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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 21 Dec 2010 14:55:55 +0000

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/2010/Dec/21/t1292943245kqqs6mcy64dc2mq.htm/, Retrieved Sat, 18 May 2024 02:54:06 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113640, Retrieved Sat, 18 May 2024 02:54:06 +0000

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User-defined keywords

Estimated Impact

121

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [Unemployment] [2010-11-29 09:05:21] [b98453cac15ba1066b407e146608df68]
- R  D    [(Partial) Autocorrelation Function] [Workshop 9; Coffe...] [2010-12-07 09:31:16] [8ffb4cfa64b4677df0d2c448735a40bb]
- R  D        [(Partial) Autocorrelation Function] [Paper; ACF Coffee...] [2010-12-21 14:55:55] [50e0b5177c9c80b42996aa89930b928a] [Current]
-   P           [(Partial) Autocorrelation Function] [Paper; ACF Coffee...] [2010-12-21 15:00:10] [8ffb4cfa64b4677df0d2c448735a40bb] 

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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	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113640&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113640&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113640&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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.896255	6.2094	0
2	0.792769	5.4925	1e-06
3	0.695811	4.8207	7e-06
4	0.643081	4.4554	2.5e-05
5	0.594228	4.1169	7.5e-05
6	0.552386	3.827	0.000187
7	0.511254	3.5421	0.000448
8	0.466344	3.2309	0.001115
9	0.425576	2.9485	0.00246
10	0.383767	2.6588	0.005312
11	0.338596	2.3459	0.011581
12	0.282503	1.9572	0.028074
13	0.222738	1.5432	0.064678
14	0.155831	1.0796	0.142852
15	0.083469	0.5783	0.282886
16	0.032283	0.2237	0.411984

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.896255 & 6.2094 & 0 \tabularnewline
2 & 0.792769 & 5.4925 & 1e-06 \tabularnewline
3 & 0.695811 & 4.8207 & 7e-06 \tabularnewline
4 & 0.643081 & 4.4554 & 2.5e-05 \tabularnewline
5 & 0.594228 & 4.1169 & 7.5e-05 \tabularnewline
6 & 0.552386 & 3.827 & 0.000187 \tabularnewline
7 & 0.511254 & 3.5421 & 0.000448 \tabularnewline
8 & 0.466344 & 3.2309 & 0.001115 \tabularnewline
9 & 0.425576 & 2.9485 & 0.00246 \tabularnewline
10 & 0.383767 & 2.6588 & 0.005312 \tabularnewline
11 & 0.338596 & 2.3459 & 0.011581 \tabularnewline
12 & 0.282503 & 1.9572 & 0.028074 \tabularnewline
13 & 0.222738 & 1.5432 & 0.064678 \tabularnewline
14 & 0.155831 & 1.0796 & 0.142852 \tabularnewline
15 & 0.083469 & 0.5783 & 0.282886 \tabularnewline
16 & 0.032283 & 0.2237 & 0.411984 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113640&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]0.896255[/C][C]6.2094[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.792769[/C][C]5.4925[/C][C]1e-06[/C][/ROW]
[ROW][C]3[/C][C]0.695811[/C][C]4.8207[/C][C]7e-06[/C][/ROW]
[ROW][C]4[/C][C]0.643081[/C][C]4.4554[/C][C]2.5e-05[/C][/ROW]
[ROW][C]5[/C][C]0.594228[/C][C]4.1169[/C][C]7.5e-05[/C][/ROW]
[ROW][C]6[/C][C]0.552386[/C][C]3.827[/C][C]0.000187[/C][/ROW]
[ROW][C]7[/C][C]0.511254[/C][C]3.5421[/C][C]0.000448[/C][/ROW]
[ROW][C]8[/C][C]0.466344[/C][C]3.2309[/C][C]0.001115[/C][/ROW]
[ROW][C]9[/C][C]0.425576[/C][C]2.9485[/C][C]0.00246[/C][/ROW]
[ROW][C]10[/C][C]0.383767[/C][C]2.6588[/C][C]0.005312[/C][/ROW]
[ROW][C]11[/C][C]0.338596[/C][C]2.3459[/C][C]0.011581[/C][/ROW]
[ROW][C]12[/C][C]0.282503[/C][C]1.9572[/C][C]0.028074[/C][/ROW]
[ROW][C]13[/C][C]0.222738[/C][C]1.5432[/C][C]0.064678[/C][/ROW]
[ROW][C]14[/C][C]0.155831[/C][C]1.0796[/C][C]0.142852[/C][/ROW]
[ROW][C]15[/C][C]0.083469[/C][C]0.5783[/C][C]0.282886[/C][/ROW]
[ROW][C]16[/C][C]0.032283[/C][C]0.2237[/C][C]0.411984[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113640&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113640&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	0.896255	6.2094	0
2	0.792769	5.4925	1e-06
3	0.695811	4.8207	7e-06
4	0.643081	4.4554	2.5e-05
5	0.594228	4.1169	7.5e-05
6	0.552386	3.827	0.000187
7	0.511254	3.5421	0.000448
8	0.466344	3.2309	0.001115
9	0.425576	2.9485	0.00246
10	0.383767	2.6588	0.005312
11	0.338596	2.3459	0.011581
12	0.282503	1.9572	0.028074
13	0.222738	1.5432	0.064678
14	0.155831	1.0796	0.142852
15	0.083469	0.5783	0.282886
16	0.032283	0.2237	0.411984

