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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 05 Mar 2015 20:16:56 +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/Mar/05/t1425586663jza36rjz59ajk6f.htm/, Retrieved Fri, 17 May 2024 15:41:58 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278009, Retrieved Fri, 17 May 2024 15:41:58 +0000

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Original text written by user:

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User-defined keywords

Estimated Impact

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

-       [(Partial) Autocorrelation Function] [opgave ] [2015-03-05 20:16:56] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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Histogram

Boxplots

12,8
12,1
11,4
11,4
10,6
10,4
10,9
11,6
13,3
15,2
17,4
19,1
19,9
19,4
18,2
15,8
13,5
12,1
10,3
8,8
8,2
6,8
5,9
4,9
3,9
3,6
2,8
4
4,2
4,2
4,8
4
3,8
4
3,7
4
4,6
4,6
4,6
4,5
4,1
4,1
4,4
4,2
4,4
3,2
2,8
1,7
-0,2
-2,9
-5,2
-5,3
-4,8
-2,2
-0,8
-1,1
-1,5
-2
-2,8
-3,4
-4,1
-5,5
-8,6
-7,6
-8,6
-8,7
-4,6
-4,3
-1,5
1,2
1,8
0

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	'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278009&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278009&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278009&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.970628	8.236	0
2	0.926665	7.863	0
3	0.870657	7.3878	0
4	0.803201	6.8154	0
5	0.73874	6.2684	0
6	0.680841	5.7771	0
7	0.623507	5.2906	1e-06
8	0.572375	4.8568	3e-06
9	0.5271	4.4726	1.4e-05
10	0.480518	4.0773	5.8e-05
11	0.434657	3.6882	0.000218
12	0.388613	3.2975	0.000759
13	0.339987	2.8849	0.002581
14	0.290264	2.463	0.008086
15	0.241926	2.0528	0.021863
16	0.195717	1.6607	0.05056
17	0.153396	1.3016	0.0986
18	0.114881	0.9748	0.166463

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.970628 & 8.236 & 0 \tabularnewline
2 & 0.926665 & 7.863 & 0 \tabularnewline
3 & 0.870657 & 7.3878 & 0 \tabularnewline
4 & 0.803201 & 6.8154 & 0 \tabularnewline
5 & 0.73874 & 6.2684 & 0 \tabularnewline
6 & 0.680841 & 5.7771 & 0 \tabularnewline
7 & 0.623507 & 5.2906 & 1e-06 \tabularnewline
8 & 0.572375 & 4.8568 & 3e-06 \tabularnewline
9 & 0.5271 & 4.4726 & 1.4e-05 \tabularnewline
10 & 0.480518 & 4.0773 & 5.8e-05 \tabularnewline
11 & 0.434657 & 3.6882 & 0.000218 \tabularnewline
12 & 0.388613 & 3.2975 & 0.000759 \tabularnewline
13 & 0.339987 & 2.8849 & 0.002581 \tabularnewline
14 & 0.290264 & 2.463 & 0.008086 \tabularnewline
15 & 0.241926 & 2.0528 & 0.021863 \tabularnewline
16 & 0.195717 & 1.6607 & 0.05056 \tabularnewline
17 & 0.153396 & 1.3016 & 0.0986 \tabularnewline
18 & 0.114881 & 0.9748 & 0.166463 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278009&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]0.970628[/C][C]8.236[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.926665[/C][C]7.863[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.870657[/C][C]7.3878[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.803201[/C][C]6.8154[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.73874[/C][C]6.2684[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.680841[/C][C]5.7771[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.623507[/C][C]5.2906[/C][C]1e-06[/C][/ROW]
[ROW][C]8[/C][C]0.572375[/C][C]4.8568[/C][C]3e-06[/C][/ROW]
[ROW][C]9[/C][C]0.5271[/C][C]4.4726[/C][C]1.4e-05[/C][/ROW]
[ROW][C]10[/C][C]0.480518[/C][C]4.0773[/C][C]5.8e-05[/C][/ROW]
[ROW][C]11[/C][C]0.434657[/C][C]3.6882[/C][C]0.000218[/C][/ROW]
[ROW][C]12[/C][C]0.388613[/C][C]3.2975[/C][C]0.000759[/C][/ROW]
[ROW][C]13[/C][C]0.339987[/C][C]2.8849[/C][C]0.002581[/C][/ROW]
[ROW][C]14[/C][C]0.290264[/C][C]2.463[/C][C]0.008086[/C][/ROW]
[ROW][C]15[/C][C]0.241926[/C][C]2.0528[/C][C]0.021863[/C][/ROW]
[ROW][C]16[/C][C]0.195717[/C][C]1.6607[/C][C]0.05056[/C][/ROW]
[ROW][C]17[/C][C]0.153396[/C][C]1.3016[/C][C]0.0986[/C][/ROW]
[ROW][C]18[/C][C]0.114881[/C][C]0.9748[/C][C]0.166463[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278009&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278009&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	0.970628	8.236	0
2	0.926665	7.863	0
3	0.870657	7.3878	0
4	0.803201	6.8154	0
5	0.73874	6.2684	0
6	0.680841	5.7771	0
7	0.623507	5.2906	1e-06
8	0.572375	4.8568	3e-06
9	0.5271	4.4726	1.4e-05
10	0.480518	4.0773	5.8e-05
11	0.434657	3.6882	0.000218
12	0.388613	3.2975	0.000759
13	0.339987	2.8849	0.002581
14	0.290264	2.463	0.008086
15	0.241926	2.0528	0.021863
16	0.195717	1.6607	0.05056
17	0.153396	1.3016	0.0986
18	0.114881	0.9748	0.166463

