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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 19 Oct 2014 04:20:51 +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/2014/Oct/19/t1413688885rocuuclyfevihcv.htm/, Retrieved Sat, 11 May 2024 08:12:56 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=243558, Retrieved Sat, 11 May 2024 08:12:56 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

107

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

-       [(Partial) Autocorrelation Function] [Gemiddelde consum...] [2014-10-19 03:20:51] [42c148e2fe69cef5ba6629e36c38849a] [Current]

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Dataseries X:

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Histogram

Boxplots

2,37
2,45
2,53
2,56
2,62
2,67
2,62
2,6
2,53
2,49
2,48
2,44
2,36
2,35
2,44
2,5
2,58
2,55
2,44
2,3
2,24
2,19
2,25
2,28
2,27
2,37
2,47
2,5
2,47
2,61
2,61
2,65
2,43
2,43
2,33
2,27
2,22
2,17
2,28
2,3
2,33
2,44
2,41
2,4
2,34
2,37
2,38
2,3
2,29
2,34
2,35
2,38
2,37
2,45
2,51
2,46
2,42
2,48
2,44
2,43
2,36
2,42
2,42
2,43
2,47
2,54
2,55
2,55
2,49
2,54
2,55
2,5

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	'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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243558&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]1 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=243558&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243558&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	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.839033	7.1194	0
2	0.616568	5.2318	1e-06
3	0.355671	3.018	0.001759
4	0.122836	1.0423	0.150379
5	-0.096184	-0.8162	0.208553
6	-0.24088	-2.0439	0.022309
7	-0.260214	-2.208	0.015216
8	-0.193213	-1.6395	0.052739
9	-0.114963	-0.9755	0.16629
10	0.001816	0.0154	0.493874
11	0.134493	1.1412	0.128782
12	0.234361	1.9886	0.025272
13	0.224685	1.9065	0.030287
14	0.140555	1.1926	0.118462
15	0.05338	0.4529	0.325975
16	-0.073688	-0.6253	0.266886
17	-0.221931	-1.8831	0.03186
18	-0.285914	-2.4261	0.008885

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.839033 & 7.1194 & 0 \tabularnewline
2 & 0.616568 & 5.2318 & 1e-06 \tabularnewline
3 & 0.355671 & 3.018 & 0.001759 \tabularnewline
4 & 0.122836 & 1.0423 & 0.150379 \tabularnewline
5 & -0.096184 & -0.8162 & 0.208553 \tabularnewline
6 & -0.24088 & -2.0439 & 0.022309 \tabularnewline
7 & -0.260214 & -2.208 & 0.015216 \tabularnewline
8 & -0.193213 & -1.6395 & 0.052739 \tabularnewline
9 & -0.114963 & -0.9755 & 0.16629 \tabularnewline
10 & 0.001816 & 0.0154 & 0.493874 \tabularnewline
11 & 0.134493 & 1.1412 & 0.128782 \tabularnewline
12 & 0.234361 & 1.9886 & 0.025272 \tabularnewline
13 & 0.224685 & 1.9065 & 0.030287 \tabularnewline
14 & 0.140555 & 1.1926 & 0.118462 \tabularnewline
15 & 0.05338 & 0.4529 & 0.325975 \tabularnewline
16 & -0.073688 & -0.6253 & 0.266886 \tabularnewline
17 & -0.221931 & -1.8831 & 0.03186 \tabularnewline
18 & -0.285914 & -2.4261 & 0.008885 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243558&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]0.839033[/C][C]7.1194[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.616568[/C][C]5.2318[/C][C]1e-06[/C][/ROW]
[ROW][C]3[/C][C]0.355671[/C][C]3.018[/C][C]0.001759[/C][/ROW]
[ROW][C]4[/C][C]0.122836[/C][C]1.0423[/C][C]0.150379[/C][/ROW]
[ROW][C]5[/C][C]-0.096184[/C][C]-0.8162[/C][C]0.208553[/C][/ROW]
[ROW][C]6[/C][C]-0.24088[/C][C]-2.0439[/C][C]0.022309[/C][/ROW]
[ROW][C]7[/C][C]-0.260214[/C][C]-2.208[/C][C]0.015216[/C][/ROW]
[ROW][C]8[/C][C]-0.193213[/C][C]-1.6395[/C][C]0.052739[/C][/ROW]
[ROW][C]9[/C][C]-0.114963[/C][C]-0.9755[/C][C]0.16629[/C][/ROW]
[ROW][C]10[/C][C]0.001816[/C][C]0.0154[/C][C]0.493874[/C][/ROW]
[ROW][C]11[/C][C]0.134493[/C][C]1.1412[/C][C]0.128782[/C][/ROW]
[ROW][C]12[/C][C]0.234361[/C][C]1.9886[/C][C]0.025272[/C][/ROW]
[ROW][C]13[/C][C]0.224685[/C][C]1.9065[/C][C]0.030287[/C][/ROW]
[ROW][C]14[/C][C]0.140555[/C][C]1.1926[/C][C]0.118462[/C][/ROW]
[ROW][C]15[/C][C]0.05338[/C][C]0.4529[/C][C]0.325975[/C][/ROW]
[ROW][C]16[/C][C]-0.073688[/C][C]-0.6253[/C][C]0.266886[/C][/ROW]
[ROW][C]17[/C][C]-0.221931[/C][C]-1.8831[/C][C]0.03186[/C][/ROW]
[ROW][C]18[/C][C]-0.285914[/C][C]-2.4261[/C][C]0.008885[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243558&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243558&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	0.839033	7.1194	0
2	0.616568	5.2318	1e-06
3	0.355671	3.018	0.001759
4	0.122836	1.0423	0.150379
5	-0.096184	-0.8162	0.208553
6	-0.24088	-2.0439	0.022309
7	-0.260214	-2.208	0.015216
8	-0.193213	-1.6395	0.052739
9	-0.114963	-0.9755	0.16629
10	0.001816	0.0154	0.493874
11	0.134493	1.1412	0.128782
12	0.234361	1.9886	0.025272
13	0.224685	1.9065	0.030287
14	0.140555	1.1926	0.118462
15	0.05338	0.4529	0.325975
16	-0.073688	-0.6253	0.266886
17	-0.221931	-1.8831	0.03186
18	-0.285914	-2.4261	0.008885

