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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 06:35:58 -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/t13949662227tdxsjetjafllua.htm/, Retrieved Tue, 14 May 2024 00:52:58 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234264, Retrieved Tue, 14 May 2024 00:52:58 +0000

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No (this computation is public)

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Estimated Impact

147

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

-       [(Partial) Autocorrelation Function] [] [2014-03-16 10:35:58] [7924821bfd3c647737470140bc76edc8] [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	4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234264&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]4 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=234264&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234264&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	4 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.959872	14.1072	0
2	0.9128	13.4154	0
3	0.864395	12.704	0
4	0.825496	12.1323	0
5	0.795826	11.6962	0
6	0.773005	11.3608	0
7	0.751732	11.0482	0
8	0.734555	10.7957	0
9	0.724025	10.6409	0
10	0.722877	10.6241	0
11	0.719786	10.5787	0
12	0.710819	10.4469	0
13	0.679038	9.9798	0
14	0.639058	9.3922	0
15	0.600868	8.8309	0
16	0.567293	8.3375	0
17	0.542791	7.9774	0
18	0.525807	7.7277	0
19	0.517152	7.6006	0
20	0.520946	7.6563	0
21	0.530096	7.7908	0
22	0.543537	7.9883	0
23	0.554796	8.1538	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.959872 & 14.1072 & 0 \tabularnewline
2 & 0.9128 & 13.4154 & 0 \tabularnewline
3 & 0.864395 & 12.704 & 0 \tabularnewline
4 & 0.825496 & 12.1323 & 0 \tabularnewline
5 & 0.795826 & 11.6962 & 0 \tabularnewline
6 & 0.773005 & 11.3608 & 0 \tabularnewline
7 & 0.751732 & 11.0482 & 0 \tabularnewline
8 & 0.734555 & 10.7957 & 0 \tabularnewline
9 & 0.724025 & 10.6409 & 0 \tabularnewline
10 & 0.722877 & 10.6241 & 0 \tabularnewline
11 & 0.719786 & 10.5787 & 0 \tabularnewline
12 & 0.710819 & 10.4469 & 0 \tabularnewline
13 & 0.679038 & 9.9798 & 0 \tabularnewline
14 & 0.639058 & 9.3922 & 0 \tabularnewline
15 & 0.600868 & 8.8309 & 0 \tabularnewline
16 & 0.567293 & 8.3375 & 0 \tabularnewline
17 & 0.542791 & 7.9774 & 0 \tabularnewline
18 & 0.525807 & 7.7277 & 0 \tabularnewline
19 & 0.517152 & 7.6006 & 0 \tabularnewline
20 & 0.520946 & 7.6563 & 0 \tabularnewline
21 & 0.530096 & 7.7908 & 0 \tabularnewline
22 & 0.543537 & 7.9883 & 0 \tabularnewline
23 & 0.554796 & 8.1538 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234264&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]0.959872[/C][C]14.1072[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.9128[/C][C]13.4154[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.864395[/C][C]12.704[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.825496[/C][C]12.1323[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.795826[/C][C]11.6962[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.773005[/C][C]11.3608[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.751732[/C][C]11.0482[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.734555[/C][C]10.7957[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.724025[/C][C]10.6409[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.722877[/C][C]10.6241[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.719786[/C][C]10.5787[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.710819[/C][C]10.4469[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.679038[/C][C]9.9798[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.639058[/C][C]9.3922[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.600868[/C][C]8.8309[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.567293[/C][C]8.3375[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.542791[/C][C]7.9774[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.525807[/C][C]7.7277[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.517152[/C][C]7.6006[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.520946[/C][C]7.6563[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.530096[/C][C]7.7908[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]0.543537[/C][C]7.9883[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]0.554796[/C][C]8.1538[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234264&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234264&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	0.959872	14.1072	0
2	0.9128	13.4154	0
3	0.864395	12.704	0
4	0.825496	12.1323	0
5	0.795826	11.6962	0
6	0.773005	11.3608	0
7	0.751732	11.0482	0
8	0.734555	10.7957	0
9	0.724025	10.6409	0
10	0.722877	10.6241	0
11	0.719786	10.5787	0
12	0.710819	10.4469	0
13	0.679038	9.9798	0
14	0.639058	9.3922	0
15	0.600868	8.8309	0
16	0.567293	8.3375	0
17	0.542791	7.9774	0
18	0.525807	7.7277	0
19	0.517152	7.6006	0
20	0.520946	7.6563	0
21	0.530096	7.7908	0
22	0.543537	7.9883	0
23	0.554796	8.1538	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.959872	14.1072	0
2	-0.108773	-1.5986	0.055683
3	-0.034374	-0.5052	0.306968
4	0.098659	1.45	0.074257
5	0.077835	1.1439	0.12696
6	0.049648	0.7297	0.233191
7	0.003201	0.047	0.481259
8	0.058435	0.8588	0.195696
9	0.09453	1.3893	0.083085
10	0.12095	1.7776	0.038439
11	-0.024067	-0.3537	0.361948
12	-0.044678	-0.6566	0.256057
13	-0.244772	-3.5974	0.000199
14	-0.059514	-0.8747	0.191361
15	0.028933	0.4252	0.335547
16	-0.016492	-0.2424	0.404359
17	0.041883	0.6156	0.269417
18	0.046012	0.6762	0.249808
19	0.096439	1.4174	0.078909
20	0.152563	2.2422	0.012982
21	0.043385	0.6376	0.262198
22	0.036853	0.5416	0.294319
23	0.034701	0.51	0.305285

