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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

Mon, 26 Dec 2011 11:39:50 -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/26/t13249176655yebary12st4y39.htm/, Retrieved Sat, 04 May 2024 01:25:23 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160819, Retrieved Sat, 04 May 2024 01:25:23 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W12

Estimated Impact

153

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

-       [(Partial) Autocorrelation Function] [T6Bis] [2011-12-26 16:39:50] [53dd883843ca194f19e2952e03e3e0b7] [Current]

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Dataseries X:

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Histogram

Boxplots

0,71
0,71
0,71
0,71
0,71
0,71
0,71
0,71
0,71
0,71
0,7
0,7
0,68
0,68
0,69
0,69
0,7
0,7
0,7
0,7
0,7
0,71
0,71
0,71
0,71
0,71
0,71
0,71
0,71
0,71
0,76
0,77
0,78
0,85
0,89
0,9
0,91
0,91
0,91
0,9
0,89
0,88
0,87
0,86
0,87
0,87
0,87
0,85
0,84
0,84
0,84
0,84
0,84
0,82
0,87
0,92
0,92
0,92
0,93
0,94
0,87
0,84
0,83
0,81
0,81
0,81
0,8
0,8
0,8
0,8
0,8
0,8

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=160819&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=160819&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160819&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	0.365925	3.0833	0.001457
2	0.094139	0.7932	0.215143
3	0.262275	2.21	0.015166
4	0.106939	0.9011	0.185294
5	-0.117404	-0.9893	0.162947
6	-0.230157	-1.9393	0.028217
7	-0.143967	-1.2131	0.114558
8	-0.13541	-1.141	0.128854
9	-0.106382	-0.8964	0.186536
10	-0.004034	-0.034	0.48649
11	-0.04456	-0.3755	0.354215
12	-0.053863	-0.4539	0.325658
13	-0.005943	-0.0501	0.480102
14	-0.043735	-0.3685	0.356791
15	-0.069682	-0.5872	0.279481
16	-0.043327	-0.3651	0.358068
17	-0.023411	-0.1973	0.422092
18	-0.007808	-0.0658	0.473864

