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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 21 Oct 2015 18:01:40 +0100

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/2015/Oct/21/t14454469273fz8go3k3nycyjy.htm/, Retrieved Wed, 15 May 2024 09:38:14 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=282741, Retrieved Wed, 15 May 2024 09:38:14 +0000

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Estimated Impact

107

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

-     [(Partial) Autocorrelation Function] [] [2015-10-21 16:56:24] [553dab97a9d8b6d0026004b85d73532b]
-   PD    [(Partial) Autocorrelation Function] [] [2015-10-21 17:01:40] [a9d02bc5e77e4ed95e8bc9cdb21bd9af] [Current]
- R P       [(Partial) Autocorrelation Function] [] [2015-10-21 17:03:42] [553dab97a9d8b6d0026004b85d73532b] 

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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	'George Udny Yule' @ yule.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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282741&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282741&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282741&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	'George Udny Yule' @ yule.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.351584	-3.2031	0.000964
2	-0.129784	-1.1824	0.120214
3	-0.000264	-0.0024	0.499043
4	0.108172	0.9855	0.163623
5	-0.134902	-1.229	0.111269
6	0.283163	2.5797	0.005825
7	-0.271735	-2.4756	0.007667
8	0.221118	2.0145	0.023599
9	-0.035537	-0.3238	0.373468
10	-0.217012	-1.9771	0.025677
11	-0.14595	-1.3297	0.093636
12	0.578589	5.2712	1e-06
13	-0.297092	-2.7066	0.004125
14	0.033828	0.3082	0.379355
15	-0.155344	-1.4152	0.080368
16	0.045333	0.413	0.340336
17	-0.046396	-0.4227	0.336808
18	0.211982	1.9312	0.028433
19	-0.255791	-2.3304	0.011107

