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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, 09 Dec 2011 05:38:56 -0500

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/2011/Dec/09/t1323427157u7abi1kei19r5i3.htm/, Retrieved Fri, 03 May 2024 03:35:05 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=153241, Retrieved Fri, 03 May 2024 03:35:05 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

162

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

-     [Univariate Data Series] [] [2010-10-06 14:13:06] [3d53bd477a917086cfdff0f854c5e476]
-   PD  [Univariate Data Series] [rozen] [2010-12-07 20:04:29] [b98453cac15ba1066b407e146608df68]
- RMPD      [(Partial) Autocorrelation Function] [Times Series - Rozen] [2011-12-09 10:38:56] [a0aae37dd27f4b65e222573f53b5a13b] [Current]

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Dataseries X:

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Histogram

Boxplots

1.35
1.91
1.31
1.19
1.3
1.14
1.1
1.02
1.11
1.18
1.24
1.36
1.29
1.73
1.41
1.15
1.31
1.15
1.08
1.1
1.14
1.24
1.33
1.49
1.38
1.96
1.36
1.24
1.35
1.23
1.09
1.08
1.33
1.35
1.38
1.5
1.47
2.09
1.52
1.29
1.52
1.27
1.35
1.29
1.41
1.39
1.45
1.53
1.45
2.11
1.53
1.38
1.54
1.35
1.29
1.33
1.47
1.47
1.54
1.59
1.5
2
1.51
1.4
1.62
1.44
1.29
1.28
1.4
1.39
1.46
1.49

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=153241&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=153241&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=153241&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	0.369431	3.1347	0.001245
2	0.250596	2.1264	0.01845
3	0.249695	2.1187	0.018782
4	-0.03346	-0.2839	0.388644
5	-0.145623	-1.2356	0.110303
6	-0.276369	-2.3451	0.010892
7	-0.147691	-1.2532	0.107094
8	-0.077377	-0.6566	0.256777
9	0.171339	1.4539	0.075165
10	0.182441	1.5481	0.062995
11	0.259693	2.2036	0.015377
12	0.753042	6.3898	0
13	0.25558	2.1687	0.016706
14	0.138277	1.1733	0.122268
15	0.14058	1.1929	0.11842
16	-0.11355	-0.9635	0.169259
17	-0.223106	-1.8931	0.031181
18	-0.315141	-2.6741	0.004634

