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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

Thu, 27 Nov 2008 15:37:06 -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/Nov/27/t1227825481m3rgq752buc8egd.htm/, Retrieved Sun, 19 May 2024 09:15:53 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=25934, Retrieved Sun, 19 May 2024 09:15:53 +0000

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Original text written by user:

d=0 D=0

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

166

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

F     [Law of Averages] [Random Walk Simul...] [2008-11-25 18:40:39] [b98453cac15ba1066b407e146608df68]
F       [Law of Averages] [Random Walk Simul...] [2008-11-27 19:45:04] [58bf45a666dc5198906262e8815a9722]
F RMPD    [Standard Deviation-Mean Plot] [Standard Deviatio...] [2008-11-27 22:08:29] [58bf45a666dc5198906262e8815a9722]
- RMPD        [(Partial) Autocorrelation Function] [(Partial) Autocor...] [2008-11-27 22:37:06] [63db34dadd44fb018112addcdefe949f] [Current]

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Summary of computational 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 computational 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=25934&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]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=25934&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25934&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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.346434	2.6835	0.004701
2	0.213002	1.6499	0.052094
3	0.446999	3.4624	0.000497
4	0.188409	1.4594	0.074834
5	0.208801	1.6174	0.055523
6	0.345383	2.6753	0.004804
7	0.062384	0.4832	0.315348
8	0.110897	0.859	0.196878
9	0.220724	1.7097	0.046242
10	0.017256	0.1337	0.447057
11	0.152712	1.1829	0.120756
12	0.421546	3.2653	0.000905
13	0.086096	0.6669	0.253696
14	0.021145	0.1638	0.435223
15	0.119499	0.9256	0.179173
16	-0.047195	-0.3656	0.357987
17	0.056425	0.4371	0.331815

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.346434 & 2.6835 & 0.004701 \tabularnewline
2 & 0.213002 & 1.6499 & 0.052094 \tabularnewline
3 & 0.446999 & 3.4624 & 0.000497 \tabularnewline
4 & 0.188409 & 1.4594 & 0.074834 \tabularnewline
5 & 0.208801 & 1.6174 & 0.055523 \tabularnewline
6 & 0.345383 & 2.6753 & 0.004804 \tabularnewline
7 & 0.062384 & 0.4832 & 0.315348 \tabularnewline
8 & 0.110897 & 0.859 & 0.196878 \tabularnewline
9 & 0.220724 & 1.7097 & 0.046242 \tabularnewline
10 & 0.017256 & 0.1337 & 0.447057 \tabularnewline
11 & 0.152712 & 1.1829 & 0.120756 \tabularnewline
12 & 0.421546 & 3.2653 & 0.000905 \tabularnewline
13 & 0.086096 & 0.6669 & 0.253696 \tabularnewline
14 & 0.021145 & 0.1638 & 0.435223 \tabularnewline
15 & 0.119499 & 0.9256 & 0.179173 \tabularnewline
16 & -0.047195 & -0.3656 & 0.357987 \tabularnewline
17 & 0.056425 & 0.4371 & 0.331815 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25934&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]0.346434[/C][C]2.6835[/C][C]0.004701[/C][/ROW]
[ROW][C]2[/C][C]0.213002[/C][C]1.6499[/C][C]0.052094[/C][/ROW]
[ROW][C]3[/C][C]0.446999[/C][C]3.4624[/C][C]0.000497[/C][/ROW]
[ROW][C]4[/C][C]0.188409[/C][C]1.4594[/C][C]0.074834[/C][/ROW]
[ROW][C]5[/C][C]0.208801[/C][C]1.6174[/C][C]0.055523[/C][/ROW]
[ROW][C]6[/C][C]0.345383[/C][C]2.6753[/C][C]0.004804[/C][/ROW]
[ROW][C]7[/C][C]0.062384[/C][C]0.4832[/C][C]0.315348[/C][/ROW]
[ROW][C]8[/C][C]0.110897[/C][C]0.859[/C][C]0.196878[/C][/ROW]
[ROW][C]9[/C][C]0.220724[/C][C]1.7097[/C][C]0.046242[/C][/ROW]
[ROW][C]10[/C][C]0.017256[/C][C]0.1337[/C][C]0.447057[/C][/ROW]
[ROW][C]11[/C][C]0.152712[/C][C]1.1829[/C][C]0.120756[/C][/ROW]
[ROW][C]12[/C][C]0.421546[/C][C]3.2653[/C][C]0.000905[/C][/ROW]
[ROW][C]13[/C][C]0.086096[/C][C]0.6669[/C][C]0.253696[/C][/ROW]
[ROW][C]14[/C][C]0.021145[/C][C]0.1638[/C][C]0.435223[/C][/ROW]
[ROW][C]15[/C][C]0.119499[/C][C]0.9256[/C][C]0.179173[/C][/ROW]
[ROW][C]16[/C][C]-0.047195[/C][C]-0.3656[/C][C]0.357987[/C][/ROW]
[ROW][C]17[/C][C]0.056425[/C][C]0.4371[/C][C]0.331815[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25934&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25934&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	0.346434	2.6835	0.004701
2	0.213002	1.6499	0.052094
3	0.446999	3.4624	0.000497
4	0.188409	1.4594	0.074834
5	0.208801	1.6174	0.055523
6	0.345383	2.6753	0.004804
7	0.062384	0.4832	0.315348
8	0.110897	0.859	0.196878
9	0.220724	1.7097	0.046242
10	0.017256	0.1337	0.447057
11	0.152712	1.1829	0.120756
12	0.421546	3.2653	0.000905
13	0.086096	0.6669	0.253696
14	0.021145	0.1638	0.435223
15	0.119499	0.9256	0.179173
16	-0.047195	-0.3656	0.357987
17	0.056425	0.4371	0.331815