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.959872 & 14.1072 & 0 \tabularnewline
2 & -0.108773 & -1.5986 & 0.055683 \tabularnewline
3 & -0.034374 & -0.5052 & 0.306968 \tabularnewline
4 & 0.098659 & 1.45 & 0.074257 \tabularnewline
5 & 0.077835 & 1.1439 & 0.12696 \tabularnewline
6 & 0.049648 & 0.7297 & 0.233191 \tabularnewline
7 & 0.003201 & 0.047 & 0.481259 \tabularnewline
8 & 0.058435 & 0.8588 & 0.195696 \tabularnewline
9 & 0.09453 & 1.3893 & 0.083085 \tabularnewline
10 & 0.12095 & 1.7776 & 0.038439 \tabularnewline
11 & -0.024067 & -0.3537 & 0.361948 \tabularnewline
12 & -0.044678 & -0.6566 & 0.256057 \tabularnewline
13 & -0.244772 & -3.5974 & 0.000199 \tabularnewline
14 & -0.059514 & -0.8747 & 0.191361 \tabularnewline
15 & 0.028933 & 0.4252 & 0.335547 \tabularnewline
16 & -0.016492 & -0.2424 & 0.404359 \tabularnewline
17 & 0.041883 & 0.6156 & 0.269417 \tabularnewline
18 & 0.046012 & 0.6762 & 0.249808 \tabularnewline
19 & 0.096439 & 1.4174 & 0.078909 \tabularnewline
20 & 0.152563 & 2.2422 & 0.012982 \tabularnewline
21 & 0.043385 & 0.6376 & 0.262198 \tabularnewline
22 & 0.036853 & 0.5416 & 0.294319 \tabularnewline
23 & 0.034701 & 0.51 & 0.305285 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234264&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]0.959872[/C][C]14.1072[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.108773[/C][C]-1.5986[/C][C]0.055683[/C][/ROW]
[ROW][C]3[/C][C]-0.034374[/C][C]-0.5052[/C][C]0.306968[/C][/ROW]
[ROW][C]4[/C][C]0.098659[/C][C]1.45[/C][C]0.074257[/C][/ROW]
[ROW][C]5[/C][C]0.077835[/C][C]1.1439[/C][C]0.12696[/C][/ROW]
[ROW][C]6[/C][C]0.049648[/C][C]0.7297[/C][C]0.233191[/C][/ROW]
[ROW][C]7[/C][C]0.003201[/C][C]0.047[/C][C]0.481259[/C][/ROW]
[ROW][C]8[/C][C]0.058435[/C][C]0.8588[/C][C]0.195696[/C][/ROW]
[ROW][C]9[/C][C]0.09453[/C][C]1.3893[/C][C]0.083085[/C][/ROW]
[ROW][C]10[/C][C]0.12095[/C][C]1.7776[/C][C]0.038439[/C][/ROW]
[ROW][C]11[/C][C]-0.024067[/C][C]-0.3537[/C][C]0.361948[/C][/ROW]
[ROW][C]12[/C][C]-0.044678[/C][C]-0.6566[/C][C]0.256057[/C][/ROW]
[ROW][C]13[/C][C]-0.244772[/C][C]-3.5974[/C][C]0.000199[/C][/ROW]
[ROW][C]14[/C][C]-0.059514[/C][C]-0.8747[/C][C]0.191361[/C][/ROW]
[ROW][C]15[/C][C]0.028933[/C][C]0.4252[/C][C]0.335547[/C][/ROW]
[ROW][C]16[/C][C]-0.016492[/C][C]-0.2424[/C][C]0.404359[/C][/ROW]
[ROW][C]17[/C][C]0.041883[/C][C]0.6156[/C][C]0.269417[/C][/ROW]
[ROW][C]18[/C][C]0.046012[/C][C]0.6762[/C][C]0.249808[/C][/ROW]
[ROW][C]19[/C][C]0.096439[/C][C]1.4174[/C][C]0.078909[/C][/ROW]
[ROW][C]20[/C][C]0.152563[/C][C]2.2422[/C][C]0.012982[/C][/ROW]
[ROW][C]21[/C][C]0.043385[/C][C]0.6376[/C][C]0.262198[/C][/ROW]
[ROW][C]22[/C][C]0.036853[/C][C]0.5416[/C][C]0.294319[/C][/ROW]
[ROW][C]23[/C][C]0.034701[/C][C]0.51[/C][C]0.305285[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234264&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234264&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	0.959872	14.1072	0
2	-0.108773	-1.5986	0.055683
3	-0.034374	-0.5052	0.306968
4	0.098659	1.45	0.074257
5	0.077835	1.1439	0.12696
6	0.049648	0.7297	0.233191
7	0.003201	0.047	0.481259
8	0.058435	0.8588	0.195696
9	0.09453	1.3893	0.083085
10	0.12095	1.7776	0.038439
11	-0.024067	-0.3537	0.361948
12	-0.044678	-0.6566	0.256057
13	-0.244772	-3.5974	0.000199
14	-0.059514	-0.8747	0.191361
15	0.028933	0.4252	0.335547
16	-0.016492	-0.2424	0.404359
17	0.041883	0.6156	0.269417
18	0.046012	0.6762	0.249808
19	0.096439	1.4174	0.078909
20	0.152563	2.2422	0.012982
21	0.043385	0.6376	0.262198
22	0.036853	0.5416	0.294319
23	0.034701	0.51	0.305285

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')

Free Statistics

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code