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.369431 & 3.1347 & 0.001245 \tabularnewline
2 & 0.250596 & 2.1264 & 0.01845 \tabularnewline
3 & 0.249695 & 2.1187 & 0.018782 \tabularnewline
4 & -0.03346 & -0.2839 & 0.388644 \tabularnewline
5 & -0.145623 & -1.2356 & 0.110303 \tabularnewline
6 & -0.276369 & -2.3451 & 0.010892 \tabularnewline
7 & -0.147691 & -1.2532 & 0.107094 \tabularnewline
8 & -0.077377 & -0.6566 & 0.256777 \tabularnewline
9 & 0.171339 & 1.4539 & 0.075165 \tabularnewline
10 & 0.182441 & 1.5481 & 0.062995 \tabularnewline
11 & 0.259693 & 2.2036 & 0.015377 \tabularnewline
12 & 0.753042 & 6.3898 & 0 \tabularnewline
13 & 0.25558 & 2.1687 & 0.016706 \tabularnewline
14 & 0.138277 & 1.1733 & 0.122268 \tabularnewline
15 & 0.14058 & 1.1929 & 0.11842 \tabularnewline
16 & -0.11355 & -0.9635 & 0.169259 \tabularnewline
17 & -0.223106 & -1.8931 & 0.031181 \tabularnewline
18 & -0.315141 & -2.6741 & 0.004634 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=153241&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]0.369431[/C][C]3.1347[/C][C]0.001245[/C][/ROW]
[ROW][C]2[/C][C]0.250596[/C][C]2.1264[/C][C]0.01845[/C][/ROW]
[ROW][C]3[/C][C]0.249695[/C][C]2.1187[/C][C]0.018782[/C][/ROW]
[ROW][C]4[/C][C]-0.03346[/C][C]-0.2839[/C][C]0.388644[/C][/ROW]
[ROW][C]5[/C][C]-0.145623[/C][C]-1.2356[/C][C]0.110303[/C][/ROW]
[ROW][C]6[/C][C]-0.276369[/C][C]-2.3451[/C][C]0.010892[/C][/ROW]
[ROW][C]7[/C][C]-0.147691[/C][C]-1.2532[/C][C]0.107094[/C][/ROW]
[ROW][C]8[/C][C]-0.077377[/C][C]-0.6566[/C][C]0.256777[/C][/ROW]
[ROW][C]9[/C][C]0.171339[/C][C]1.4539[/C][C]0.075165[/C][/ROW]
[ROW][C]10[/C][C]0.182441[/C][C]1.5481[/C][C]0.062995[/C][/ROW]
[ROW][C]11[/C][C]0.259693[/C][C]2.2036[/C][C]0.015377[/C][/ROW]
[ROW][C]12[/C][C]0.753042[/C][C]6.3898[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.25558[/C][C]2.1687[/C][C]0.016706[/C][/ROW]
[ROW][C]14[/C][C]0.138277[/C][C]1.1733[/C][C]0.122268[/C][/ROW]
[ROW][C]15[/C][C]0.14058[/C][C]1.1929[/C][C]0.11842[/C][/ROW]
[ROW][C]16[/C][C]-0.11355[/C][C]-0.9635[/C][C]0.169259[/C][/ROW]
[ROW][C]17[/C][C]-0.223106[/C][C]-1.8931[/C][C]0.031181[/C][/ROW]
[ROW][C]18[/C][C]-0.315141[/C][C]-2.6741[/C][C]0.004634[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=153241&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=153241&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	0.369431	3.1347	0.001245
2	0.250596	2.1264	0.01845
3	0.249695	2.1187	0.018782
4	-0.03346	-0.2839	0.388644
5	-0.145623	-1.2356	0.110303
6	-0.276369	-2.3451	0.010892
7	-0.147691	-1.2532	0.107094
8	-0.077377	-0.6566	0.256777
9	0.171339	1.4539	0.075165
10	0.182441	1.5481	0.062995
11	0.259693	2.2036	0.015377
12	0.753042	6.3898	0
13	0.25558	2.1687	0.016706
14	0.138277	1.1733	0.122268
15	0.14058	1.1929	0.11842
16	-0.11355	-0.9635	0.169259
17	-0.223106	-1.8931	0.031181
18	-0.315141	-2.6741	0.004634

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.369431	3.1347	0.001245
2	0.132153	1.1214	0.132931
3	0.142061	1.2054	0.115993
4	-0.220147	-1.868	0.032915
5	-0.1666	-1.4136	0.080887
6	-0.236851	-2.0097	0.024103
7	0.126622	1.0744	0.143111
8	0.114768	0.9738	0.166698
9	0.39364	3.3401	0.000665
10	0.010462	0.0888	0.464753
11	0.060052	0.5096	0.305959
12	0.622905	5.2855	1e-06
13	-0.332285	-2.8195	0.003104
14	-0.171402	-1.4544	0.075092
15	-0.14737	-1.2505	0.107588
16	-0.03641	-0.309	0.379126
17	-0.009392	-0.0797	0.468351
18	0.046281	0.3927	0.347847

