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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 07 Dec 2007 04:35:27 -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/2007/Dec/07/t1197026534ew9t3kqes779ewz.htm/, Retrieved Mon, 29 Apr 2024 06:45:33 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2757, Retrieved Mon, 29 Apr 2024 06:45:33 +0000

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No (this computation is public)

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Estimated Impact

216

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

-       [(Partial) Autocorrelation Function] [paper olieprijzen...] [2007-12-07 11:35:27] [e24e91da8d334fb8882bf413603fde71] [Current]

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Summary of compuational 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 compuational 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=2757&T=0

[TABLE]
[ROW][C]Summary of compuational 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=2757&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2757&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 compuational 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
0	1	7.6811	0
1	0.008319	0.0639	0.474634
2	-0.167371	-1.2856	0.898197
3	0.039763	0.3054	0.380558
4	0.02179	0.1674	0.433826
5	0.038707	0.2973	0.383636
6	-0.188079	-1.4447	0.923079
7	0.075705	0.5815	0.281558
8	-0.169904	-1.3051	0.90153
9	-0.254732	-1.9566	0.972436
10	0.19476	1.496	0.069994
11	0.184486	1.4171	0.080862
12	-0.059842	-0.4597	0.676273
13	-0.195805	-1.504	0.931043
14	-0.010174	-0.0781	0.531011
15	0.131056	1.0067	0.159104
16	-0.134057	-1.0297	0.846326

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.6811 & 0 \tabularnewline
1 & 0.008319 & 0.0639 & 0.474634 \tabularnewline
2 & -0.167371 & -1.2856 & 0.898197 \tabularnewline
3 & 0.039763 & 0.3054 & 0.380558 \tabularnewline
4 & 0.02179 & 0.1674 & 0.433826 \tabularnewline
5 & 0.038707 & 0.2973 & 0.383636 \tabularnewline
6 & -0.188079 & -1.4447 & 0.923079 \tabularnewline
7 & 0.075705 & 0.5815 & 0.281558 \tabularnewline
8 & -0.169904 & -1.3051 & 0.90153 \tabularnewline
9 & -0.254732 & -1.9566 & 0.972436 \tabularnewline
10 & 0.19476 & 1.496 & 0.069994 \tabularnewline
11 & 0.184486 & 1.4171 & 0.080862 \tabularnewline
12 & -0.059842 & -0.4597 & 0.676273 \tabularnewline
13 & -0.195805 & -1.504 & 0.931043 \tabularnewline
14 & -0.010174 & -0.0781 & 0.531011 \tabularnewline
15 & 0.131056 & 1.0067 & 0.159104 \tabularnewline
16 & -0.134057 & -1.0297 & 0.846326 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2757&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]0[/C][C]1[/C][C]7.6811[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.008319[/C][C]0.0639[/C][C]0.474634[/C][/ROW]
[ROW][C]2[/C][C]-0.167371[/C][C]-1.2856[/C][C]0.898197[/C][/ROW]
[ROW][C]3[/C][C]0.039763[/C][C]0.3054[/C][C]0.380558[/C][/ROW]
[ROW][C]4[/C][C]0.02179[/C][C]0.1674[/C][C]0.433826[/C][/ROW]
[ROW][C]5[/C][C]0.038707[/C][C]0.2973[/C][C]0.383636[/C][/ROW]
[ROW][C]6[/C][C]-0.188079[/C][C]-1.4447[/C][C]0.923079[/C][/ROW]
[ROW][C]7[/C][C]0.075705[/C][C]0.5815[/C][C]0.281558[/C][/ROW]
[ROW][C]8[/C][C]-0.169904[/C][C]-1.3051[/C][C]0.90153[/C][/ROW]
[ROW][C]9[/C][C]-0.254732[/C][C]-1.9566[/C][C]0.972436[/C][/ROW]
[ROW][C]10[/C][C]0.19476[/C][C]1.496[/C][C]0.069994[/C][/ROW]
[ROW][C]11[/C][C]0.184486[/C][C]1.4171[/C][C]0.080862[/C][/ROW]
[ROW][C]12[/C][C]-0.059842[/C][C]-0.4597[/C][C]0.676273[/C][/ROW]
[ROW][C]13[/C][C]-0.195805[/C][C]-1.504[/C][C]0.931043[/C][/ROW]
[ROW][C]14[/C][C]-0.010174[/C][C]-0.0781[/C][C]0.531011[/C][/ROW]
[ROW][C]15[/C][C]0.131056[/C][C]1.0067[/C][C]0.159104[/C][/ROW]
[ROW][C]16[/C][C]-0.134057[/C][C]-1.0297[/C][C]0.846326[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2757&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2757&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
0	1	7.6811	0
1	0.008319	0.0639	0.474634
2	-0.167371	-1.2856	0.898197
3	0.039763	0.3054	0.380558
4	0.02179	0.1674	0.433826
5	0.038707	0.2973	0.383636
6	-0.188079	-1.4447	0.923079
7	0.075705	0.5815	0.281558
8	-0.169904	-1.3051	0.90153
9	-0.254732	-1.9566	0.972436
10	0.19476	1.496	0.069994
11	0.184486	1.4171	0.080862
12	-0.059842	-0.4597	0.676273
13	-0.195805	-1.504	0.931043
14	-0.010174	-0.0781	0.531011
15	0.131056	1.0067	0.159104
16	-0.134057	-1.0297	0.846326

