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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 04 Dec 2009 08:09:00 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/04/t1259939386rhgfnvqws6m8eze.htm/, Retrieved Sat, 27 Apr 2024 17:15:46 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63720, Retrieved Sat, 27 Apr 2024 17:15:46 +0000

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No (this computation is public)

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Estimated Impact

146

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [] [2009-11-27 14:46:03] [b98453cac15ba1066b407e146608df68]
- R PD    [(Partial) Autocorrelation Function] [] [2009-12-01 17:11:01] [ee35698a38947a6c6c039b1e3deafc05]
- R  D        [(Partial) Autocorrelation Function] [AutoCF d=0,D=0] [2009-12-04 15:09:00] [18c0746232b29e9668aa6bedcb8dd698] [Current]

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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	'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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63720&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63720&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63720&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.863793	6.6909	0
2	0.682049	5.2831	1e-06
3	0.429836	3.3295	0.000746
4	0.300333	2.3264	0.011697
5	0.21257	1.6466	0.052438
6	0.183261	1.4195	0.08046
7	0.118483	0.9178	0.181207
8	0.028691	0.2222	0.412441
9	-0.115036	-0.8911	0.188227
10	-0.272688	-2.1122	0.019419
11	-0.412092	-3.1921	0.001125
12	-0.483303	-3.7437	0.000204
13	-0.48033	-3.7206	0.00022
14	-0.408538	-3.1645	0.00122
15	-0.317849	-2.462	0.008352
16	-0.230294	-1.7839	0.039753
17	-0.174139	-1.3489	0.091223

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.863793 & 6.6909 & 0 \tabularnewline
2 & 0.682049 & 5.2831 & 1e-06 \tabularnewline
3 & 0.429836 & 3.3295 & 0.000746 \tabularnewline
4 & 0.300333 & 2.3264 & 0.011697 \tabularnewline
5 & 0.21257 & 1.6466 & 0.052438 \tabularnewline
6 & 0.183261 & 1.4195 & 0.08046 \tabularnewline
7 & 0.118483 & 0.9178 & 0.181207 \tabularnewline
8 & 0.028691 & 0.2222 & 0.412441 \tabularnewline
9 & -0.115036 & -0.8911 & 0.188227 \tabularnewline
10 & -0.272688 & -2.1122 & 0.019419 \tabularnewline
11 & -0.412092 & -3.1921 & 0.001125 \tabularnewline
12 & -0.483303 & -3.7437 & 0.000204 \tabularnewline
13 & -0.48033 & -3.7206 & 0.00022 \tabularnewline
14 & -0.408538 & -3.1645 & 0.00122 \tabularnewline
15 & -0.317849 & -2.462 & 0.008352 \tabularnewline
16 & -0.230294 & -1.7839 & 0.039753 \tabularnewline
17 & -0.174139 & -1.3489 & 0.091223 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63720&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]0.863793[/C][C]6.6909[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.682049[/C][C]5.2831[/C][C]1e-06[/C][/ROW]
[ROW][C]3[/C][C]0.429836[/C][C]3.3295[/C][C]0.000746[/C][/ROW]
[ROW][C]4[/C][C]0.300333[/C][C]2.3264[/C][C]0.011697[/C][/ROW]
[ROW][C]5[/C][C]0.21257[/C][C]1.6466[/C][C]0.052438[/C][/ROW]
[ROW][C]6[/C][C]0.183261[/C][C]1.4195[/C][C]0.08046[/C][/ROW]
[ROW][C]7[/C][C]0.118483[/C][C]0.9178[/C][C]0.181207[/C][/ROW]
[ROW][C]8[/C][C]0.028691[/C][C]0.2222[/C][C]0.412441[/C][/ROW]
[ROW][C]9[/C][C]-0.115036[/C][C]-0.8911[/C][C]0.188227[/C][/ROW]
[ROW][C]10[/C][C]-0.272688[/C][C]-2.1122[/C][C]0.019419[/C][/ROW]
[ROW][C]11[/C][C]-0.412092[/C][C]-3.1921[/C][C]0.001125[/C][/ROW]
[ROW][C]12[/C][C]-0.483303[/C][C]-3.7437[/C][C]0.000204[/C][/ROW]
[ROW][C]13[/C][C]-0.48033[/C][C]-3.7206[/C][C]0.00022[/C][/ROW]
[ROW][C]14[/C][C]-0.408538[/C][C]-3.1645[/C][C]0.00122[/C][/ROW]
[ROW][C]15[/C][C]-0.317849[/C][C]-2.462[/C][C]0.008352[/C][/ROW]
[ROW][C]16[/C][C]-0.230294[/C][C]-1.7839[/C][C]0.039753[/C][/ROW]
[ROW][C]17[/C][C]-0.174139[/C][C]-1.3489[/C][C]0.091223[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63720&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63720&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	0.863793	6.6909	0
2	0.682049	5.2831	1e-06
3	0.429836	3.3295	0.000746
4	0.300333	2.3264	0.011697
5	0.21257	1.6466	0.052438
6	0.183261	1.4195	0.08046
7	0.118483	0.9178	0.181207
8	0.028691	0.2222	0.412441
9	-0.115036	-0.8911	0.188227
10	-0.272688	-2.1122	0.019419
11	-0.412092	-3.1921	0.001125
12	-0.483303	-3.7437	0.000204
13	-0.48033	-3.7206	0.00022
14	-0.408538	-3.1645	0.00122
15	-0.317849	-2.462	0.008352
16	-0.230294	-1.7839	0.039753
17	-0.174139	-1.3489	0.091223

