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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 21 Dec 2008 15:22:06 -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/2008/Dec/21/t12298981574zf2midg7dxiklp.htm/, Retrieved Sat, 18 May 2024 20:42:09 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35881, Retrieved Sat, 18 May 2024 20:42:09 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

160

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

-     [(Partial) Autocorrelation Function] [autocorrelation m...] [2008-12-21 22:13:26] [4ddbf81f78ea7c738951638c7e93f6ee]
-   P   [(Partial) Autocorrelation Function] [autocorrelation m...] [2008-12-21 22:16:00] [4ddbf81f78ea7c738951638c7e93f6ee]
-   PD    [(Partial) Autocorrelation Function] [autocorrelation v...] [2008-12-21 22:17:35] [4ddbf81f78ea7c738951638c7e93f6ee]
-   PD      [(Partial) Autocorrelation Function] [autocorrelation m...] [2008-12-21 22:19:34] [4ddbf81f78ea7c738951638c7e93f6ee]
-             [(Partial) Autocorrelation Function] [autocorrelation m...] [2008-12-21 22:20:27] [4ddbf81f78ea7c738951638c7e93f6ee]
-   P             [(Partial) Autocorrelation Function] [autocorrelation m...] [2008-12-21 22:22:06] [e8f764b122b426f433a1e1038b457077] [Current]
-   PD              [(Partial) Autocorrelation Function] [autocorrelation t...] [2008-12-21 22:23:36] [4ddbf81f78ea7c738951638c7e93f6ee] 
-   PD                [(Partial) Autocorrelation Function] [autocorrelation m...] [2008-12-21 22:24:49] [4ddbf81f78ea7c738951638c7e93f6ee] 
-   P                   [(Partial) Autocorrelation Function] [autocorrelation m...] [2008-12-21 22:26:12] [4ddbf81f78ea7c738951638c7e93f6ee] 
- RMPD                [Spectral Analysis] [cumulatieve perio...] [2008-12-21 22:30:15] [4ddbf81f78ea7c738951638c7e93f6ee] 
-    D                  [Spectral Analysis] [cumulatieve perio...] [2008-12-21 22:31:42] [4ddbf81f78ea7c738951638c7e93f6ee] 
-    D                    [Spectral Analysis] [cumulatieve perio...] [2008-12-21 22:33:19] [4ddbf81f78ea7c738951638c7e93f6ee] 

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Dataseries X:

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Histogram

Boxplots

9.4
9.5
9.1
9
9.3
9.9
9.8
9.4
8.3
8
8.5
10.4
11.1
10.9
9.9
9.2
9.2
9.5
9.6
9.5
9.1
8.9
9
10.1
10.3
10.2
9.6
9.2
9.3
9.4
9.4
9.2
9
9
9
9.8
10
9.9
9.3
9
9
9.1
9.1
9.1
9.2
8.8
8.3
8.4
8.1
7.8
7.9
7.9
8
7.9
7.5
7.2
6.9
6.6
6.7
7.3

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=35881&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=35881&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35881&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	0.592042	3.5026	0.00064
2	0.074943	0.4434	0.330114
3	-0.328013	-1.9405	0.030201
4	-0.451978	-2.6739	0.005658
5	-0.342656	-2.0272	0.025157
6	-0.048477	-0.2868	0.387982
7	0.312551	1.8491	0.036454
8	0.42392	2.5079	0.008466
9	0.281537	1.6656	0.052361
10	-0.039791	-0.2354	0.407633
11	-0.243565	-1.441	0.079243
12	-0.377308	-2.2322	0.016051
13	-0.268895	-1.5908	0.060323
14	-0.026785	-0.1585	0.437502
15	0.191451	1.1326	0.132533
16	0.248931	1.4727	0.074885
17	0.136789	0.8093	0.211917