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.896255	6.2094	0
2	-0.05339	-0.3699	0.356542
3	-0.024445	-0.1694	0.433112
4	0.168367	1.1665	0.124591
5	-0.014984	-0.1038	0.458876
6	0.013683	0.0948	0.462435
7	0.020117	0.1394	0.444868
8	-0.039004	-0.2702	0.394071
9	0.009301	0.0644	0.474444
10	-0.02315	-0.1604	0.436623
11	-0.050853	-0.3523	0.363069
12	-0.077251	-0.5352	0.297488
13	-0.061939	-0.4291	0.334877
14	-0.093649	-0.6488	0.259773
15	-0.105894	-0.7337	0.233363
16	0.034618	0.2398	0.405738

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.896255 & 6.2094 & 0 \tabularnewline
2 & -0.05339 & -0.3699 & 0.356542 \tabularnewline
3 & -0.024445 & -0.1694 & 0.433112 \tabularnewline
4 & 0.168367 & 1.1665 & 0.124591 \tabularnewline
5 & -0.014984 & -0.1038 & 0.458876 \tabularnewline
6 & 0.013683 & 0.0948 & 0.462435 \tabularnewline
7 & 0.020117 & 0.1394 & 0.444868 \tabularnewline
8 & -0.039004 & -0.2702 & 0.394071 \tabularnewline
9 & 0.009301 & 0.0644 & 0.474444 \tabularnewline
10 & -0.02315 & -0.1604 & 0.436623 \tabularnewline
11 & -0.050853 & -0.3523 & 0.363069 \tabularnewline
12 & -0.077251 & -0.5352 & 0.297488 \tabularnewline
13 & -0.061939 & -0.4291 & 0.334877 \tabularnewline
14 & -0.093649 & -0.6488 & 0.259773 \tabularnewline
15 & -0.105894 & -0.7337 & 0.233363 \tabularnewline
16 & 0.034618 & 0.2398 & 0.405738 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113640&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]0.896255[/C][C]6.2094[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.05339[/C][C]-0.3699[/C][C]0.356542[/C][/ROW]
[ROW][C]3[/C][C]-0.024445[/C][C]-0.1694[/C][C]0.433112[/C][/ROW]
[ROW][C]4[/C][C]0.168367[/C][C]1.1665[/C][C]0.124591[/C][/ROW]
[ROW][C]5[/C][C]-0.014984[/C][C]-0.1038[/C][C]0.458876[/C][/ROW]
[ROW][C]6[/C][C]0.013683[/C][C]0.0948[/C][C]0.462435[/C][/ROW]
[ROW][C]7[/C][C]0.020117[/C][C]0.1394[/C][C]0.444868[/C][/ROW]
[ROW][C]8[/C][C]-0.039004[/C][C]-0.2702[/C][C]0.394071[/C][/ROW]
[ROW][C]9[/C][C]0.009301[/C][C]0.0644[/C][C]0.474444[/C][/ROW]
[ROW][C]10[/C][C]-0.02315[/C][C]-0.1604[/C][C]0.436623[/C][/ROW]
[ROW][C]11[/C][C]-0.050853[/C][C]-0.3523[/C][C]0.363069[/C][/ROW]
[ROW][C]12[/C][C]-0.077251[/C][C]-0.5352[/C][C]0.297488[/C][/ROW]
[ROW][C]13[/C][C]-0.061939[/C][C]-0.4291[/C][C]0.334877[/C][/ROW]
[ROW][C]14[/C][C]-0.093649[/C][C]-0.6488[/C][C]0.259773[/C][/ROW]
[ROW][C]15[/C][C]-0.105894[/C][C]-0.7337[/C][C]0.233363[/C][/ROW]
[ROW][C]16[/C][C]0.034618[/C][C]0.2398[/C][C]0.405738[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113640&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113640&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	0.896255	6.2094	0
2	-0.05339	-0.3699	0.356542
3	-0.024445	-0.1694	0.433112
4	0.168367	1.1665	0.124591
5	-0.014984	-0.1038	0.458876
6	0.013683	0.0948	0.462435
7	0.020117	0.1394	0.444868
8	-0.039004	-0.2702	0.394071
9	0.009301	0.0644	0.474444
10	-0.02315	-0.1604	0.436623
11	-0.050853	-0.3523	0.363069
12	-0.077251	-0.5352	0.297488
13	-0.061939	-0.4291	0.334877
14	-0.093649	-0.6488	0.259773
15	-0.105894	-0.7337	0.233363
16	0.034618	0.2398	0.405738

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

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 (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
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