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.365925 & 3.0833 & 0.001457 \tabularnewline
2 & 0.094139 & 0.7932 & 0.215143 \tabularnewline
3 & 0.262275 & 2.21 & 0.015166 \tabularnewline
4 & 0.106939 & 0.9011 & 0.185294 \tabularnewline
5 & -0.117404 & -0.9893 & 0.162947 \tabularnewline
6 & -0.230157 & -1.9393 & 0.028217 \tabularnewline
7 & -0.143967 & -1.2131 & 0.114558 \tabularnewline
8 & -0.13541 & -1.141 & 0.128854 \tabularnewline
9 & -0.106382 & -0.8964 & 0.186536 \tabularnewline
10 & -0.004034 & -0.034 & 0.48649 \tabularnewline
11 & -0.04456 & -0.3755 & 0.354215 \tabularnewline
12 & -0.053863 & -0.4539 & 0.325658 \tabularnewline
13 & -0.005943 & -0.0501 & 0.480102 \tabularnewline
14 & -0.043735 & -0.3685 & 0.356791 \tabularnewline
15 & -0.069682 & -0.5872 & 0.279481 \tabularnewline
16 & -0.043327 & -0.3651 & 0.358068 \tabularnewline
17 & -0.023411 & -0.1973 & 0.422092 \tabularnewline
18 & -0.007808 & -0.0658 & 0.473864 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160819&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]0.365925[/C][C]3.0833[/C][C]0.001457[/C][/ROW]
[ROW][C]2[/C][C]0.094139[/C][C]0.7932[/C][C]0.215143[/C][/ROW]
[ROW][C]3[/C][C]0.262275[/C][C]2.21[/C][C]0.015166[/C][/ROW]
[ROW][C]4[/C][C]0.106939[/C][C]0.9011[/C][C]0.185294[/C][/ROW]
[ROW][C]5[/C][C]-0.117404[/C][C]-0.9893[/C][C]0.162947[/C][/ROW]
[ROW][C]6[/C][C]-0.230157[/C][C]-1.9393[/C][C]0.028217[/C][/ROW]
[ROW][C]7[/C][C]-0.143967[/C][C]-1.2131[/C][C]0.114558[/C][/ROW]
[ROW][C]8[/C][C]-0.13541[/C][C]-1.141[/C][C]0.128854[/C][/ROW]
[ROW][C]9[/C][C]-0.106382[/C][C]-0.8964[/C][C]0.186536[/C][/ROW]
[ROW][C]10[/C][C]-0.004034[/C][C]-0.034[/C][C]0.48649[/C][/ROW]
[ROW][C]11[/C][C]-0.04456[/C][C]-0.3755[/C][C]0.354215[/C][/ROW]
[ROW][C]12[/C][C]-0.053863[/C][C]-0.4539[/C][C]0.325658[/C][/ROW]
[ROW][C]13[/C][C]-0.005943[/C][C]-0.0501[/C][C]0.480102[/C][/ROW]
[ROW][C]14[/C][C]-0.043735[/C][C]-0.3685[/C][C]0.356791[/C][/ROW]
[ROW][C]15[/C][C]-0.069682[/C][C]-0.5872[/C][C]0.279481[/C][/ROW]
[ROW][C]16[/C][C]-0.043327[/C][C]-0.3651[/C][C]0.358068[/C][/ROW]
[ROW][C]17[/C][C]-0.023411[/C][C]-0.1973[/C][C]0.422092[/C][/ROW]
[ROW][C]18[/C][C]-0.007808[/C][C]-0.0658[/C][C]0.473864[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160819&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160819&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	0.365925	3.0833	0.001457
2	0.094139	0.7932	0.215143
3	0.262275	2.21	0.015166
4	0.106939	0.9011	0.185294
5	-0.117404	-0.9893	0.162947
6	-0.230157	-1.9393	0.028217
7	-0.143967	-1.2131	0.114558
8	-0.13541	-1.141	0.128854
9	-0.106382	-0.8964	0.186536
10	-0.004034	-0.034	0.48649
11	-0.04456	-0.3755	0.354215
12	-0.053863	-0.4539	0.325658
13	-0.005943	-0.0501	0.480102
14	-0.043735	-0.3685	0.356791
15	-0.069682	-0.5872	0.279481
16	-0.043327	-0.3651	0.358068
17	-0.023411	-0.1973	0.422092
18	-0.007808	-0.0658	0.473864

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.365925	3.0833	0.001457
2	-0.045909	-0.3868	0.350016
3	0.281214	2.3695	0.010266
4	-0.10714	-0.9028	0.184849
5	-0.139313	-1.1739	0.122184
6	-0.248532	-2.0942	0.019908
7	0.002278	0.0192	0.492371
8	-0.038406	-0.3236	0.373592
9	0.112674	0.9494	0.172818
10	0.061231	0.5159	0.303749
11	-0.088737	-0.7477	0.228552
12	-0.097984	-0.8256	0.205891
13	-0.066299	-0.5586	0.289082
14	-0.062779	-0.529	0.299232
15	0.009851	0.083	0.467039
16	0.02971	0.2503	0.401524
17	0.003991	0.0336	0.486633
18	0.002647	0.0223	0.491134