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.970628	8.236	0
2	-0.266972	-2.2653	0.013251
3	-0.182048	-1.5447	0.063398
4	-0.164371	-1.3947	0.083692
5	0.120419	1.0218	0.15515
6	0.107047	0.9083	0.183369
7	-0.084375	-0.7159	0.23817
8	0.00529	0.0449	0.48216
9	0.019437	0.1649	0.434733
10	-0.080519	-0.6832	0.248328
11	-0.045971	-0.3901	0.348815
12	-0.04164	-0.3533	0.362439
13	-0.031662	-0.2687	0.39448
14	-0.039069	-0.3315	0.370611
15	-0.006461	-0.0548	0.478215
16	0.017601	0.1493	0.440848
17	0.007694	0.0653	0.474062
18	-0.028536	-0.2421	0.404681

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.970628 & 8.236 & 0 \tabularnewline
2 & -0.266972 & -2.2653 & 0.013251 \tabularnewline
3 & -0.182048 & -1.5447 & 0.063398 \tabularnewline
4 & -0.164371 & -1.3947 & 0.083692 \tabularnewline
5 & 0.120419 & 1.0218 & 0.15515 \tabularnewline
6 & 0.107047 & 0.9083 & 0.183369 \tabularnewline
7 & -0.084375 & -0.7159 & 0.23817 \tabularnewline
8 & 0.00529 & 0.0449 & 0.48216 \tabularnewline
9 & 0.019437 & 0.1649 & 0.434733 \tabularnewline
10 & -0.080519 & -0.6832 & 0.248328 \tabularnewline
11 & -0.045971 & -0.3901 & 0.348815 \tabularnewline
12 & -0.04164 & -0.3533 & 0.362439 \tabularnewline
13 & -0.031662 & -0.2687 & 0.39448 \tabularnewline
14 & -0.039069 & -0.3315 & 0.370611 \tabularnewline
15 & -0.006461 & -0.0548 & 0.478215 \tabularnewline
16 & 0.017601 & 0.1493 & 0.440848 \tabularnewline
17 & 0.007694 & 0.0653 & 0.474062 \tabularnewline
18 & -0.028536 & -0.2421 & 0.404681 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278009&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]0.970628[/C][C]8.236[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.266972[/C][C]-2.2653[/C][C]0.013251[/C][/ROW]
[ROW][C]3[/C][C]-0.182048[/C][C]-1.5447[/C][C]0.063398[/C][/ROW]
[ROW][C]4[/C][C]-0.164371[/C][C]-1.3947[/C][C]0.083692[/C][/ROW]
[ROW][C]5[/C][C]0.120419[/C][C]1.0218[/C][C]0.15515[/C][/ROW]
[ROW][C]6[/C][C]0.107047[/C][C]0.9083[/C][C]0.183369[/C][/ROW]
[ROW][C]7[/C][C]-0.084375[/C][C]-0.7159[/C][C]0.23817[/C][/ROW]
[ROW][C]8[/C][C]0.00529[/C][C]0.0449[/C][C]0.48216[/C][/ROW]
[ROW][C]9[/C][C]0.019437[/C][C]0.1649[/C][C]0.434733[/C][/ROW]
[ROW][C]10[/C][C]-0.080519[/C][C]-0.6832[/C][C]0.248328[/C][/ROW]
[ROW][C]11[/C][C]-0.045971[/C][C]-0.3901[/C][C]0.348815[/C][/ROW]
[ROW][C]12[/C][C]-0.04164[/C][C]-0.3533[/C][C]0.362439[/C][/ROW]
[ROW][C]13[/C][C]-0.031662[/C][C]-0.2687[/C][C]0.39448[/C][/ROW]
[ROW][C]14[/C][C]-0.039069[/C][C]-0.3315[/C][C]0.370611[/C][/ROW]
[ROW][C]15[/C][C]-0.006461[/C][C]-0.0548[/C][C]0.478215[/C][/ROW]
[ROW][C]16[/C][C]0.017601[/C][C]0.1493[/C][C]0.440848[/C][/ROW]
[ROW][C]17[/C][C]0.007694[/C][C]0.0653[/C][C]0.474062[/C][/ROW]
[ROW][C]18[/C][C]-0.028536[/C][C]-0.2421[/C][C]0.404681[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278009&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278009&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	0.970628	8.236	0
2	-0.266972	-2.2653	0.013251
3	-0.182048	-1.5447	0.063398
4	-0.164371	-1.3947	0.083692
5	0.120419	1.0218	0.15515
6	0.107047	0.9083	0.183369
7	-0.084375	-0.7159	0.23817
8	0.00529	0.0449	0.48216
9	0.019437	0.1649	0.434733
10	-0.080519	-0.6832	0.248328
11	-0.045971	-0.3901	0.348815
12	-0.04164	-0.3533	0.362439
13	-0.031662	-0.2687	0.39448
14	-0.039069	-0.3315	0.370611
15	-0.006461	-0.0548	0.478215
16	0.017601	0.1493	0.440848
17	0.007694	0.0653	0.474062
18	-0.028536	-0.2421	0.404681

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