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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 16 Mar 2014 07:27:36 -0400

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/2014/Mar/16/t1394969348vdn4eq2ugp3frzl.htm/, Retrieved Tue, 14 May 2024 07:46:18 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234272, Retrieved Tue, 14 May 2024 07:46:18 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

137

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

-       [(Partial) Autocorrelation Function] [] [2014-03-16 11:27:36] [73938b6dd5218abd99a1a1df7750ee20] [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	3 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

\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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234272&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234272&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234272&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	3 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.283078	2.579	0.005837
2	0.072604	0.6615	0.255077
3	0.041654	0.3795	0.35265
4	-0.049879	-0.4544	0.325358
5	0.115708	1.0542	0.147437
6	0.114231	1.0407	0.15052
7	-0.080336	-0.7319	0.233146
8	-0.069806	-0.636	0.263275
9	-0.010248	-0.0934	0.462919
10	0.073878	0.6731	0.25139
11	0.086354	0.7867	0.216843
12	0.061214	0.5577	0.289279
13	0.022365	0.2038	0.419521
14	-0.096796	-0.8819	0.190202
15	0.072137	0.6572	0.256437
16	-0.026774	-0.2439	0.403945
17	-0.072793	-0.6632	0.254529
18	-0.244083	-2.2237	0.014442
19	-0.179411	-1.6345	0.05297

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.283078 & 2.579 & 0.005837 \tabularnewline
2 & 0.072604 & 0.6615 & 0.255077 \tabularnewline
3 & 0.041654 & 0.3795 & 0.35265 \tabularnewline
4 & -0.049879 & -0.4544 & 0.325358 \tabularnewline
5 & 0.115708 & 1.0542 & 0.147437 \tabularnewline
6 & 0.114231 & 1.0407 & 0.15052 \tabularnewline
7 & -0.080336 & -0.7319 & 0.233146 \tabularnewline
8 & -0.069806 & -0.636 & 0.263275 \tabularnewline
9 & -0.010248 & -0.0934 & 0.462919 \tabularnewline
10 & 0.073878 & 0.6731 & 0.25139 \tabularnewline
11 & 0.086354 & 0.7867 & 0.216843 \tabularnewline
12 & 0.061214 & 0.5577 & 0.289279 \tabularnewline
13 & 0.022365 & 0.2038 & 0.419521 \tabularnewline
14 & -0.096796 & -0.8819 & 0.190202 \tabularnewline
15 & 0.072137 & 0.6572 & 0.256437 \tabularnewline
16 & -0.026774 & -0.2439 & 0.403945 \tabularnewline
17 & -0.072793 & -0.6632 & 0.254529 \tabularnewline
18 & -0.244083 & -2.2237 & 0.014442 \tabularnewline
19 & -0.179411 & -1.6345 & 0.05297 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234272&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]0.283078[/C][C]2.579[/C][C]0.005837[/C][/ROW]
[ROW][C]2[/C][C]0.072604[/C][C]0.6615[/C][C]0.255077[/C][/ROW]
[ROW][C]3[/C][C]0.041654[/C][C]0.3795[/C][C]0.35265[/C][/ROW]
[ROW][C]4[/C][C]-0.049879[/C][C]-0.4544[/C][C]0.325358[/C][/ROW]
[ROW][C]5[/C][C]0.115708[/C][C]1.0542[/C][C]0.147437[/C][/ROW]
[ROW][C]6[/C][C]0.114231[/C][C]1.0407[/C][C]0.15052[/C][/ROW]
[ROW][C]7[/C][C]-0.080336[/C][C]-0.7319[/C][C]0.233146[/C][/ROW]
[ROW][C]8[/C][C]-0.069806[/C][C]-0.636[/C][C]0.263275[/C][/ROW]
[ROW][C]9[/C][C]-0.010248[/C][C]-0.0934[/C][C]0.462919[/C][/ROW]
[ROW][C]10[/C][C]0.073878[/C][C]0.6731[/C][C]0.25139[/C][/ROW]
[ROW][C]11[/C][C]0.086354[/C][C]0.7867[/C][C]0.216843[/C][/ROW]
[ROW][C]12[/C][C]0.061214[/C][C]0.5577[/C][C]0.289279[/C][/ROW]
[ROW][C]13[/C][C]0.022365[/C][C]0.2038[/C][C]0.419521[/C][/ROW]
[ROW][C]14[/C][C]-0.096796[/C][C]-0.8819[/C][C]0.190202[/C][/ROW]
[ROW][C]15[/C][C]0.072137[/C][C]0.6572[/C][C]0.256437[/C][/ROW]
[ROW][C]16[/C][C]-0.026774[/C][C]-0.2439[/C][C]0.403945[/C][/ROW]
[ROW][C]17[/C][C]-0.072793[/C][C]-0.6632[/C][C]0.254529[/C][/ROW]
[ROW][C]18[/C][C]-0.244083[/C][C]-2.2237[/C][C]0.014442[/C][/ROW]
[ROW][C]19[/C][C]-0.179411[/C][C]-1.6345[/C][C]0.05297[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234272&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234272&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	0.283078	2.579	0.005837
2	0.072604	0.6615	0.255077
3	0.041654	0.3795	0.35265
4	-0.049879	-0.4544	0.325358
5	0.115708	1.0542	0.147437
6	0.114231	1.0407	0.15052
7	-0.080336	-0.7319	0.233146
8	-0.069806	-0.636	0.263275
9	-0.010248	-0.0934	0.462919
10	0.073878	0.6731	0.25139
11	0.086354	0.7867	0.216843
12	0.061214	0.5577	0.289279
13	0.022365	0.2038	0.419521
14	-0.096796	-0.8819	0.190202
15	0.072137	0.6572	0.256437
16	-0.026774	-0.2439	0.403945
17	-0.072793	-0.6632	0.254529
18	-0.244083	-2.2237	0.014442
19	-0.179411	-1.6345	0.05297

