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*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 25 Nov 2009 09:37:53 -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/2009/Nov/25/t12591672002epu9slq7rq808w.htm/, Retrieved Tue, 07 May 2024 11:07:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=59453, Retrieved Tue, 07 May 2024 11:07:10 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

126

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

-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [(Partial) Autocorrelation Function] [Identifying Integ...] [2009-11-22 12:16:10] [b98453cac15ba1066b407e146608df68]
- R PD          [(Partial) Autocorrelation Function] [Model 1 (autocorr...] [2009-11-25 16:37:53] [d5837f25ec8937f9733a894c487f865c] [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	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=59453&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=59453&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59453&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	0.945875	7.3267	0
2	0.888171	6.8797	0
3	0.834078	6.4607	0
4	0.767736	5.9469	0
5	0.708534	5.4883	0
6	0.652193	5.0519	2e-06
7	0.584738	4.5294	1.4e-05
8	0.507962	3.9347	0.00011
9	0.430284	3.333	0.000738
10	0.346113	2.681	0.004733
11	0.25715	1.9919	0.025471
12	0.186169	1.4421	0.077242

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.945875 & 7.3267 & 0 \tabularnewline
2 & 0.888171 & 6.8797 & 0 \tabularnewline
3 & 0.834078 & 6.4607 & 0 \tabularnewline
4 & 0.767736 & 5.9469 & 0 \tabularnewline
5 & 0.708534 & 5.4883 & 0 \tabularnewline
6 & 0.652193 & 5.0519 & 2e-06 \tabularnewline
7 & 0.584738 & 4.5294 & 1.4e-05 \tabularnewline
8 & 0.507962 & 3.9347 & 0.00011 \tabularnewline
9 & 0.430284 & 3.333 & 0.000738 \tabularnewline
10 & 0.346113 & 2.681 & 0.004733 \tabularnewline
11 & 0.25715 & 1.9919 & 0.025471 \tabularnewline
12 & 0.186169 & 1.4421 & 0.077242 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59453&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]0.945875[/C][C]7.3267[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.888171[/C][C]6.8797[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.834078[/C][C]6.4607[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.767736[/C][C]5.9469[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.708534[/C][C]5.4883[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.652193[/C][C]5.0519[/C][C]2e-06[/C][/ROW]
[ROW][C]7[/C][C]0.584738[/C][C]4.5294[/C][C]1.4e-05[/C][/ROW]
[ROW][C]8[/C][C]0.507962[/C][C]3.9347[/C][C]0.00011[/C][/ROW]
[ROW][C]9[/C][C]0.430284[/C][C]3.333[/C][C]0.000738[/C][/ROW]
[ROW][C]10[/C][C]0.346113[/C][C]2.681[/C][C]0.004733[/C][/ROW]
[ROW][C]11[/C][C]0.25715[/C][C]1.9919[/C][C]0.025471[/C][/ROW]
[ROW][C]12[/C][C]0.186169[/C][C]1.4421[/C][C]0.077242[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59453&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59453&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	0.945875	7.3267	0
2	0.888171	6.8797	0
3	0.834078	6.4607	0
4	0.767736	5.9469	0
5	0.708534	5.4883	0
6	0.652193	5.0519	2e-06
7	0.584738	4.5294	1.4e-05
8	0.507962	3.9347	0.00011
9	0.430284	3.333	0.000738
10	0.346113	2.681	0.004733
11	0.25715	1.9919	0.025471
12	0.186169	1.4421	0.077242

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.945875	7.3267	0
2	-0.061806	-0.4787	0.316929
3	0.00493	0.0382	0.484832
4	-0.148545	-1.1506	0.127225
5	0.040999	0.3176	0.375955
6	-0.021372	-0.1655	0.434536
7	-0.125199	-0.9698	0.168023
8	-0.142	-1.0999	0.137879
9	-0.062385	-0.4832	0.315345
10	-0.104013	-0.8057	0.211805
11	-0.106168	-0.8224	0.207061
12	0.089993	0.6971	0.244221

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.945875 & 7.3267 & 0 \tabularnewline
2 & -0.061806 & -0.4787 & 0.316929 \tabularnewline
3 & 0.00493 & 0.0382 & 0.484832 \tabularnewline
4 & -0.148545 & -1.1506 & 0.127225 \tabularnewline
5 & 0.040999 & 0.3176 & 0.375955 \tabularnewline
6 & -0.021372 & -0.1655 & 0.434536 \tabularnewline
7 & -0.125199 & -0.9698 & 0.168023 \tabularnewline
8 & -0.142 & -1.0999 & 0.137879 \tabularnewline
9 & -0.062385 & -0.4832 & 0.315345 \tabularnewline
10 & -0.104013 & -0.8057 & 0.211805 \tabularnewline
11 & -0.106168 & -0.8224 & 0.207061 \tabularnewline
12 & 0.089993 & 0.6971 & 0.244221 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59453&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]0.945875[/C][C]7.3267[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.061806[/C][C]-0.4787[/C][C]0.316929[/C][/ROW]
[ROW][C]3[/C][C]0.00493[/C][C]0.0382[/C][C]0.484832[/C][/ROW]
[ROW][C]4[/C][C]-0.148545[/C][C]-1.1506[/C][C]0.127225[/C][/ROW]
[ROW][C]5[/C][C]0.040999[/C][C]0.3176[/C][C]0.375955[/C][/ROW]
[ROW][C]6[/C][C]-0.021372[/C][C]-0.1655[/C][C]0.434536[/C][/ROW]
[ROW][C]7[/C][C]-0.125199[/C][C]-0.9698[/C][C]0.168023[/C][/ROW]
[ROW][C]8[/C][C]-0.142[/C][C]-1.0999[/C][C]0.137879[/C][/ROW]
[ROW][C]9[/C][C]-0.062385[/C][C]-0.4832[/C][C]0.315345[/C][/ROW]
[ROW][C]10[/C][C]-0.104013[/C][C]-0.8057[/C][C]0.211805[/C][/ROW]
[ROW][C]11[/C][C]-0.106168[/C][C]-0.8224[/C][C]0.207061[/C][/ROW]
[ROW][C]12[/C][C]0.089993[/C][C]0.6971[/C][C]0.244221[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59453&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59453&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	0.945875	7.3267	0
2	-0.061806	-0.4787	0.316929
3	0.00493	0.0382	0.484832
4	-0.148545	-1.1506	0.127225
5	0.040999	0.3176	0.375955
6	-0.021372	-0.1655	0.434536
7	-0.125199	-0.9698	0.168023
8	-0.142	-1.0999	0.137879
9	-0.062385	-0.4832	0.315345
10	-0.104013	-0.8057	0.211805
11	-0.106168	-0.8224	0.207061
12	0.089993	0.6971	0.244221

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 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 12 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

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 (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
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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Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code