabularnewline
9 & 0.056927 & 0.441 & 0.330416 \tabularnewline
10 & 0.0918 & 0.7111 & 0.239895 \tabularnewline
11 & 0.151256 & 1.1716 & 0.12299 \tabularnewline
12 & 0.177313 & 1.3735 & 0.08736 \tabularnewline
13 & 0.09097 & 0.7047 & 0.241876 \tabularnewline
14 & 0.001181 & 0.0091 & 0.496365 \tabularnewline
15 & -0.019743 & -0.1529 & 0.439483 \tabularnewline
16 & 0.025095 & 0.1944 & 0.423265 \tabularnewline
17 & 0.104136 & 0.8066 & 0.211531 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284369&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]0.844534[/C][C]6.5417[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.561764[/C][C]4.3514[/C][C]2.7e-05[/C][/ROW]
[ROW][C]3[/C][C]0.301996[/C][C]2.3392[/C][C]0.011335[/C][/ROW]
[ROW][C]4[/C][C]0.12482[/C][C]0.9668[/C][C]0.168751[/C][/ROW]
[ROW][C]5[/C][C]0.053754[/C][C]0.4164[/C][C]0.339309[/C][/ROW]
[ROW][C]6[/C][C]0.043656[/C][C]0.3382[/C][C]0.368211[/C][/ROW]
[ROW][C]7[/C][C]0.037062[/C][C]0.2871[/C][C]0.38752[/C][/ROW]
[ROW][C]8[/C][C]0.03331[/C][C]0.258[/C][C]0.398637[/C][/ROW]
[ROW][C]9[/C][C]0.056927[/C][C]0.441[/C][C]0.330416[/C][/ROW]
[ROW][C]10[/C][C]0.0918[/C][C]0.7111[/C][C]0.239895[/C][/ROW]
[ROW][C]11[/C][C]0.151256[/C][C]1.1716[/C][C]0.12299[/C][/ROW]
[ROW][C]12[/C][C]0.177313[/C][C]1.3735[/C][C]0.08736[/C][/ROW]
[ROW][C]13[/C][C]0.09097[/C][C]0.7047[/C][C]0.241876[/C][/ROW]
[ROW][C]14[/C][C]0.001181[/C][C]0.0091[/C][C]0.496365[/C][/ROW]
[ROW][C]15[/C][C]-0.019743[/C][C]-0.1529[/C][C]0.439483[/C][/ROW]
[ROW][C]16[/C][C]0.025095[/C][C]0.1944[/C][C]0.423265[/C][/ROW]
[ROW][C]17[/C][C]0.104136[/C][C]0.8066[/C][C]0.211531[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284369&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284369&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	0.844534	6.5417	0
2	0.561764	4.3514	2.7e-05
3	0.301996	2.3392	0.011335
4	0.12482	0.9668	0.168751
5	0.053754	0.4164	0.339309
6	0.043656	0.3382	0.368211
7	0.037062	0.2871	0.38752
8	0.03331	0.258	0.398637
9	0.056927	0.441	0.330416
10	0.0918	0.7111	0.239895
11	0.151256	1.1716	0.12299
12	0.177313	1.3735	0.08736
13	0.09097	0.7047	0.241876
14	0.001181	0.0091	0.496365
15	-0.019743	-0.1529	0.439483
16	0.025095	0.1944	0.423265
17	0.104136	0.8066	0.211531

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.844534	6.5417	0
2	-0.528223	-4.0916	6.5e-05
3	0.111562	0.8642	0.195473
4	0.003236	0.0251	0.490042
5	0.121188	0.9387	0.17582
6	-0.063628	-0.4929	0.311954
7	-0.054579	-0.4228	0.336987
8	0.08	0.6197	0.268909
9	0.120603	0.9342	0.176976
10	-0.030267	-0.2345	0.407717
11	0.166378	1.2888	0.101214
12	-0.190045	-1.4721	0.073112
13	-0.265575	-2.0571	0.022014
14	0.371112	2.8746	0.002795
15	0.04919	0.381	0.352267
16	0.007207	0.0558	0.477833
17	-0.036608	-0.2836	0.388861