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.351584 & -3.2031 & 0.000964 \tabularnewline
2 & -0.129784 & -1.1824 & 0.120214 \tabularnewline
3 & -0.000264 & -0.0024 & 0.499043 \tabularnewline
4 & 0.108172 & 0.9855 & 0.163623 \tabularnewline
5 & -0.134902 & -1.229 & 0.111269 \tabularnewline
6 & 0.283163 & 2.5797 & 0.005825 \tabularnewline
7 & -0.271735 & -2.4756 & 0.007667 \tabularnewline
8 & 0.221118 & 2.0145 & 0.023599 \tabularnewline
9 & -0.035537 & -0.3238 & 0.373468 \tabularnewline
10 & -0.217012 & -1.9771 & 0.025677 \tabularnewline
11 & -0.14595 & -1.3297 & 0.093636 \tabularnewline
12 & 0.578589 & 5.2712 & 1e-06 \tabularnewline
13 & -0.297092 & -2.7066 & 0.004125 \tabularnewline
14 & 0.033828 & 0.3082 & 0.379355 \tabularnewline
15 & -0.155344 & -1.4152 & 0.080368 \tabularnewline
16 & 0.045333 & 0.413 & 0.340336 \tabularnewline
17 & -0.046396 & -0.4227 & 0.336808 \tabularnewline
18 & 0.211982 & 1.9312 & 0.028433 \tabularnewline
19 & -0.255791 & -2.3304 & 0.011107 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282741&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]-0.351584[/C][C]-3.2031[/C][C]0.000964[/C][/ROW]
[ROW][C]2[/C][C]-0.129784[/C][C]-1.1824[/C][C]0.120214[/C][/ROW]
[ROW][C]3[/C][C]-0.000264[/C][C]-0.0024[/C][C]0.499043[/C][/ROW]
[ROW][C]4[/C][C]0.108172[/C][C]0.9855[/C][C]0.163623[/C][/ROW]
[ROW][C]5[/C][C]-0.134902[/C][C]-1.229[/C][C]0.111269[/C][/ROW]
[ROW][C]6[/C][C]0.283163[/C][C]2.5797[/C][C]0.005825[/C][/ROW]
[ROW][C]7[/C][C]-0.271735[/C][C]-2.4756[/C][C]0.007667[/C][/ROW]
[ROW][C]8[/C][C]0.221118[/C][C]2.0145[/C][C]0.023599[/C][/ROW]
[ROW][C]9[/C][C]-0.035537[/C][C]-0.3238[/C][C]0.373468[/C][/ROW]
[ROW][C]10[/C][C]-0.217012[/C][C]-1.9771[/C][C]0.025677[/C][/ROW]
[ROW][C]11[/C][C]-0.14595[/C][C]-1.3297[/C][C]0.093636[/C][/ROW]
[ROW][C]12[/C][C]0.578589[/C][C]5.2712[/C][C]1e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.297092[/C][C]-2.7066[/C][C]0.004125[/C][/ROW]
[ROW][C]14[/C][C]0.033828[/C][C]0.3082[/C][C]0.379355[/C][/ROW]
[ROW][C]15[/C][C]-0.155344[/C][C]-1.4152[/C][C]0.080368[/C][/ROW]
[ROW][C]16[/C][C]0.045333[/C][C]0.413[/C][C]0.340336[/C][/ROW]
[ROW][C]17[/C][C]-0.046396[/C][C]-0.4227[/C][C]0.336808[/C][/ROW]
[ROW][C]18[/C][C]0.211982[/C][C]1.9312[/C][C]0.028433[/C][/ROW]
[ROW][C]19[/C][C]-0.255791[/C][C]-2.3304[/C][C]0.011107[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282741&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282741&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	-0.351584	-3.2031	0.000964
2	-0.129784	-1.1824	0.120214
3	-0.000264	-0.0024	0.499043
4	0.108172	0.9855	0.163623
5	-0.134902	-1.229	0.111269
6	0.283163	2.5797	0.005825
7	-0.271735	-2.4756	0.007667
8	0.221118	2.0145	0.023599
9	-0.035537	-0.3238	0.373468
10	-0.217012	-1.9771	0.025677
11	-0.14595	-1.3297	0.093636
12	0.578589	5.2712	1e-06
13	-0.297092	-2.7066	0.004125
14	0.033828	0.3082	0.379355
15	-0.155344	-1.4152	0.080368
16	0.045333	0.413	0.340336
17	-0.046396	-0.4227	0.336808
18	0.211982	1.9312	0.028433
19	-0.255791	-2.3304	0.011107

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.351584	-3.2031	0.000964
2	-0.289136	-2.6342	0.00503
3	-0.200148	-1.8234	0.035919
4	-0.015086	-0.1374	0.445508
5	-0.144881	-1.3199	0.095244
6	0.259536	2.3645	0.010195
7	-0.111057	-1.0118	0.157292
8	0.247962	2.259	0.013251
9	0.115831	1.0553	0.147182
10	-0.231952	-2.1132	0.018794
11	-0.362674	-3.3041	0.000704
12	0.292362	2.6635	0.004643
13	0.033659	0.3066	0.37994
14	0.095634	0.8713	0.193061
15	-0.143217	-1.3048	0.097789
16	-0.101879	-0.9282	0.178007
17	-0.142946	-1.3023	0.098208
18	-0.002594	-0.0236	0.490601
19	0.0183	0.1667	0.433997