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.369431 & 3.1347 & 0.001245 \tabularnewline
2 & 0.132153 & 1.1214 & 0.132931 \tabularnewline
3 & 0.142061 & 1.2054 & 0.115993 \tabularnewline
4 & -0.220147 & -1.868 & 0.032915 \tabularnewline
5 & -0.1666 & -1.4136 & 0.080887 \tabularnewline
6 & -0.236851 & -2.0097 & 0.024103 \tabularnewline
7 & 0.126622 & 1.0744 & 0.143111 \tabularnewline
8 & 0.114768 & 0.9738 & 0.166698 \tabularnewline
9 & 0.39364 & 3.3401 & 0.000665 \tabularnewline
10 & 0.010462 & 0.0888 & 0.464753 \tabularnewline
11 & 0.060052 & 0.5096 & 0.305959 \tabularnewline
12 & 0.622905 & 5.2855 & 1e-06 \tabularnewline
13 & -0.332285 & -2.8195 & 0.003104 \tabularnewline
14 & -0.171402 & -1.4544 & 0.075092 \tabularnewline
15 & -0.14737 & -1.2505 & 0.107588 \tabularnewline
16 & -0.03641 & -0.309 & 0.379126 \tabularnewline
17 & -0.009392 & -0.0797 & 0.468351 \tabularnewline
18 & 0.046281 & 0.3927 & 0.347847 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=153241&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]0.369431[/C][C]3.1347[/C][C]0.001245[/C][/ROW]
[ROW][C]2[/C][C]0.132153[/C][C]1.1214[/C][C]0.132931[/C][/ROW]
[ROW][C]3[/C][C]0.142061[/C][C]1.2054[/C][C]0.115993[/C][/ROW]
[ROW][C]4[/C][C]-0.220147[/C][C]-1.868[/C][C]0.032915[/C][/ROW]
[ROW][C]5[/C][C]-0.1666[/C][C]-1.4136[/C][C]0.080887[/C][/ROW]
[ROW][C]6[/C][C]-0.236851[/C][C]-2.0097[/C][C]0.024103[/C][/ROW]
[ROW][C]7[/C][C]0.126622[/C][C]1.0744[/C][C]0.143111[/C][/ROW]
[ROW][C]8[/C][C]0.114768[/C][C]0.9738[/C][C]0.166698[/C][/ROW]
[ROW][C]9[/C][C]0.39364[/C][C]3.3401[/C][C]0.000665[/C][/ROW]
[ROW][C]10[/C][C]0.010462[/C][C]0.0888[/C][C]0.464753[/C][/ROW]
[ROW][C]11[/C][C]0.060052[/C][C]0.5096[/C][C]0.305959[/C][/ROW]
[ROW][C]12[/C][C]0.622905[/C][C]5.2855[/C][C]1e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.332285[/C][C]-2.8195[/C][C]0.003104[/C][/ROW]
[ROW][C]14[/C][C]-0.171402[/C][C]-1.4544[/C][C]0.075092[/C][/ROW]
[ROW][C]15[/C][C]-0.14737[/C][C]-1.2505[/C][C]0.107588[/C][/ROW]
[ROW][C]16[/C][C]-0.03641[/C][C]-0.309[/C][C]0.379126[/C][/ROW]
[ROW][C]17[/C][C]-0.009392[/C][C]-0.0797[/C][C]0.468351[/C][/ROW]
[ROW][C]18[/C][C]0.046281[/C][C]0.3927[/C][C]0.347847[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=153241&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=153241&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	0.369431	3.1347	0.001245
2	0.132153	1.1214	0.132931
3	0.142061	1.2054	0.115993
4	-0.220147	-1.868	0.032915
5	-0.1666	-1.4136	0.080887
6	-0.236851	-2.0097	0.024103
7	0.126622	1.0744	0.143111
8	0.114768	0.9738	0.166698
9	0.39364	3.3401	0.000665
10	0.010462	0.0888	0.464753
11	0.060052	0.5096	0.305959
12	0.622905	5.2855	1e-06
13	-0.332285	-2.8195	0.003104
14	-0.171402	-1.4544	0.075092
15	-0.14737	-1.2505	0.107588
16	-0.03641	-0.309	0.379126
17	-0.009392	-0.0797	0.468351
18	0.046281	0.3927	0.347847

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