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.863793	6.6909	0
2	-0.252458	-1.9555	0.027591
3	-0.378563	-2.9323	0.002378
4	0.472656	3.6612	0.000266
5	-0.032357	-0.2506	0.401477
6	-0.269341	-2.0863	0.020605
7	-0.028711	-0.2224	0.412382
8	-0.069919	-0.5416	0.295052
9	-0.267378	-2.0711	0.021329
10	-0.213916	-1.657	0.051372
11	0.031133	0.2412	0.405128
12	0.049454	0.3831	0.351512
13	-0.05777	-0.4475	0.328068
14	0.103323	0.8003	0.213337
15	0.091836	0.7114	0.23981
16	0.009493	0.0735	0.470815
17	0.008046	0.0623	0.475256

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.863793 & 6.6909 & 0 \tabularnewline
2 & -0.252458 & -1.9555 & 0.027591 \tabularnewline
3 & -0.378563 & -2.9323 & 0.002378 \tabularnewline
4 & 0.472656 & 3.6612 & 0.000266 \tabularnewline
5 & -0.032357 & -0.2506 & 0.401477 \tabularnewline
6 & -0.269341 & -2.0863 & 0.020605 \tabularnewline
7 & -0.028711 & -0.2224 & 0.412382 \tabularnewline
8 & -0.069919 & -0.5416 & 0.295052 \tabularnewline
9 & -0.267378 & -2.0711 & 0.021329 \tabularnewline
10 & -0.213916 & -1.657 & 0.051372 \tabularnewline
11 & 0.031133 & 0.2412 & 0.405128 \tabularnewline
12 & 0.049454 & 0.3831 & 0.351512 \tabularnewline
13 & -0.05777 & -0.4475 & 0.328068 \tabularnewline
14 & 0.103323 & 0.8003 & 0.213337 \tabularnewline
15 & 0.091836 & 0.7114 & 0.23981 \tabularnewline
16 & 0.009493 & 0.0735 & 0.470815 \tabularnewline
17 & 0.008046 & 0.0623 & 0.475256 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63720&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]0.863793[/C][C]6.6909[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.252458[/C][C]-1.9555[/C][C]0.027591[/C][/ROW]
[ROW][C]3[/C][C]-0.378563[/C][C]-2.9323[/C][C]0.002378[/C][/ROW]
[ROW][C]4[/C][C]0.472656[/C][C]3.6612[/C][C]0.000266[/C][/ROW]
[ROW][C]5[/C][C]-0.032357[/C][C]-0.2506[/C][C]0.401477[/C][/ROW]
[ROW][C]6[/C][C]-0.269341[/C][C]-2.0863[/C][C]0.020605[/C][/ROW]
[ROW][C]7[/C][C]-0.028711[/C][C]-0.2224[/C][C]0.412382[/C][/ROW]
[ROW][C]8[/C][C]-0.069919[/C][C]-0.5416[/C][C]0.295052[/C][/ROW]
[ROW][C]9[/C][C]-0.267378[/C][C]-2.0711[/C][C]0.021329[/C][/ROW]
[ROW][C]10[/C][C]-0.213916[/C][C]-1.657[/C][C]0.051372[/C][/ROW]
[ROW][C]11[/C][C]0.031133[/C][C]0.2412[/C][C]0.405128[/C][/ROW]
[ROW][C]12[/C][C]0.049454[/C][C]0.3831[/C][C]0.351512[/C][/ROW]
[ROW][C]13[/C][C]-0.05777[/C][C]-0.4475[/C][C]0.328068[/C][/ROW]
[ROW][C]14[/C][C]0.103323[/C][C]0.8003[/C][C]0.213337[/C][/ROW]
[ROW][C]15[/C][C]0.091836[/C][C]0.7114[/C][C]0.23981[/C][/ROW]
[ROW][C]16[/C][C]0.009493[/C][C]0.0735[/C][C]0.470815[/C][/ROW]
[ROW][C]17[/C][C]0.008046[/C][C]0.0623[/C][C]0.475256[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63720&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63720&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	0.863793	6.6909	0
2	-0.252458	-1.9555	0.027591
3	-0.378563	-2.9323	0.002378
4	0.472656	3.6612	0.000266
5	-0.032357	-0.2506	0.401477
6	-0.269341	-2.0863	0.020605
7	-0.028711	-0.2224	0.412382
8	-0.069919	-0.5416	0.295052
9	-0.267378	-2.0711	0.021329
10	-0.213916	-1.657	0.051372
11	0.031133	0.2412	0.405128
12	0.049454	0.3831	0.351512
13	-0.05777	-0.4475	0.328068
14	0.103323	0.8003	0.213337
15	0.091836	0.7114	0.23981
16	0.009493	0.0735	0.470815
17	0.008046	0.0623	0.475256

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = MA ; 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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code