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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 06 Dec 2007 07:19:23 -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/06/t1196950046q5f1e11150sksft.htm/, Retrieved Fri, 03 May 2024 14:41:13 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2618, Retrieved Fri, 03 May 2024 14:41:13 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

215

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

-       [(Partial) Autocorrelation Function] [WS4: Q2 werkloosheid] [2007-12-06 14:19:23] [9b75aacdafaeee3fe66fbd4de075ccd6] [Current]
-   PD    [(Partial) Autocorrelation Function] [Autocorrelation VSA] [2008-12-14 17:43:20] [74be16979710d4c4e7c6647856088456] 
-   PD    [(Partial) Autocorrelation Function] [Autocorrelation J...] [2008-12-14 17:49:08] [74be16979710d4c4e7c6647856088456] 

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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	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2618&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2618&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2618&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	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	7.746	0
1	0.850261	6.5861	0
2	0.637862	4.9409	3e-06
3	0.469057	3.6333	0.000291
4	0.355417	2.753	0.0039
5	0.311911	2.416	0.009375
6	0.263375	2.0401	0.022875
7	0.174992	1.3555	0.090172
8	0.0721	0.5585	0.289296
9	0.049705	0.385	0.350794
10	0.137555	1.0655	0.145461
11	0.26074	2.0197	0.023944
12	0.33619	2.6041	0.005797
13	0.234403	1.8157	0.037209
14	0.073657	0.5705	0.28522
15	-0.054099	-0.4191	0.661662
16	-0.131279	-1.0169	0.843355

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.746 & 0 \tabularnewline
1 & 0.850261 & 6.5861 & 0 \tabularnewline
2 & 0.637862 & 4.9409 & 3e-06 \tabularnewline
3 & 0.469057 & 3.6333 & 0.000291 \tabularnewline
4 & 0.355417 & 2.753 & 0.0039 \tabularnewline
5 & 0.311911 & 2.416 & 0.009375 \tabularnewline
6 & 0.263375 & 2.0401 & 0.022875 \tabularnewline
7 & 0.174992 & 1.3555 & 0.090172 \tabularnewline
8 & 0.0721 & 0.5585 & 0.289296 \tabularnewline
9 & 0.049705 & 0.385 & 0.350794 \tabularnewline
10 & 0.137555 & 1.0655 & 0.145461 \tabularnewline
11 & 0.26074 & 2.0197 & 0.023944 \tabularnewline
12 & 0.33619 & 2.6041 & 0.005797 \tabularnewline
13 & 0.234403 & 1.8157 & 0.037209 \tabularnewline
14 & 0.073657 & 0.5705 & 0.28522 \tabularnewline
15 & -0.054099 & -0.4191 & 0.661662 \tabularnewline
16 & -0.131279 & -1.0169 & 0.843355 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2618&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]7.746[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.850261[/C][C]6.5861[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.637862[/C][C]4.9409[/C][C]3e-06[/C][/ROW]
[ROW][C]3[/C][C]0.469057[/C][C]3.6333[/C][C]0.000291[/C][/ROW]
[ROW][C]4[/C][C]0.355417[/C][C]2.753[/C][C]0.0039[/C][/ROW]
[ROW][C]5[/C][C]0.311911[/C][C]2.416[/C][C]0.009375[/C][/ROW]
[ROW][C]6[/C][C]0.263375[/C][C]2.0401[/C][C]0.022875[/C][/ROW]
[ROW][C]7[/C][C]0.174992[/C][C]1.3555[/C][C]0.090172[/C][/ROW]
[ROW][C]8[/C][C]0.0721[/C][C]0.5585[/C][C]0.289296[/C][/ROW]
[ROW][C]9[/C][C]0.049705[/C][C]0.385[/C][C]0.350794[/C][/ROW]
[ROW][C]10[/C][C]0.137555[/C][C]1.0655[/C][C]0.145461[/C][/ROW]
[ROW][C]11[/C][C]0.26074[/C][C]2.0197[/C][C]0.023944[/C][/ROW]
[ROW][C]12[/C][C]0.33619[/C][C]2.6041[/C][C]0.005797[/C][/ROW]
[ROW][C]13[/C][C]0.234403[/C][C]1.8157[/C][C]0.037209[/C][/ROW]
[ROW][C]14[/C][C]0.073657[/C][C]0.5705[/C][C]0.28522[/C][/ROW]
[ROW][C]15[/C][C]-0.054099[/C][C]-0.4191[/C][C]0.661662[/C][/ROW]
[ROW][C]16[/C][C]-0.131279[/C][C]-1.0169[/C][C]0.843355[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2618&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2618&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	7.746	0
1	0.850261	6.5861	0
2	0.637862	4.9409	3e-06
3	0.469057	3.6333	0.000291
4	0.355417	2.753	0.0039
5	0.311911	2.416	0.009375
6	0.263375	2.0401	0.022875
7	0.174992	1.3555	0.090172
8	0.0721	0.5585	0.289296
9	0.049705	0.385	0.350794
10	0.137555	1.0655	0.145461
11	0.26074	2.0197	0.023944
12	0.33619	2.6041	0.005797
13	0.234403	1.8157	0.037209
14	0.073657	0.5705	0.28522
15	-0.054099	-0.4191	0.661662
16	-0.131279	-1.0169	0.843355

