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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 16 Jan 2008 10:22:33 -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/Jan/16/t1200503887o12oe4f7ob66xhu.htm/, Retrieved Sun, 05 May 2024 20:17:41 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7998, Retrieved Sun, 05 May 2024 20:17:41 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

274

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

-     [Hierarchical Clustering] [paper] [2007-12-05 22:51:14] [8d3192ea84fef628e5e980e3df2ac42d]
- RMPD    [(Partial) Autocorrelation Function] [] [2008-01-16 17:22:33] [d41d8cd98f00b204e9800998ecf8427e] [Current]
- RMPD      [(Partial) Autocorrelation Function] [WS8 1] [2010-11-25 16:31:47] [717f3d787904f94c39256c5c1fc72d4c] 

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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=7998&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=7998&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7998&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	7.746	0
1	0.929646	7.201	0
2	0.865138	6.7013	0
3	0.820736	6.3574	0
4	0.76137	5.8975	0
5	0.682562	5.2871	1e-06
6	0.61574	4.7695	6e-06
7	0.557221	4.3162	3e-05
8	0.464017	3.5943	0.000329
9	0.393426	3.0475	0.001714
10	0.341925	2.6485	0.005158
11	0.289011	2.2387	0.014449
12	0.235125	1.8213	0.036776
13	0.201377	1.5599	0.062026
14	0.175797	1.3617	0.089189
15	0.142631	1.1048	0.136826
16	0.110981	0.8597	0.196701

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.746 & 0 \tabularnewline
1 & 0.929646 & 7.201 & 0 \tabularnewline
2 & 0.865138 & 6.7013 & 0 \tabularnewline
3 & 0.820736 & 6.3574 & 0 \tabularnewline
4 & 0.76137 & 5.8975 & 0 \tabularnewline
5 & 0.682562 & 5.2871 & 1e-06 \tabularnewline
6 & 0.61574 & 4.7695 & 6e-06 \tabularnewline
7 & 0.557221 & 4.3162 & 3e-05 \tabularnewline
8 & 0.464017 & 3.5943 & 0.000329 \tabularnewline
9 & 0.393426 & 3.0475 & 0.001714 \tabularnewline
10 & 0.341925 & 2.6485 & 0.005158 \tabularnewline
11 & 0.289011 & 2.2387 & 0.014449 \tabularnewline
12 & 0.235125 & 1.8213 & 0.036776 \tabularnewline
13 & 0.201377 & 1.5599 & 0.062026 \tabularnewline
14 & 0.175797 & 1.3617 & 0.089189 \tabularnewline
15 & 0.142631 & 1.1048 & 0.136826 \tabularnewline
16 & 0.110981 & 0.8597 & 0.196701 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7998&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]0.929646[/C][C]7.201[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.865138[/C][C]6.7013[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.820736[/C][C]6.3574[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.76137[/C][C]5.8975[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.682562[/C][C]5.2871[/C][C]1e-06[/C][/ROW]
[ROW][C]6[/C][C]0.61574[/C][C]4.7695[/C][C]6e-06[/C][/ROW]
[ROW][C]7[/C][C]0.557221[/C][C]4.3162[/C][C]3e-05[/C][/ROW]
[ROW][C]8[/C][C]0.464017[/C][C]3.5943[/C][C]0.000329[/C][/ROW]
[ROW][C]9[/C][C]0.393426[/C][C]3.0475[/C][C]0.001714[/C][/ROW]
[ROW][C]10[/C][C]0.341925[/C][C]2.6485[/C][C]0.005158[/C][/ROW]
[ROW][C]11[/C][C]0.289011[/C][C]2.2387[/C][C]0.014449[/C][/ROW]
[ROW][C]12[/C][C]0.235125[/C][C]1.8213[/C][C]0.036776[/C][/ROW]
[ROW][C]13[/C][C]0.201377[/C][C]1.5599[/C][C]0.062026[/C][/ROW]
[ROW][C]14[/C][C]0.175797[/C][C]1.3617[/C][C]0.089189[/C][/ROW]
[ROW][C]15[/C][C]0.142631[/C][C]1.1048[/C][C]0.136826[/C][/ROW]
[ROW][C]16[/C][C]0.110981[/C][C]0.8597[/C][C]0.196701[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7998&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7998&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	0.929646	7.201	0
2	0.865138	6.7013	0
3	0.820736	6.3574	0
4	0.76137	5.8975	0
5	0.682562	5.2871	1e-06
6	0.61574	4.7695	6e-06
7	0.557221	4.3162	3e-05
8	0.464017	3.5943	0.000329
9	0.393426	3.0475	0.001714
10	0.341925	2.6485	0.005158
11	0.289011	2.2387	0.014449
12	0.235125	1.8213	0.036776
13	0.201377	1.5599	0.062026
14	0.175797	1.3617	0.089189
15	0.142631	1.1048	0.136826
16	0.110981	0.8597	0.196701

