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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 28 Nov 2009 11:23:35 -0700

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/2009/Nov/28/t12594326990tj15ly3xh2ahty.htm/, Retrieved Sun, 05 May 2024 17:58:59 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=61517, Retrieved Sun, 05 May 2024 17:58:59 +0000

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Estimated Impact

147

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

-       [(Partial) Autocorrelation Function] [Workshop 8] [2009-11-28 18:23:35] [aef022288383377281176d9807aba5bf] [Current]
-   PD    [(Partial) Autocorrelation Function] [Oplossing ACF d=D...] [2009-12-04 15:46:52] [4395c69e961f9a13a0559fd2f0a72538] 
-   P       [(Partial) Autocorrelation Function] [oplossing ACF d=D...] [2009-12-04 15:53:40] [4395c69e961f9a13a0559fd2f0a72538] 

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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=61517&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=61517&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61517&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	0.908559	7.0377	0
2	0.798468	6.1849	0
3	0.645861	5.0028	3e-06
4	0.485193	3.7583	0.000195
5	0.305073	2.3631	0.010691
6	0.146212	1.1325	0.130955
7	-0.019383	-0.1501	0.440579
8	-0.164772	-1.2763	0.10338
9	-0.301259	-2.3335	0.011494
10	-0.413518	-3.2031	0.001089
11	-0.499993	-3.8729	0.000134
12	-0.549516	-4.2565	3.7e-05
13	-0.537942	-4.1669	5e-05
14	-0.503058	-3.8967	0.000124
15	-0.445705	-3.4524	0.000512
16	-0.389723	-3.0188	0.001861
17	-0.325513	-2.5214	0.007181

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.908559 & 7.0377 & 0 \tabularnewline
2 & 0.798468 & 6.1849 & 0 \tabularnewline
3 & 0.645861 & 5.0028 & 3e-06 \tabularnewline
4 & 0.485193 & 3.7583 & 0.000195 \tabularnewline
5 & 0.305073 & 2.3631 & 0.010691 \tabularnewline
6 & 0.146212 & 1.1325 & 0.130955 \tabularnewline
7 & -0.019383 & -0.1501 & 0.440579 \tabularnewline
8 & -0.164772 & -1.2763 & 0.10338 \tabularnewline
9 & -0.301259 & -2.3335 & 0.011494 \tabularnewline
10 & -0.413518 & -3.2031 & 0.001089 \tabularnewline
11 & -0.499993 & -3.8729 & 0.000134 \tabularnewline
12 & -0.549516 & -4.2565 & 3.7e-05 \tabularnewline
13 & -0.537942 & -4.1669 & 5e-05 \tabularnewline
14 & -0.503058 & -3.8967 & 0.000124 \tabularnewline
15 & -0.445705 & -3.4524 & 0.000512 \tabularnewline
16 & -0.389723 & -3.0188 & 0.001861 \tabularnewline
17 & -0.325513 & -2.5214 & 0.007181 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61517&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]0.908559[/C][C]7.0377[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.798468[/C][C]6.1849[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.645861[/C][C]5.0028[/C][C]3e-06[/C][/ROW]
[ROW][C]4[/C][C]0.485193[/C][C]3.7583[/C][C]0.000195[/C][/ROW]
[ROW][C]5[/C][C]0.305073[/C][C]2.3631[/C][C]0.010691[/C][/ROW]
[ROW][C]6[/C][C]0.146212[/C][C]1.1325[/C][C]0.130955[/C][/ROW]
[ROW][C]7[/C][C]-0.019383[/C][C]-0.1501[/C][C]0.440579[/C][/ROW]
[ROW][C]8[/C][C]-0.164772[/C][C]-1.2763[/C][C]0.10338[/C][/ROW]
[ROW][C]9[/C][C]-0.301259[/C][C]-2.3335[/C][C]0.011494[/C][/ROW]
[ROW][C]10[/C][C]-0.413518[/C][C]-3.2031[/C][C]0.001089[/C][/ROW]
[ROW][C]11[/C][C]-0.499993[/C][C]-3.8729[/C][C]0.000134[/C][/ROW]
[ROW][C]12[/C][C]-0.549516[/C][C]-4.2565[/C][C]3.7e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.537942[/C][C]-4.1669[/C][C]5e-05[/C][/ROW]
[ROW][C]14[/C][C]-0.503058[/C][C]-3.8967[/C][C]0.000124[/C][/ROW]
[ROW][C]15[/C][C]-0.445705[/C][C]-3.4524[/C][C]0.000512[/C][/ROW]
[ROW][C]16[/C][C]-0.389723[/C][C]-3.0188[/C][C]0.001861[/C][/ROW]
[ROW][C]17[/C][C]-0.325513[/C][C]-2.5214[/C][C]0.007181[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61517&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61517&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	0.908559	7.0377	0
2	0.798468	6.1849	0
3	0.645861	5.0028	3e-06
4	0.485193	3.7583	0.000195
5	0.305073	2.3631	0.010691
6	0.146212	1.1325	0.130955
7	-0.019383	-0.1501	0.440579
8	-0.164772	-1.2763	0.10338
9	-0.301259	-2.3335	0.011494
10	-0.413518	-3.2031	0.001089
11	-0.499993	-3.8729	0.000134
12	-0.549516	-4.2565	3.7e-05
13	-0.537942	-4.1669	5e-05
14	-0.503058	-3.8967	0.000124
15	-0.445705	-3.4524	0.000512
16	-0.389723	-3.0188	0.001861
17	-0.325513	-2.5214	0.007181

