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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, 22 Nov 2010 13:53:41 +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/2010/Nov/22/t1290433997kiwg4givltuo6ht.htm/, Retrieved Fri, 03 May 2024 20:50:16 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=98518, Retrieved Fri, 03 May 2024 20:50:16 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W12

Estimated Impact

122

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

-       [(Partial) Autocorrelation Function] [] [2010-11-22 13:53:41] [9b9daabfb4dd89dd7e1d590f0423e9fb] [Current]

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Dataseries X:

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Histogram

Boxplots

3.65
3.59
3.31
3.89
4.31
4.35
4.11
3.90
3.75
3.75
3.88
3.93
3.97
3.97
4.33
4.16
4.93
3.86
4.06
4.18
4.08
4.38
4.48
4.41
4.37
4.56
4.71
4.94
5.03
5.08
5.05
4.83
4.68
4.69
4.58
4.54
4.75
4.71
4.50
4.62
4.69
5.05
4.93
4.53
4.33
4.33
3.87
3.74
3.31
3.21
2.93
3.19
3.46
3.73
3.60
3.46
3.25
3.19
2.82
1.89
1.98
2.30
2.42
2.47
2.81
3.37
3.14
3.21
3.02
2.96
2.92
3.07

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	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=98518&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=98518&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=98518&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.923907	7.8396	0
2	0.847565	7.1918	0
3	0.761347	6.4602	0
4	0.691749	5.8697	0
5	0.633577	5.3761	0
6	0.58784	4.988	2e-06
7	0.563297	4.7797	5e-06
8	0.541104	4.5914	9e-06
9	0.520484	4.4165	1.7e-05
10	0.491995	4.1747	4.1e-05
11	0.453454	3.8477	0.000128
12	0.379677	3.2217	0.000957

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.923907 & 7.8396 & 0 \tabularnewline
2 & 0.847565 & 7.1918 & 0 \tabularnewline
3 & 0.761347 & 6.4602 & 0 \tabularnewline
4 & 0.691749 & 5.8697 & 0 \tabularnewline
5 & 0.633577 & 5.3761 & 0 \tabularnewline
6 & 0.58784 & 4.988 & 2e-06 \tabularnewline
7 & 0.563297 & 4.7797 & 5e-06 \tabularnewline
8 & 0.541104 & 4.5914 & 9e-06 \tabularnewline
9 & 0.520484 & 4.4165 & 1.7e-05 \tabularnewline
10 & 0.491995 & 4.1747 & 4.1e-05 \tabularnewline
11 & 0.453454 & 3.8477 & 0.000128 \tabularnewline
12 & 0.379677 & 3.2217 & 0.000957 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=98518&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]0.923907[/C][C]7.8396[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.847565[/C][C]7.1918[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.761347[/C][C]6.4602[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.691749[/C][C]5.8697[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.633577[/C][C]5.3761[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.58784[/C][C]4.988[/C][C]2e-06[/C][/ROW]
[ROW][C]7[/C][C]0.563297[/C][C]4.7797[/C][C]5e-06[/C][/ROW]
[ROW][C]8[/C][C]0.541104[/C][C]4.5914[/C][C]9e-06[/C][/ROW]
[ROW][C]9[/C][C]0.520484[/C][C]4.4165[/C][C]1.7e-05[/C][/ROW]
[ROW][C]10[/C][C]0.491995[/C][C]4.1747[/C][C]4.1e-05[/C][/ROW]
[ROW][C]11[/C][C]0.453454[/C][C]3.8477[/C][C]0.000128[/C][/ROW]
[ROW][C]12[/C][C]0.379677[/C][C]3.2217[/C][C]0.000957[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=98518&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=98518&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	0.923907	7.8396	0
2	0.847565	7.1918	0
3	0.761347	6.4602	0
4	0.691749	5.8697	0
5	0.633577	5.3761	0
6	0.58784	4.988	2e-06
7	0.563297	4.7797	5e-06
8	0.541104	4.5914	9e-06
9	0.520484	4.4165	1.7e-05
10	0.491995	4.1747	4.1e-05
11	0.453454	3.8477	0.000128
12	0.379677	3.2217	0.000957

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.923907	7.8396	0
2	-0.04125	-0.35	0.363674
3	-0.108898	-0.924	0.179279
4	0.065927	0.5594	0.288808
5	0.041502	0.3522	0.362874
6	0.034416	0.292	0.385552
7	0.116987	0.9927	0.162099
8	0.002141	0.0182	0.492777
9	-0.005985	-0.0508	0.47982
10	-0.034616	-0.2937	0.384908
11	-0.065187	-0.5531	0.290944
12	-0.247414	-2.0994	0.019645

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.923907 & 7.8396 & 0 \tabularnewline
2 & -0.04125 & -0.35 & 0.363674 \tabularnewline
3 & -0.108898 & -0.924 & 0.179279 \tabularnewline
4 & 0.065927 & 0.5594 & 0.288808 \tabularnewline
5 & 0.041502 & 0.3522 & 0.362874 \tabularnewline
6 & 0.034416 & 0.292 & 0.385552 \tabularnewline
7 & 0.116987 & 0.9927 & 0.162099 \tabularnewline
8 & 0.002141 & 0.0182 & 0.492777 \tabularnewline
9 & -0.005985 & -0.0508 & 0.47982 \tabularnewline
10 & -0.034616 & -0.2937 & 0.384908 \tabularnewline
11 & -0.065187 & -0.5531 & 0.290944 \tabularnewline
12 & -0.247414 & -2.0994 & 0.019645 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=98518&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]0.923907[/C][C]7.8396[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.04125[/C][C]-0.35[/C][C]0.363674[/C][/ROW]
[ROW][C]3[/C][C]-0.108898[/C][C]-0.924[/C][C]0.179279[/C][/ROW]
[ROW][C]4[/C][C]0.065927[/C][C]0.5594[/C][C]0.288808[/C][/ROW]
[ROW][C]5[/C][C]0.041502[/C][C]0.3522[/C][C]0.362874[/C][/ROW]
[ROW][C]6[/C][C]0.034416[/C][C]0.292[/C][C]0.385552[/C][/ROW]
[ROW][C]7[/C][C]0.116987[/C][C]0.9927[/C][C]0.162099[/C][/ROW]
[ROW][C]8[/C][C]0.002141[/C][C]0.0182[/C][C]0.492777[/C][/ROW]
[ROW][C]9[/C][C]-0.005985[/C][C]-0.0508[/C][C]0.47982[/C][/ROW]
[ROW][C]10[/C][C]-0.034616[/C][C]-0.2937[/C][C]0.384908[/C][/ROW]
[ROW][C]11[/C][C]-0.065187[/C][C]-0.5531[/C][C]0.290944[/C][/ROW]
[ROW][C]12[/C][C]-0.247414[/C][C]-2.0994[/C][C]0.019645[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=98518&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=98518&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	0.923907	7.8396	0
2	-0.04125	-0.35	0.363674
3	-0.108898	-0.924	0.179279
4	0.065927	0.5594	0.288808
5	0.041502	0.3522	0.362874
6	0.034416	0.292	0.385552
7	0.116987	0.9927	0.162099
8	0.002141	0.0182	0.492777
9	-0.005985	-0.0508	0.47982
10	-0.034616	-0.2937	0.384908
11	-0.065187	-0.5531	0.290944
12	-0.247414	-2.0994	0.019645

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 12 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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 (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')
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