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.850261	6.5861	0
1	-0.307091	-2.3787	0.989714
2	0.084743	0.6564	0.257034
3	0.023354	0.1809	0.428529
4	0.141454	1.0957	0.138794
5	-0.137474	-1.0649	0.854399
6	-0.10849	-0.8404	0.797979
7	-0.0557	-0.4315	0.666157
8	0.267272	2.0703	0.021369
9	0.245186	1.8992	0.031174
10	0.076278	0.5909	0.27842
11	-0.070086	-0.5429	0.705389
12	-0.521642	-4.0406	0.999923
13	-0.003709	-0.0287	0.511412
14	-0.057119	-0.4424	0.670119
15	0.025275	0.1958	0.422723
16	-0.060081	-0.4654	0.678331

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.850261 & 6.5861 & 0 \tabularnewline
1 & -0.307091 & -2.3787 & 0.989714 \tabularnewline
2 & 0.084743 & 0.6564 & 0.257034 \tabularnewline
3 & 0.023354 & 0.1809 & 0.428529 \tabularnewline
4 & 0.141454 & 1.0957 & 0.138794 \tabularnewline
5 & -0.137474 & -1.0649 & 0.854399 \tabularnewline
6 & -0.10849 & -0.8404 & 0.797979 \tabularnewline
7 & -0.0557 & -0.4315 & 0.666157 \tabularnewline
8 & 0.267272 & 2.0703 & 0.021369 \tabularnewline
9 & 0.245186 & 1.8992 & 0.031174 \tabularnewline
10 & 0.076278 & 0.5909 & 0.27842 \tabularnewline
11 & -0.070086 & -0.5429 & 0.705389 \tabularnewline
12 & -0.521642 & -4.0406 & 0.999923 \tabularnewline
13 & -0.003709 & -0.0287 & 0.511412 \tabularnewline
14 & -0.057119 & -0.4424 & 0.670119 \tabularnewline
15 & 0.025275 & 0.1958 & 0.422723 \tabularnewline
16 & -0.060081 & -0.4654 & 0.678331 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2618&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]0.850261[/C][C]6.5861[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.307091[/C][C]-2.3787[/C][C]0.989714[/C][/ROW]
[ROW][C]2[/C][C]0.084743[/C][C]0.6564[/C][C]0.257034[/C][/ROW]
[ROW][C]3[/C][C]0.023354[/C][C]0.1809[/C][C]0.428529[/C][/ROW]
[ROW][C]4[/C][C]0.141454[/C][C]1.0957[/C][C]0.138794[/C][/ROW]
[ROW][C]5[/C][C]-0.137474[/C][C]-1.0649[/C][C]0.854399[/C][/ROW]
[ROW][C]6[/C][C]-0.10849[/C][C]-0.8404[/C][C]0.797979[/C][/ROW]
[ROW][C]7[/C][C]-0.0557[/C][C]-0.4315[/C][C]0.666157[/C][/ROW]
[ROW][C]8[/C][C]0.267272[/C][C]2.0703[/C][C]0.021369[/C][/ROW]
[ROW][C]9[/C][C]0.245186[/C][C]1.8992[/C][C]0.031174[/C][/ROW]
[ROW][C]10[/C][C]0.076278[/C][C]0.5909[/C][C]0.27842[/C][/ROW]
[ROW][C]11[/C][C]-0.070086[/C][C]-0.5429[/C][C]0.705389[/C][/ROW]
[ROW][C]12[/C][C]-0.521642[/C][C]-4.0406[/C][C]0.999923[/C][/ROW]
[ROW][C]13[/C][C]-0.003709[/C][C]-0.0287[/C][C]0.511412[/C][/ROW]
[ROW][C]14[/C][C]-0.057119[/C][C]-0.4424[/C][C]0.670119[/C][/ROW]
[ROW][C]15[/C][C]0.025275[/C][C]0.1958[/C][C]0.422723[/C][/ROW]
[ROW][C]16[/C][C]-0.060081[/C][C]-0.4654[/C][C]0.678331[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2618&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2618&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	0.850261	6.5861	0
1	-0.307091	-2.3787	0.989714
2	0.084743	0.6564	0.257034
3	0.023354	0.1809	0.428529
4	0.141454	1.0957	0.138794
5	-0.137474	-1.0649	0.854399
6	-0.10849	-0.8404	0.797979
7	-0.0557	-0.4315	0.666157
8	0.267272	2.0703	0.021369
9	0.245186	1.8992	0.031174
10	0.076278	0.5909	0.27842
11	-0.070086	-0.5429	0.705389
12	-0.521642	-4.0406	0.999923
13	-0.003709	-0.0287	0.511412
14	-0.057119	-0.4424	0.670119
15	0.025275	0.1958	0.422723
16	-0.060081	-0.4654	0.678331

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 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code