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.929646	7.201	0
1	0.006604	0.0512	0.479685
2	0.115182	0.8922	0.187926
3	-0.124869	-0.9672	0.831345
4	-0.167444	-1.297	0.900204
5	0.00542	0.042	0.483327
6	0.001105	0.0086	0.496599
7	-0.259418	-2.0094	0.975503
8	0.121042	0.9376	0.176109
9	0.028713	0.2224	0.412376
10	0.02491	0.193	0.423824
11	0.017802	0.1379	0.445394
12	0.051204	0.3966	0.346525
13	0.002591	0.0201	0.492028
14	0.009313	0.0721	0.471366
15	-0.104018	-0.8057	0.788206
16	0.02829	0.2191	0.413645

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.929646 & 7.201 & 0 \tabularnewline
1 & 0.006604 & 0.0512 & 0.479685 \tabularnewline
2 & 0.115182 & 0.8922 & 0.187926 \tabularnewline
3 & -0.124869 & -0.9672 & 0.831345 \tabularnewline
4 & -0.167444 & -1.297 & 0.900204 \tabularnewline
5 & 0.00542 & 0.042 & 0.483327 \tabularnewline
6 & 0.001105 & 0.0086 & 0.496599 \tabularnewline
7 & -0.259418 & -2.0094 & 0.975503 \tabularnewline
8 & 0.121042 & 0.9376 & 0.176109 \tabularnewline
9 & 0.028713 & 0.2224 & 0.412376 \tabularnewline
10 & 0.02491 & 0.193 & 0.423824 \tabularnewline
11 & 0.017802 & 0.1379 & 0.445394 \tabularnewline
12 & 0.051204 & 0.3966 & 0.346525 \tabularnewline
13 & 0.002591 & 0.0201 & 0.492028 \tabularnewline
14 & 0.009313 & 0.0721 & 0.471366 \tabularnewline
15 & -0.104018 & -0.8057 & 0.788206 \tabularnewline
16 & 0.02829 & 0.2191 & 0.413645 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7998&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]0.929646[/C][C]7.201[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.006604[/C][C]0.0512[/C][C]0.479685[/C][/ROW]
[ROW][C]2[/C][C]0.115182[/C][C]0.8922[/C][C]0.187926[/C][/ROW]
[ROW][C]3[/C][C]-0.124869[/C][C]-0.9672[/C][C]0.831345[/C][/ROW]
[ROW][C]4[/C][C]-0.167444[/C][C]-1.297[/C][C]0.900204[/C][/ROW]
[ROW][C]5[/C][C]0.00542[/C][C]0.042[/C][C]0.483327[/C][/ROW]
[ROW][C]6[/C][C]0.001105[/C][C]0.0086[/C][C]0.496599[/C][/ROW]
[ROW][C]7[/C][C]-0.259418[/C][C]-2.0094[/C][C]0.975503[/C][/ROW]
[ROW][C]8[/C][C]0.121042[/C][C]0.9376[/C][C]0.176109[/C][/ROW]
[ROW][C]9[/C][C]0.028713[/C][C]0.2224[/C][C]0.412376[/C][/ROW]
[ROW][C]10[/C][C]0.02491[/C][C]0.193[/C][C]0.423824[/C][/ROW]
[ROW][C]11[/C][C]0.017802[/C][C]0.1379[/C][C]0.445394[/C][/ROW]
[ROW][C]12[/C][C]0.051204[/C][C]0.3966[/C][C]0.346525[/C][/ROW]
[ROW][C]13[/C][C]0.002591[/C][C]0.0201[/C][C]0.492028[/C][/ROW]
[ROW][C]14[/C][C]0.009313[/C][C]0.0721[/C][C]0.471366[/C][/ROW]
[ROW][C]15[/C][C]-0.104018[/C][C]-0.8057[/C][C]0.788206[/C][/ROW]
[ROW][C]16[/C][C]0.02829[/C][C]0.2191[/C][C]0.413645[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7998&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7998&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	0.929646	7.201	0
1	0.006604	0.0512	0.479685
2	0.115182	0.8922	0.187926
3	-0.124869	-0.9672	0.831345
4	-0.167444	-1.297	0.900204
5	0.00542	0.042	0.483327
6	0.001105	0.0086	0.496599
7	-0.259418	-2.0094	0.975503
8	0.121042	0.9376	0.176109
9	0.028713	0.2224	0.412376
10	0.02491	0.193	0.423824
11	0.017802	0.1379	0.445394
12	0.051204	0.3966	0.346525
13	0.002591	0.0201	0.492028
14	0.009313	0.0721	0.471366
15	-0.104018	-0.8057	0.788206
16	0.02829	0.2191	0.413645

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)

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Input Parameters & R Code