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.844534 & 6.5417 & 0 \tabularnewline
2 & -0.528223 & -4.0916 & 6.5e-05 \tabularnewline
3 & 0.111562 & 0.8642 & 0.195473 \tabularnewline
4 & 0.003236 & 0.0251 & 0.490042 \tabularnewline
5 & 0.121188 & 0.9387 & 0.17582 \tabularnewline
6 & -0.063628 & -0.4929 & 0.311954 \tabularnewline
7 & -0.054579 & -0.4228 & 0.336987 \tabularnewline
8 & 0.08 & 0.6197 & 0.268909 \tabularnewline
9 & 0.120603 & 0.9342 & 0.176976 \tabularnewline
10 & -0.030267 & -0.2345 & 0.407717 \tabularnewline
11 & 0.166378 & 1.2888 & 0.101214 \tabularnewline
12 & -0.190045 & -1.4721 & 0.073112 \tabularnewline
13 & -0.265575 & -2.0571 & 0.022014 \tabularnewline
14 & 0.371112 & 2.8746 & 0.002795 \tabularnewline
15 & 0.04919 & 0.381 & 0.352267 \tabularnewline
16 & 0.007207 & 0.0558 & 0.477833 \tabularnewline
17 & -0.036608 & -0.2836 & 0.388861 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284369&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]0.844534[/C][C]6.5417[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.528223[/C][C]-4.0916[/C][C]6.5e-05[/C][/ROW]
[ROW][C]3[/C][C]0.111562[/C][C]0.8642[/C][C]0.195473[/C][/ROW]
[ROW][C]4[/C][C]0.003236[/C][C]0.0251[/C][C]0.490042[/C][/ROW]
[ROW][C]5[/C][C]0.121188[/C][C]0.9387[/C][C]0.17582[/C][/ROW]
[ROW][C]6[/C][C]-0.063628[/C][C]-0.4929[/C][C]0.311954[/C][/ROW]
[ROW][C]7[/C][C]-0.054579[/C][C]-0.4228[/C][C]0.336987[/C][/ROW]
[ROW][C]8[/C][C]0.08[/C][C]0.6197[/C][C]0.268909[/C][/ROW]
[ROW][C]9[/C][C]0.120603[/C][C]0.9342[/C][C]0.176976[/C][/ROW]
[ROW][C]10[/C][C]-0.030267[/C][C]-0.2345[/C][C]0.407717[/C][/ROW]
[ROW][C]11[/C][C]0.166378[/C][C]1.2888[/C][C]0.101214[/C][/ROW]
[ROW][C]12[/C][C]-0.190045[/C][C]-1.4721[/C][C]0.073112[/C][/ROW]
[ROW][C]13[/C][C]-0.265575[/C][C]-2.0571[/C][C]0.022014[/C][/ROW]
[ROW][C]14[/C][C]0.371112[/C][C]2.8746[/C][C]0.002795[/C][/ROW]
[ROW][C]15[/C][C]0.04919[/C][C]0.381[/C][C]0.352267[/C][/ROW]
[ROW][C]16[/C][C]0.007207[/C][C]0.0558[/C][C]0.477833[/C][/ROW]
[ROW][C]17[/C][C]-0.036608[/C][C]-0.2836[/C][C]0.388861[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284369&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284369&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	0.844534	6.5417	0
2	-0.528223	-4.0916	6.5e-05
3	0.111562	0.8642	0.195473
4	0.003236	0.0251	0.490042
5	0.121188	0.9387	0.17582
6	-0.063628	-0.4929	0.311954
7	-0.054579	-0.4228	0.336987
8	0.08	0.6197	0.268909
9	0.120603	0.9342	0.176976
10	-0.030267	-0.2345	0.407717
11	0.166378	1.2888	0.101214
12	-0.190045	-1.4721	0.073112
13	-0.265575	-2.0571	0.022014
14	0.371112	2.8746	0.002795
15	0.04919	0.381	0.352267
16	0.007207	0.0558	0.477833
17	-0.036608	-0.2836	0.388861

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 = 0 ;

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)
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