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.365925 & 3.0833 & 0.001457 \tabularnewline
2 & -0.045909 & -0.3868 & 0.350016 \tabularnewline
3 & 0.281214 & 2.3695 & 0.010266 \tabularnewline
4 & -0.10714 & -0.9028 & 0.184849 \tabularnewline
5 & -0.139313 & -1.1739 & 0.122184 \tabularnewline
6 & -0.248532 & -2.0942 & 0.019908 \tabularnewline
7 & 0.002278 & 0.0192 & 0.492371 \tabularnewline
8 & -0.038406 & -0.3236 & 0.373592 \tabularnewline
9 & 0.112674 & 0.9494 & 0.172818 \tabularnewline
10 & 0.061231 & 0.5159 & 0.303749 \tabularnewline
11 & -0.088737 & -0.7477 & 0.228552 \tabularnewline
12 & -0.097984 & -0.8256 & 0.205891 \tabularnewline
13 & -0.066299 & -0.5586 & 0.289082 \tabularnewline
14 & -0.062779 & -0.529 & 0.299232 \tabularnewline
15 & 0.009851 & 0.083 & 0.467039 \tabularnewline
16 & 0.02971 & 0.2503 & 0.401524 \tabularnewline
17 & 0.003991 & 0.0336 & 0.486633 \tabularnewline
18 & 0.002647 & 0.0223 & 0.491134 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160819&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]0.365925[/C][C]3.0833[/C][C]0.001457[/C][/ROW]
[ROW][C]2[/C][C]-0.045909[/C][C]-0.3868[/C][C]0.350016[/C][/ROW]
[ROW][C]3[/C][C]0.281214[/C][C]2.3695[/C][C]0.010266[/C][/ROW]
[ROW][C]4[/C][C]-0.10714[/C][C]-0.9028[/C][C]0.184849[/C][/ROW]
[ROW][C]5[/C][C]-0.139313[/C][C]-1.1739[/C][C]0.122184[/C][/ROW]
[ROW][C]6[/C][C]-0.248532[/C][C]-2.0942[/C][C]0.019908[/C][/ROW]
[ROW][C]7[/C][C]0.002278[/C][C]0.0192[/C][C]0.492371[/C][/ROW]
[ROW][C]8[/C][C]-0.038406[/C][C]-0.3236[/C][C]0.373592[/C][/ROW]
[ROW][C]9[/C][C]0.112674[/C][C]0.9494[/C][C]0.172818[/C][/ROW]
[ROW][C]10[/C][C]0.061231[/C][C]0.5159[/C][C]0.303749[/C][/ROW]
[ROW][C]11[/C][C]-0.088737[/C][C]-0.7477[/C][C]0.228552[/C][/ROW]
[ROW][C]12[/C][C]-0.097984[/C][C]-0.8256[/C][C]0.205891[/C][/ROW]
[ROW][C]13[/C][C]-0.066299[/C][C]-0.5586[/C][C]0.289082[/C][/ROW]
[ROW][C]14[/C][C]-0.062779[/C][C]-0.529[/C][C]0.299232[/C][/ROW]
[ROW][C]15[/C][C]0.009851[/C][C]0.083[/C][C]0.467039[/C][/ROW]
[ROW][C]16[/C][C]0.02971[/C][C]0.2503[/C][C]0.401524[/C][/ROW]
[ROW][C]17[/C][C]0.003991[/C][C]0.0336[/C][C]0.486633[/C][/ROW]
[ROW][C]18[/C][C]0.002647[/C][C]0.0223[/C][C]0.491134[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160819&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160819&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	0.365925	3.0833	0.001457
2	-0.045909	-0.3868	0.350016
3	0.281214	2.3695	0.010266
4	-0.10714	-0.9028	0.184849
5	-0.139313	-1.1739	0.122184
6	-0.248532	-2.0942	0.019908
7	0.002278	0.0192	0.492371
8	-0.038406	-0.3236	0.373592
9	0.112674	0.9494	0.172818
10	0.061231	0.5159	0.303749
11	-0.088737	-0.7477	0.228552
12	-0.097984	-0.8256	0.205891
13	-0.066299	-0.5586	0.289082
14	-0.062779	-0.529	0.299232
15	0.009851	0.083	0.467039
16	0.02971	0.2503	0.401524
17	0.003991	0.0336	0.486633
18	0.002647	0.0223	0.491134

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 = 0.1 ; par2 = 1 ; par3 = 0.1 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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