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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 27 Nov 2007 03:09:52 -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/Nov/27/t1196157669tqtbtvge8020a8a.htm/, Retrieved Sun, 05 May 2024 14:16:48 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6801, Retrieved Sun, 05 May 2024 14:16:48 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

183

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

-       [(Partial) Autocorrelation Function] [Opdracht3 Q2 Kolom4] [2007-11-27 10:09:52] [00ef4a509c2a49a63e98610ffa741e39] [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	2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6801&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]2 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=6801&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6801&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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	8.4853	0
1	0.556102	4.7187	6e-06
2	0.447654	3.7985	0.000151
3	0.146963	1.247	0.108216
4	0.081088	0.6881	0.246815
5	0.011663	0.099	0.460721
6	0.081227	0.6892	0.246446
7	0.123582	1.0486	0.148929
8	0.193319	1.6404	0.052645
9	0.275735	2.3397	0.011038
10	0.34328	2.9128	0.002383
11	0.37245	3.1603	0.001153

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.4853 & 0 \tabularnewline
1 & 0.556102 & 4.7187 & 6e-06 \tabularnewline
2 & 0.447654 & 3.7985 & 0.000151 \tabularnewline
3 & 0.146963 & 1.247 & 0.108216 \tabularnewline
4 & 0.081088 & 0.6881 & 0.246815 \tabularnewline
5 & 0.011663 & 0.099 & 0.460721 \tabularnewline
6 & 0.081227 & 0.6892 & 0.246446 \tabularnewline
7 & 0.123582 & 1.0486 & 0.148929 \tabularnewline
8 & 0.193319 & 1.6404 & 0.052645 \tabularnewline
9 & 0.275735 & 2.3397 & 0.011038 \tabularnewline
10 & 0.34328 & 2.9128 & 0.002383 \tabularnewline
11 & 0.37245 & 3.1603 & 0.001153 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6801&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]8.4853[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.556102[/C][C]4.7187[/C][C]6e-06[/C][/ROW]
[ROW][C]2[/C][C]0.447654[/C][C]3.7985[/C][C]0.000151[/C][/ROW]
[ROW][C]3[/C][C]0.146963[/C][C]1.247[/C][C]0.108216[/C][/ROW]
[ROW][C]4[/C][C]0.081088[/C][C]0.6881[/C][C]0.246815[/C][/ROW]
[ROW][C]5[/C][C]0.011663[/C][C]0.099[/C][C]0.460721[/C][/ROW]
[ROW][C]6[/C][C]0.081227[/C][C]0.6892[/C][C]0.246446[/C][/ROW]
[ROW][C]7[/C][C]0.123582[/C][C]1.0486[/C][C]0.148929[/C][/ROW]
[ROW][C]8[/C][C]0.193319[/C][C]1.6404[/C][C]0.052645[/C][/ROW]
[ROW][C]9[/C][C]0.275735[/C][C]2.3397[/C][C]0.011038[/C][/ROW]
[ROW][C]10[/C][C]0.34328[/C][C]2.9128[/C][C]0.002383[/C][/ROW]
[ROW][C]11[/C][C]0.37245[/C][C]3.1603[/C][C]0.001153[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6801&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6801&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	8.4853	0
1	0.556102	4.7187	6e-06
2	0.447654	3.7985	0.000151
3	0.146963	1.247	0.108216
4	0.081088	0.6881	0.246815
5	0.011663	0.099	0.460721
6	0.081227	0.6892	0.246446
7	0.123582	1.0486	0.148929
8	0.193319	1.6404	0.052645
9	0.275735	2.3397	0.011038
10	0.34328	2.9128	0.002383
11	0.37245	3.1603	0.001153

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.556102	4.7187	6e-06
1	0.200369	1.7002	0.046706
2	-0.246636	-2.0928	0.980053
3	0.01098	0.0932	0.463013
4	0.053073	0.4503	0.326909
5	0.106786	0.9061	0.18395
6	0.077033	0.6537	0.25771
7	0.070086	0.5947	0.276954
8	0.163466	1.3871	0.084853
9	0.159441	1.3529	0.09016
10	0.111062	0.9424	0.174571
11	0.141234	1.1984	0.117343

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.556102 & 4.7187 & 6e-06 \tabularnewline
1 & 0.200369 & 1.7002 & 0.046706 \tabularnewline
2 & -0.246636 & -2.0928 & 0.980053 \tabularnewline
3 & 0.01098 & 0.0932 & 0.463013 \tabularnewline
4 & 0.053073 & 0.4503 & 0.326909 \tabularnewline
5 & 0.106786 & 0.9061 & 0.18395 \tabularnewline
6 & 0.077033 & 0.6537 & 0.25771 \tabularnewline
7 & 0.070086 & 0.5947 & 0.276954 \tabularnewline
8 & 0.163466 & 1.3871 & 0.084853 \tabularnewline
9 & 0.159441 & 1.3529 & 0.09016 \tabularnewline
10 & 0.111062 & 0.9424 & 0.174571 \tabularnewline
11 & 0.141234 & 1.1984 & 0.117343 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6801&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]0.556102[/C][C]4.7187[/C][C]6e-06[/C][/ROW]
[ROW][C]1[/C][C]0.200369[/C][C]1.7002[/C][C]0.046706[/C][/ROW]
[ROW][C]2[/C][C]-0.246636[/C][C]-2.0928[/C][C]0.980053[/C][/ROW]
[ROW][C]3[/C][C]0.01098[/C][C]0.0932[/C][C]0.463013[/C][/ROW]
[ROW][C]4[/C][C]0.053073[/C][C]0.4503[/C][C]0.326909[/C][/ROW]
[ROW][C]5[/C][C]0.106786[/C][C]0.9061[/C][C]0.18395[/C][/ROW]
[ROW][C]6[/C][C]0.077033[/C][C]0.6537[/C][C]0.25771[/C][/ROW]
[ROW][C]7[/C][C]0.070086[/C][C]0.5947[/C][C]0.276954[/C][/ROW]
[ROW][C]8[/C][C]0.163466[/C][C]1.3871[/C][C]0.084853[/C][/ROW]
[ROW][C]9[/C][C]0.159441[/C][C]1.3529[/C][C]0.09016[/C][/ROW]
[ROW][C]10[/C][C]0.111062[/C][C]0.9424[/C][C]0.174571[/C][/ROW]
[ROW][C]11[/C][C]0.141234[/C][C]1.1984[/C][C]0.117343[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6801&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6801&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	0.556102	4.7187	6e-06
1	0.200369	1.7002	0.046706
2	-0.246636	-2.0928	0.980053
3	0.01098	0.0932	0.463013
4	0.053073	0.4503	0.326909
5	0.106786	0.9061	0.18395
6	0.077033	0.6537	0.25771
7	0.070086	0.5947	0.276954
8	0.163466	1.3871	0.084853
9	0.159441	1.3529	0.09016
10	0.111062	0.9424	0.174571
11	0.141234	1.1984	0.117343

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

par1 = 12 ; 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')

Free Statistics

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code