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.283078	2.579	0.005837
2	-0.008185	-0.0746	0.470368
3	0.025277	0.2303	0.409219
4	-0.073772	-0.6721	0.251696
5	0.162165	1.4774	0.071678
6	0.044012	0.401	0.344737
7	-0.143534	-1.3077	0.097299
8	-0.03089	-0.2814	0.389543
9	0.048871	0.4452	0.328655
10	0.087413	0.7964	0.214045
11	-0.001009	-0.0092	0.496345
12	0.038394	0.3498	0.363692
13	0.029214	0.2662	0.395391
14	-0.12189	-1.1105	0.135001
15	0.117222	1.0679	0.144322
16	-0.107853	-0.9826	0.164333
17	-0.037659	-0.3431	0.3662
18	-0.277576	-2.5288	0.006668
19	0.035564	0.324	0.373374

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.283078 & 2.579 & 0.005837 \tabularnewline
2 & -0.008185 & -0.0746 & 0.470368 \tabularnewline
3 & 0.025277 & 0.2303 & 0.409219 \tabularnewline
4 & -0.073772 & -0.6721 & 0.251696 \tabularnewline
5 & 0.162165 & 1.4774 & 0.071678 \tabularnewline
6 & 0.044012 & 0.401 & 0.344737 \tabularnewline
7 & -0.143534 & -1.3077 & 0.097299 \tabularnewline
8 & -0.03089 & -0.2814 & 0.389543 \tabularnewline
9 & 0.048871 & 0.4452 & 0.328655 \tabularnewline
10 & 0.087413 & 0.7964 & 0.214045 \tabularnewline
11 & -0.001009 & -0.0092 & 0.496345 \tabularnewline
12 & 0.038394 & 0.3498 & 0.363692 \tabularnewline
13 & 0.029214 & 0.2662 & 0.395391 \tabularnewline
14 & -0.12189 & -1.1105 & 0.135001 \tabularnewline
15 & 0.117222 & 1.0679 & 0.144322 \tabularnewline
16 & -0.107853 & -0.9826 & 0.164333 \tabularnewline
17 & -0.037659 & -0.3431 & 0.3662 \tabularnewline
18 & -0.277576 & -2.5288 & 0.006668 \tabularnewline
19 & 0.035564 & 0.324 & 0.373374 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234272&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]0.283078[/C][C]2.579[/C][C]0.005837[/C][/ROW]
[ROW][C]2[/C][C]-0.008185[/C][C]-0.0746[/C][C]0.470368[/C][/ROW]
[ROW][C]3[/C][C]0.025277[/C][C]0.2303[/C][C]0.409219[/C][/ROW]
[ROW][C]4[/C][C]-0.073772[/C][C]-0.6721[/C][C]0.251696[/C][/ROW]
[ROW][C]5[/C][C]0.162165[/C][C]1.4774[/C][C]0.071678[/C][/ROW]
[ROW][C]6[/C][C]0.044012[/C][C]0.401[/C][C]0.344737[/C][/ROW]
[ROW][C]7[/C][C]-0.143534[/C][C]-1.3077[/C][C]0.097299[/C][/ROW]
[ROW][C]8[/C][C]-0.03089[/C][C]-0.2814[/C][C]0.389543[/C][/ROW]
[ROW][C]9[/C][C]0.048871[/C][C]0.4452[/C][C]0.328655[/C][/ROW]
[ROW][C]10[/C][C]0.087413[/C][C]0.7964[/C][C]0.214045[/C][/ROW]
[ROW][C]11[/C][C]-0.001009[/C][C]-0.0092[/C][C]0.496345[/C][/ROW]
[ROW][C]12[/C][C]0.038394[/C][C]0.3498[/C][C]0.363692[/C][/ROW]
[ROW][C]13[/C][C]0.029214[/C][C]0.2662[/C][C]0.395391[/C][/ROW]
[ROW][C]14[/C][C]-0.12189[/C][C]-1.1105[/C][C]0.135001[/C][/ROW]
[ROW][C]15[/C][C]0.117222[/C][C]1.0679[/C][C]0.144322[/C][/ROW]
[ROW][C]16[/C][C]-0.107853[/C][C]-0.9826[/C][C]0.164333[/C][/ROW]
[ROW][C]17[/C][C]-0.037659[/C][C]-0.3431[/C][C]0.3662[/C][/ROW]
[ROW][C]18[/C][C]-0.277576[/C][C]-2.5288[/C][C]0.006668[/C][/ROW]
[ROW][C]19[/C][C]0.035564[/C][C]0.324[/C][C]0.373374[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234272&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234272&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	0.283078	2.579	0.005837
2	-0.008185	-0.0746	0.470368
3	0.025277	0.2303	0.409219
4	-0.073772	-0.6721	0.251696
5	0.162165	1.4774	0.071678
6	0.044012	0.401	0.344737
7	-0.143534	-1.3077	0.097299
8	-0.03089	-0.2814	0.389543
9	0.048871	0.4452	0.328655
10	0.087413	0.7964	0.214045
11	-0.001009	-0.0092	0.496345
12	0.038394	0.3498	0.363692
13	0.029214	0.2662	0.395391
14	-0.12189	-1.1105	0.135001
15	0.117222	1.0679	0.144322
16	-0.107853	-0.9826	0.164333
17	-0.037659	-0.3431	0.3662
18	-0.277576	-2.5288	0.006668
19	0.035564	0.324	0.373374

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 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code