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.351584 & -3.2031 & 0.000964 \tabularnewline
2 & -0.289136 & -2.6342 & 0.00503 \tabularnewline
3 & -0.200148 & -1.8234 & 0.035919 \tabularnewline
4 & -0.015086 & -0.1374 & 0.445508 \tabularnewline
5 & -0.144881 & -1.3199 & 0.095244 \tabularnewline
6 & 0.259536 & 2.3645 & 0.010195 \tabularnewline
7 & -0.111057 & -1.0118 & 0.157292 \tabularnewline
8 & 0.247962 & 2.259 & 0.013251 \tabularnewline
9 & 0.115831 & 1.0553 & 0.147182 \tabularnewline
10 & -0.231952 & -2.1132 & 0.018794 \tabularnewline
11 & -0.362674 & -3.3041 & 0.000704 \tabularnewline
12 & 0.292362 & 2.6635 & 0.004643 \tabularnewline
13 & 0.033659 & 0.3066 & 0.37994 \tabularnewline
14 & 0.095634 & 0.8713 & 0.193061 \tabularnewline
15 & -0.143217 & -1.3048 & 0.097789 \tabularnewline
16 & -0.101879 & -0.9282 & 0.178007 \tabularnewline
17 & -0.142946 & -1.3023 & 0.098208 \tabularnewline
18 & -0.002594 & -0.0236 & 0.490601 \tabularnewline
19 & 0.0183 & 0.1667 & 0.433997 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282741&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]-0.351584[/C][C]-3.2031[/C][C]0.000964[/C][/ROW]
[ROW][C]2[/C][C]-0.289136[/C][C]-2.6342[/C][C]0.00503[/C][/ROW]
[ROW][C]3[/C][C]-0.200148[/C][C]-1.8234[/C][C]0.035919[/C][/ROW]
[ROW][C]4[/C][C]-0.015086[/C][C]-0.1374[/C][C]0.445508[/C][/ROW]
[ROW][C]5[/C][C]-0.144881[/C][C]-1.3199[/C][C]0.095244[/C][/ROW]
[ROW][C]6[/C][C]0.259536[/C][C]2.3645[/C][C]0.010195[/C][/ROW]
[ROW][C]7[/C][C]-0.111057[/C][C]-1.0118[/C][C]0.157292[/C][/ROW]
[ROW][C]8[/C][C]0.247962[/C][C]2.259[/C][C]0.013251[/C][/ROW]
[ROW][C]9[/C][C]0.115831[/C][C]1.0553[/C][C]0.147182[/C][/ROW]
[ROW][C]10[/C][C]-0.231952[/C][C]-2.1132[/C][C]0.018794[/C][/ROW]
[ROW][C]11[/C][C]-0.362674[/C][C]-3.3041[/C][C]0.000704[/C][/ROW]
[ROW][C]12[/C][C]0.292362[/C][C]2.6635[/C][C]0.004643[/C][/ROW]
[ROW][C]13[/C][C]0.033659[/C][C]0.3066[/C][C]0.37994[/C][/ROW]
[ROW][C]14[/C][C]0.095634[/C][C]0.8713[/C][C]0.193061[/C][/ROW]
[ROW][C]15[/C][C]-0.143217[/C][C]-1.3048[/C][C]0.097789[/C][/ROW]
[ROW][C]16[/C][C]-0.101879[/C][C]-0.9282[/C][C]0.178007[/C][/ROW]
[ROW][C]17[/C][C]-0.142946[/C][C]-1.3023[/C][C]0.098208[/C][/ROW]
[ROW][C]18[/C][C]-0.002594[/C][C]-0.0236[/C][C]0.490601[/C][/ROW]
[ROW][C]19[/C][C]0.0183[/C][C]0.1667[/C][C]0.433997[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282741&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282741&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	-0.351584	-3.2031	0.000964
2	-0.289136	-2.6342	0.00503
3	-0.200148	-1.8234	0.035919
4	-0.015086	-0.1374	0.445508
5	-0.144881	-1.3199	0.095244
6	0.259536	2.3645	0.010195
7	-0.111057	-1.0118	0.157292
8	0.247962	2.259	0.013251
9	0.115831	1.0553	0.147182
10	-0.231952	-2.1132	0.018794
11	-0.362674	-3.3041	0.000704
12	0.292362	2.6635	0.004643
13	0.033659	0.3066	0.37994
14	0.095634	0.8713	0.193061
15	-0.143217	-1.3048	0.097789
16	-0.101879	-0.9282	0.178007
17	-0.142946	-1.3023	0.098208
18	-0.002594	-0.0236	0.490601
19	0.0183	0.1667	0.433997

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