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.346434	2.6835	0.004701
2	0.105667	0.8185	0.208157
3	0.395788	3.0658	0.001626
4	-0.088427	-0.6849	0.248007
5	0.139053	1.0771	0.142874
6	0.119035	0.922	0.1801
7	-0.151511	-1.1736	0.122597
8	0.031561	0.2445	0.403851
9	0.021035	0.1629	0.435559
10	-0.051663	-0.4002	0.345223
11	0.128192	0.993	0.162357
12	0.351228	2.7206	0.004257
13	-0.115635	-0.8957	0.186996
14	-0.164137	-1.2714	0.104246
15	-0.174242	-1.3497	0.091096
16	-0.088298	-0.684	0.248318
17	0.04308	0.3337	0.369886

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.346434 & 2.6835 & 0.004701 \tabularnewline
2 & 0.105667 & 0.8185 & 0.208157 \tabularnewline
3 & 0.395788 & 3.0658 & 0.001626 \tabularnewline
4 & -0.088427 & -0.6849 & 0.248007 \tabularnewline
5 & 0.139053 & 1.0771 & 0.142874 \tabularnewline
6 & 0.119035 & 0.922 & 0.1801 \tabularnewline
7 & -0.151511 & -1.1736 & 0.122597 \tabularnewline
8 & 0.031561 & 0.2445 & 0.403851 \tabularnewline
9 & 0.021035 & 0.1629 & 0.435559 \tabularnewline
10 & -0.051663 & -0.4002 & 0.345223 \tabularnewline
11 & 0.128192 & 0.993 & 0.162357 \tabularnewline
12 & 0.351228 & 2.7206 & 0.004257 \tabularnewline
13 & -0.115635 & -0.8957 & 0.186996 \tabularnewline
14 & -0.164137 & -1.2714 & 0.104246 \tabularnewline
15 & -0.174242 & -1.3497 & 0.091096 \tabularnewline
16 & -0.088298 & -0.684 & 0.248318 \tabularnewline
17 & 0.04308 & 0.3337 & 0.369886 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25934&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]0.346434[/C][C]2.6835[/C][C]0.004701[/C][/ROW]
[ROW][C]2[/C][C]0.105667[/C][C]0.8185[/C][C]0.208157[/C][/ROW]
[ROW][C]3[/C][C]0.395788[/C][C]3.0658[/C][C]0.001626[/C][/ROW]
[ROW][C]4[/C][C]-0.088427[/C][C]-0.6849[/C][C]0.248007[/C][/ROW]
[ROW][C]5[/C][C]0.139053[/C][C]1.0771[/C][C]0.142874[/C][/ROW]
[ROW][C]6[/C][C]0.119035[/C][C]0.922[/C][C]0.1801[/C][/ROW]
[ROW][C]7[/C][C]-0.151511[/C][C]-1.1736[/C][C]0.122597[/C][/ROW]
[ROW][C]8[/C][C]0.031561[/C][C]0.2445[/C][C]0.403851[/C][/ROW]
[ROW][C]9[/C][C]0.021035[/C][C]0.1629[/C][C]0.435559[/C][/ROW]
[ROW][C]10[/C][C]-0.051663[/C][C]-0.4002[/C][C]0.345223[/C][/ROW]
[ROW][C]11[/C][C]0.128192[/C][C]0.993[/C][C]0.162357[/C][/ROW]
[ROW][C]12[/C][C]0.351228[/C][C]2.7206[/C][C]0.004257[/C][/ROW]
[ROW][C]13[/C][C]-0.115635[/C][C]-0.8957[/C][C]0.186996[/C][/ROW]
[ROW][C]14[/C][C]-0.164137[/C][C]-1.2714[/C][C]0.104246[/C][/ROW]
[ROW][C]15[/C][C]-0.174242[/C][C]-1.3497[/C][C]0.091096[/C][/ROW]
[ROW][C]16[/C][C]-0.088298[/C][C]-0.684[/C][C]0.248318[/C][/ROW]
[ROW][C]17[/C][C]0.04308[/C][C]0.3337[/C][C]0.369886[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25934&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25934&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	0.346434	2.6835	0.004701
2	0.105667	0.8185	0.208157
3	0.395788	3.0658	0.001626
4	-0.088427	-0.6849	0.248007
5	0.139053	1.0771	0.142874
6	0.119035	0.922	0.1801
7	-0.151511	-1.1736	0.122597
8	0.031561	0.2445	0.403851
9	0.021035	0.1629	0.435559
10	-0.051663	-0.4002	0.345223
11	0.128192	0.993	0.162357
12	0.351228	2.7206	0.004257
13	-0.115635	-0.8957	0.186996
14	-0.164137	-1.2714	0.104246
15	-0.174242	-1.3497	0.091096
16	-0.088298	-0.684	0.248318
17	0.04308	0.3337	0.369886

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 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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code