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.592042 & 3.5026 & 0.00064 \tabularnewline
2 & 0.074943 & 0.4434 & 0.330114 \tabularnewline
3 & -0.328013 & -1.9405 & 0.030201 \tabularnewline
4 & -0.451978 & -2.6739 & 0.005658 \tabularnewline
5 & -0.342656 & -2.0272 & 0.025157 \tabularnewline
6 & -0.048477 & -0.2868 & 0.387982 \tabularnewline
7 & 0.312551 & 1.8491 & 0.036454 \tabularnewline
8 & 0.42392 & 2.5079 & 0.008466 \tabularnewline
9 & 0.281537 & 1.6656 & 0.052361 \tabularnewline
10 & -0.039791 & -0.2354 & 0.407633 \tabularnewline
11 & -0.243565 & -1.441 & 0.079243 \tabularnewline
12 & -0.377308 & -2.2322 & 0.016051 \tabularnewline
13 & -0.268895 & -1.5908 & 0.060323 \tabularnewline
14 & -0.026785 & -0.1585 & 0.437502 \tabularnewline
15 & 0.191451 & 1.1326 & 0.132533 \tabularnewline
16 & 0.248931 & 1.4727 & 0.074885 \tabularnewline
17 & 0.136789 & 0.8093 & 0.211917 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35881&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]0.592042[/C][C]3.5026[/C][C]0.00064[/C][/ROW]
[ROW][C]2[/C][C]0.074943[/C][C]0.4434[/C][C]0.330114[/C][/ROW]
[ROW][C]3[/C][C]-0.328013[/C][C]-1.9405[/C][C]0.030201[/C][/ROW]
[ROW][C]4[/C][C]-0.451978[/C][C]-2.6739[/C][C]0.005658[/C][/ROW]
[ROW][C]5[/C][C]-0.342656[/C][C]-2.0272[/C][C]0.025157[/C][/ROW]
[ROW][C]6[/C][C]-0.048477[/C][C]-0.2868[/C][C]0.387982[/C][/ROW]
[ROW][C]7[/C][C]0.312551[/C][C]1.8491[/C][C]0.036454[/C][/ROW]
[ROW][C]8[/C][C]0.42392[/C][C]2.5079[/C][C]0.008466[/C][/ROW]
[ROW][C]9[/C][C]0.281537[/C][C]1.6656[/C][C]0.052361[/C][/ROW]
[ROW][C]10[/C][C]-0.039791[/C][C]-0.2354[/C][C]0.407633[/C][/ROW]
[ROW][C]11[/C][C]-0.243565[/C][C]-1.441[/C][C]0.079243[/C][/ROW]
[ROW][C]12[/C][C]-0.377308[/C][C]-2.2322[/C][C]0.016051[/C][/ROW]
[ROW][C]13[/C][C]-0.268895[/C][C]-1.5908[/C][C]0.060323[/C][/ROW]
[ROW][C]14[/C][C]-0.026785[/C][C]-0.1585[/C][C]0.437502[/C][/ROW]
[ROW][C]15[/C][C]0.191451[/C][C]1.1326[/C][C]0.132533[/C][/ROW]
[ROW][C]16[/C][C]0.248931[/C][C]1.4727[/C][C]0.074885[/C][/ROW]
[ROW][C]17[/C][C]0.136789[/C][C]0.8093[/C][C]0.211917[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35881&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35881&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	0.592042	3.5026	0.00064
2	0.074943	0.4434	0.330114
3	-0.328013	-1.9405	0.030201
4	-0.451978	-2.6739	0.005658
5	-0.342656	-2.0272	0.025157
6	-0.048477	-0.2868	0.387982
7	0.312551	1.8491	0.036454
8	0.42392	2.5079	0.008466
9	0.281537	1.6656	0.052361
10	-0.039791	-0.2354	0.407633
11	-0.243565	-1.441	0.079243
12	-0.377308	-2.2322	0.016051
13	-0.268895	-1.5908	0.060323
14	-0.026785	-0.1585	0.437502
15	0.191451	1.1326	0.132533
16	0.248931	1.4727	0.074885
17	0.136789	0.8093	0.211917

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.592042	3.5026	0.00064
2	-0.42429	-2.5101	0.008422
3	-0.262899	-1.5553	0.064432
4	-0.08299	-0.491	0.313255
5	-0.059905	-0.3544	0.362581
6	0.11474	0.6788	0.250861
7	0.250394	1.4814	0.07373
8	-0.041255	-0.2441	0.404301
9	-0.022448	-0.1328	0.447554
10	-0.118282	-0.6998	0.24435
11	0.071294	0.4218	0.337882
12	-0.187404	-1.1087	0.137561
13	0.073872	0.437	0.332386
14	-0.007567	-0.0448	0.482275
15	-0.038714	-0.229	0.410087
16	-0.047362	-0.2802	0.390488
17	-0.003639	-0.0215	0.491473