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.908559	7.0377	0
2	-0.15478	-1.1989	0.117636
3	-0.300892	-2.3307	0.011574
4	-0.112708	-0.873	0.193063
5	-0.184042	-1.4256	0.079586
6	0.012472	0.0966	0.461681
7	-0.16268	-1.2601	0.106253
8	-0.084747	-0.6564	0.257022
9	-0.112449	-0.871	0.193607
10	-0.09263	-0.7175	0.237922
11	-0.02727	-0.2112	0.41671
12	-0.014997	-0.1162	0.453955
13	0.205403	1.591	0.058427
14	-0.056648	-0.4388	0.331193
15	-0.07253	-0.5618	0.288168
16	-0.152966	-1.1849	0.12037
17	-0.080589	-0.6242	0.267419

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.908559 & 7.0377 & 0 \tabularnewline
2 & -0.15478 & -1.1989 & 0.117636 \tabularnewline
3 & -0.300892 & -2.3307 & 0.011574 \tabularnewline
4 & -0.112708 & -0.873 & 0.193063 \tabularnewline
5 & -0.184042 & -1.4256 & 0.079586 \tabularnewline
6 & 0.012472 & 0.0966 & 0.461681 \tabularnewline
7 & -0.16268 & -1.2601 & 0.106253 \tabularnewline
8 & -0.084747 & -0.6564 & 0.257022 \tabularnewline
9 & -0.112449 & -0.871 & 0.193607 \tabularnewline
10 & -0.09263 & -0.7175 & 0.237922 \tabularnewline
11 & -0.02727 & -0.2112 & 0.41671 \tabularnewline
12 & -0.014997 & -0.1162 & 0.453955 \tabularnewline
13 & 0.205403 & 1.591 & 0.058427 \tabularnewline
14 & -0.056648 & -0.4388 & 0.331193 \tabularnewline
15 & -0.07253 & -0.5618 & 0.288168 \tabularnewline
16 & -0.152966 & -1.1849 & 0.12037 \tabularnewline
17 & -0.080589 & -0.6242 & 0.267419 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61517&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]0.908559[/C][C]7.0377[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.15478[/C][C]-1.1989[/C][C]0.117636[/C][/ROW]
[ROW][C]3[/C][C]-0.300892[/C][C]-2.3307[/C][C]0.011574[/C][/ROW]
[ROW][C]4[/C][C]-0.112708[/C][C]-0.873[/C][C]0.193063[/C][/ROW]
[ROW][C]5[/C][C]-0.184042[/C][C]-1.4256[/C][C]0.079586[/C][/ROW]
[ROW][C]6[/C][C]0.012472[/C][C]0.0966[/C][C]0.461681[/C][/ROW]
[ROW][C]7[/C][C]-0.16268[/C][C]-1.2601[/C][C]0.106253[/C][/ROW]
[ROW][C]8[/C][C]-0.084747[/C][C]-0.6564[/C][C]0.257022[/C][/ROW]
[ROW][C]9[/C][C]-0.112449[/C][C]-0.871[/C][C]0.193607[/C][/ROW]
[ROW][C]10[/C][C]-0.09263[/C][C]-0.7175[/C][C]0.237922[/C][/ROW]
[ROW][C]11[/C][C]-0.02727[/C][C]-0.2112[/C][C]0.41671[/C][/ROW]
[ROW][C]12[/C][C]-0.014997[/C][C]-0.1162[/C][C]0.453955[/C][/ROW]
[ROW][C]13[/C][C]0.205403[/C][C]1.591[/C][C]0.058427[/C][/ROW]
[ROW][C]14[/C][C]-0.056648[/C][C]-0.4388[/C][C]0.331193[/C][/ROW]
[ROW][C]15[/C][C]-0.07253[/C][C]-0.5618[/C][C]0.288168[/C][/ROW]
[ROW][C]16[/C][C]-0.152966[/C][C]-1.1849[/C][C]0.12037[/C][/ROW]
[ROW][C]17[/C][C]-0.080589[/C][C]-0.6242[/C][C]0.267419[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61517&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61517&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	0.908559	7.0377	0
2	-0.15478	-1.1989	0.117636
3	-0.300892	-2.3307	0.011574
4	-0.112708	-0.873	0.193063
5	-0.184042	-1.4256	0.079586
6	0.012472	0.0966	0.461681
7	-0.16268	-1.2601	0.106253
8	-0.084747	-0.6564	0.257022
9	-0.112449	-0.871	0.193607
10	-0.09263	-0.7175	0.237922
11	-0.02727	-0.2112	0.41671
12	-0.014997	-0.1162	0.453955
13	0.205403	1.591	0.058427
14	-0.056648	-0.4388	0.331193
15	-0.07253	-0.5618	0.288168
16	-0.152966	-1.1849	0.12037
17	-0.080589	-0.6242	0.267419

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 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; 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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code