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.008319	0.0639	0.474634
1	-0.167451	-1.2862	0.898304
2	0.044019	0.3381	0.368238
3	-0.007581	-0.0582	0.52312
4	0.054132	0.4158	0.339534
5	-0.195456	-1.5013	0.930698
6	0.106761	0.82	0.207745
7	-0.267605	-2.0555	0.977868
8	-0.204756	-1.5728	0.939439
9	0.138066	1.0605	0.146619
10	0.161157	1.2379	0.110334
11	-0.060902	-0.4678	0.679174
12	-0.130048	-0.9989	0.839042
13	-0.111557	-0.8569	0.802513
14	0.015257	0.1172	0.453553
15	-0.125263	-0.9622	0.830054
16	-0.063399	-0.487	0.68596

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.008319 & 0.0639 & 0.474634 \tabularnewline
1 & -0.167451 & -1.2862 & 0.898304 \tabularnewline
2 & 0.044019 & 0.3381 & 0.368238 \tabularnewline
3 & -0.007581 & -0.0582 & 0.52312 \tabularnewline
4 & 0.054132 & 0.4158 & 0.339534 \tabularnewline
5 & -0.195456 & -1.5013 & 0.930698 \tabularnewline
6 & 0.106761 & 0.82 & 0.207745 \tabularnewline
7 & -0.267605 & -2.0555 & 0.977868 \tabularnewline
8 & -0.204756 & -1.5728 & 0.939439 \tabularnewline
9 & 0.138066 & 1.0605 & 0.146619 \tabularnewline
10 & 0.161157 & 1.2379 & 0.110334 \tabularnewline
11 & -0.060902 & -0.4678 & 0.679174 \tabularnewline
12 & -0.130048 & -0.9989 & 0.839042 \tabularnewline
13 & -0.111557 & -0.8569 & 0.802513 \tabularnewline
14 & 0.015257 & 0.1172 & 0.453553 \tabularnewline
15 & -0.125263 & -0.9622 & 0.830054 \tabularnewline
16 & -0.063399 & -0.487 & 0.68596 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2757&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]0[/C][C]0.008319[/C][C]0.0639[/C][C]0.474634[/C][/ROW]
[ROW][C]1[/C][C]-0.167451[/C][C]-1.2862[/C][C]0.898304[/C][/ROW]
[ROW][C]2[/C][C]0.044019[/C][C]0.3381[/C][C]0.368238[/C][/ROW]
[ROW][C]3[/C][C]-0.007581[/C][C]-0.0582[/C][C]0.52312[/C][/ROW]
[ROW][C]4[/C][C]0.054132[/C][C]0.4158[/C][C]0.339534[/C][/ROW]
[ROW][C]5[/C][C]-0.195456[/C][C]-1.5013[/C][C]0.930698[/C][/ROW]
[ROW][C]6[/C][C]0.106761[/C][C]0.82[/C][C]0.207745[/C][/ROW]
[ROW][C]7[/C][C]-0.267605[/C][C]-2.0555[/C][C]0.977868[/C][/ROW]
[ROW][C]8[/C][C]-0.204756[/C][C]-1.5728[/C][C]0.939439[/C][/ROW]
[ROW][C]9[/C][C]0.138066[/C][C]1.0605[/C][C]0.146619[/C][/ROW]
[ROW][C]10[/C][C]0.161157[/C][C]1.2379[/C][C]0.110334[/C][/ROW]
[ROW][C]11[/C][C]-0.060902[/C][C]-0.4678[/C][C]0.679174[/C][/ROW]
[ROW][C]12[/C][C]-0.130048[/C][C]-0.9989[/C][C]0.839042[/C][/ROW]
[ROW][C]13[/C][C]-0.111557[/C][C]-0.8569[/C][C]0.802513[/C][/ROW]
[ROW][C]14[/C][C]0.015257[/C][C]0.1172[/C][C]0.453553[/C][/ROW]
[ROW][C]15[/C][C]-0.125263[/C][C]-0.9622[/C][C]0.830054[/C][/ROW]
[ROW][C]16[/C][C]-0.063399[/C][C]-0.487[/C][C]0.68596[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2757&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2757&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
0	0.008319	0.0639	0.474634
1	-0.167451	-1.2862	0.898304
2	0.044019	0.3381	0.368238
3	-0.007581	-0.0582	0.52312
4	0.054132	0.4158	0.339534
5	-0.195456	-1.5013	0.930698
6	0.106761	0.82	0.207745
7	-0.267605	-2.0555	0.977868
8	-0.204756	-1.5728	0.939439
9	0.138066	1.0605	0.146619
10	0.161157	1.2379	0.110334
11	-0.060902	-0.4678	0.679174
12	-0.130048	-0.9989	0.839042
13	-0.111557	-0.8569	0.802513
14	0.015257	0.1172	0.453553
15	-0.125263	-0.9622	0.830054
16	-0.063399	-0.487	0.68596

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ;

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 (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='lags',ylab='ACF')
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 1:par1) {
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(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-1,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(mytstat,lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

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