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.839033	7.1194	0
2	-0.295277	-2.5055	0.007245
3	-0.246678	-2.0931	0.01993
4	-0.055389	-0.47	0.319889
5	-0.177508	-1.5062	0.068195
6	0.021419	0.1817	0.428146
7	0.233378	1.9803	0.025747
8	0.074119	0.6289	0.265695
9	-0.124649	-1.0577	0.146869
10	0.140452	1.1918	0.118632
11	0.101515	0.8614	0.195943
12	-0.053239	-0.4517	0.326405
13	-0.193438	-1.6414	0.05254
14	-0.095519	-0.8105	0.21016
15	0.088034	0.747	0.22875
16	-0.152923	-1.2976	0.099284
17	-0.103048	-0.8744	0.192407
18	0.281007	2.3844	0.009871

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.839033 & 7.1194 & 0 \tabularnewline
2 & -0.295277 & -2.5055 & 0.007245 \tabularnewline
3 & -0.246678 & -2.0931 & 0.01993 \tabularnewline
4 & -0.055389 & -0.47 & 0.319889 \tabularnewline
5 & -0.177508 & -1.5062 & 0.068195 \tabularnewline
6 & 0.021419 & 0.1817 & 0.428146 \tabularnewline
7 & 0.233378 & 1.9803 & 0.025747 \tabularnewline
8 & 0.074119 & 0.6289 & 0.265695 \tabularnewline
9 & -0.124649 & -1.0577 & 0.146869 \tabularnewline
10 & 0.140452 & 1.1918 & 0.118632 \tabularnewline
11 & 0.101515 & 0.8614 & 0.195943 \tabularnewline
12 & -0.053239 & -0.4517 & 0.326405 \tabularnewline
13 & -0.193438 & -1.6414 & 0.05254 \tabularnewline
14 & -0.095519 & -0.8105 & 0.21016 \tabularnewline
15 & 0.088034 & 0.747 & 0.22875 \tabularnewline
16 & -0.152923 & -1.2976 & 0.099284 \tabularnewline
17 & -0.103048 & -0.8744 & 0.192407 \tabularnewline
18 & 0.281007 & 2.3844 & 0.009871 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243558&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]0.839033[/C][C]7.1194[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.295277[/C][C]-2.5055[/C][C]0.007245[/C][/ROW]
[ROW][C]3[/C][C]-0.246678[/C][C]-2.0931[/C][C]0.01993[/C][/ROW]
[ROW][C]4[/C][C]-0.055389[/C][C]-0.47[/C][C]0.319889[/C][/ROW]
[ROW][C]5[/C][C]-0.177508[/C][C]-1.5062[/C][C]0.068195[/C][/ROW]
[ROW][C]6[/C][C]0.021419[/C][C]0.1817[/C][C]0.428146[/C][/ROW]
[ROW][C]7[/C][C]0.233378[/C][C]1.9803[/C][C]0.025747[/C][/ROW]
[ROW][C]8[/C][C]0.074119[/C][C]0.6289[/C][C]0.265695[/C][/ROW]
[ROW][C]9[/C][C]-0.124649[/C][C]-1.0577[/C][C]0.146869[/C][/ROW]
[ROW][C]10[/C][C]0.140452[/C][C]1.1918[/C][C]0.118632[/C][/ROW]
[ROW][C]11[/C][C]0.101515[/C][C]0.8614[/C][C]0.195943[/C][/ROW]
[ROW][C]12[/C][C]-0.053239[/C][C]-0.4517[/C][C]0.326405[/C][/ROW]
[ROW][C]13[/C][C]-0.193438[/C][C]-1.6414[/C][C]0.05254[/C][/ROW]
[ROW][C]14[/C][C]-0.095519[/C][C]-0.8105[/C][C]0.21016[/C][/ROW]
[ROW][C]15[/C][C]0.088034[/C][C]0.747[/C][C]0.22875[/C][/ROW]
[ROW][C]16[/C][C]-0.152923[/C][C]-1.2976[/C][C]0.099284[/C][/ROW]
[ROW][C]17[/C][C]-0.103048[/C][C]-0.8744[/C][C]0.192407[/C][/ROW]
[ROW][C]18[/C][C]0.281007[/C][C]2.3844[/C][C]0.009871[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243558&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243558&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	0.839033	7.1194	0
2	-0.295277	-2.5055	0.007245
3	-0.246678	-2.0931	0.01993
4	-0.055389	-0.47	0.319889
5	-0.177508	-1.5062	0.068195
6	0.021419	0.1817	0.428146
7	0.233378	1.9803	0.025747
8	0.074119	0.6289	0.265695
9	-0.124649	-1.0577	0.146869
10	0.140452	1.1918	0.118632
11	0.101515	0.8614	0.195943
12	-0.053239	-0.4517	0.326405
13	-0.193438	-1.6414	0.05254
14	-0.095519	-0.8105	0.21016
15	0.088034	0.747	0.22875
16	-0.152923	-1.2976	0.099284
17	-0.103048	-0.8744	0.192407
18	0.281007	2.3844	0.009871

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 = 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)
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