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.592042 & 3.5026 & 0.00064 \tabularnewline
2 & -0.42429 & -2.5101 & 0.008422 \tabularnewline
3 & -0.262899 & -1.5553 & 0.064432 \tabularnewline
4 & -0.08299 & -0.491 & 0.313255 \tabularnewline
5 & -0.059905 & -0.3544 & 0.362581 \tabularnewline
6 & 0.11474 & 0.6788 & 0.250861 \tabularnewline
7 & 0.250394 & 1.4814 & 0.07373 \tabularnewline
8 & -0.041255 & -0.2441 & 0.404301 \tabularnewline
9 & -0.022448 & -0.1328 & 0.447554 \tabularnewline
10 & -0.118282 & -0.6998 & 0.24435 \tabularnewline
11 & 0.071294 & 0.4218 & 0.337882 \tabularnewline
12 & -0.187404 & -1.1087 & 0.137561 \tabularnewline
13 & 0.073872 & 0.437 & 0.332386 \tabularnewline
14 & -0.007567 & -0.0448 & 0.482275 \tabularnewline
15 & -0.038714 & -0.229 & 0.410087 \tabularnewline
16 & -0.047362 & -0.2802 & 0.390488 \tabularnewline
17 & -0.003639 & -0.0215 & 0.491473 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35881&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]0.592042[/C][C]3.5026[/C][C]0.00064[/C][/ROW]
[ROW][C]2[/C][C]-0.42429[/C][C]-2.5101[/C][C]0.008422[/C][/ROW]
[ROW][C]3[/C][C]-0.262899[/C][C]-1.5553[/C][C]0.064432[/C][/ROW]
[ROW][C]4[/C][C]-0.08299[/C][C]-0.491[/C][C]0.313255[/C][/ROW]
[ROW][C]5[/C][C]-0.059905[/C][C]-0.3544[/C][C]0.362581[/C][/ROW]
[ROW][C]6[/C][C]0.11474[/C][C]0.6788[/C][C]0.250861[/C][/ROW]
[ROW][C]7[/C][C]0.250394[/C][C]1.4814[/C][C]0.07373[/C][/ROW]
[ROW][C]8[/C][C]-0.041255[/C][C]-0.2441[/C][C]0.404301[/C][/ROW]
[ROW][C]9[/C][C]-0.022448[/C][C]-0.1328[/C][C]0.447554[/C][/ROW]
[ROW][C]10[/C][C]-0.118282[/C][C]-0.6998[/C][C]0.24435[/C][/ROW]
[ROW][C]11[/C][C]0.071294[/C][C]0.4218[/C][C]0.337882[/C][/ROW]
[ROW][C]12[/C][C]-0.187404[/C][C]-1.1087[/C][C]0.137561[/C][/ROW]
[ROW][C]13[/C][C]0.073872[/C][C]0.437[/C][C]0.332386[/C][/ROW]
[ROW][C]14[/C][C]-0.007567[/C][C]-0.0448[/C][C]0.482275[/C][/ROW]
[ROW][C]15[/C][C]-0.038714[/C][C]-0.229[/C][C]0.410087[/C][/ROW]
[ROW][C]16[/C][C]-0.047362[/C][C]-0.2802[/C][C]0.390488[/C][/ROW]
[ROW][C]17[/C][C]-0.003639[/C][C]-0.0215[/C][C]0.491473[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35881&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35881&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	0.592042	3.5026	0.00064
2	-0.42429	-2.5101	0.008422
3	-0.262899	-1.5553	0.064432
4	-0.08299	-0.491	0.313255
5	-0.059905	-0.3544	0.362581
6	0.11474	0.6788	0.250861
7	0.250394	1.4814	0.07373
8	-0.041255	-0.2441	0.404301
9	-0.022448	-0.1328	0.447554
10	-0.118282	-0.6998	0.24435
11	0.071294	0.4218	0.337882
12	-0.187404	-1.1087	0.137561
13	0.073872	0.437	0.332386
14	-0.007567	-0.0448	0.482275
15	-0.038714	-0.229	0.410087
16	-0.047362	-0.2802	0.390488
17	-0.003639	-0.0215	0.491473

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 = 2 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 2 ; 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 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