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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 15 Mar 2016 11:36:29 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Mar/15/t14580418258dryvuxmwi199vf.htm/, Retrieved Tue, 30 Apr 2024 09:04:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294072, Retrieved Tue, 30 Apr 2024 09:04:35 +0000

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-     [(Partial) Autocorrelation Function] [] [2016-03-15 11:05:27] [eb84577074ca016fc26a8bcabc390030]
-    D    [(Partial) Autocorrelation Function] [] [2016-03-15 11:36:29] [73c24565f080d314e595da727a2003f4] [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	'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=294072&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=294072&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294072&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	-0.03651	-0.2804	0.390061
2	-0.017558	-0.1349	0.446587
3	-0.050778	-0.39	0.348957
4	0.082708	0.6353	0.263848
5	-0.117084	-0.8993	0.186063
6	0.064636	0.4965	0.310702
7	-0.110687	-0.8502	0.199326
8	0.051851	0.3983	0.345932
9	-0.082591	-0.6344	0.264138
10	-0.025676	-0.1972	0.422166
11	0.112159	0.8615	0.196222
12	0.306809	2.3566	0.01089
13	-0.018836	-0.1447	0.442727
14	8.3e-05	6e-04	0.499747
15	0.00624	0.0479	0.480966
16	0.03715	0.2854	0.388185
17	-0.128736	-0.9888	0.163389

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.03651 & -0.2804 & 0.390061 \tabularnewline
2 & -0.017558 & -0.1349 & 0.446587 \tabularnewline
3 & -0.050778 & -0.39 & 0.348957 \tabularnewline
4 & 0.082708 & 0.6353 & 0.263848 \tabularnewline
5 & -0.117084 & -0.8993 & 0.186063 \tabularnewline
6 & 0.064636 & 0.4965 & 0.310702 \tabularnewline
7 & -0.110687 & -0.8502 & 0.199326 \tabularnewline
8 & 0.051851 & 0.3983 & 0.345932 \tabularnewline
9 & -0.082591 & -0.6344 & 0.264138 \tabularnewline
10 & -0.025676 & -0.1972 & 0.422166 \tabularnewline
11 & 0.112159 & 0.8615 & 0.196222 \tabularnewline
12 & 0.306809 & 2.3566 & 0.01089 \tabularnewline
13 & -0.018836 & -0.1447 & 0.442727 \tabularnewline
14 & 8.3e-05 & 6e-04 & 0.499747 \tabularnewline
15 & 0.00624 & 0.0479 & 0.480966 \tabularnewline
16 & 0.03715 & 0.2854 & 0.388185 \tabularnewline
17 & -0.128736 & -0.9888 & 0.163389 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294072&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]-0.03651[/C][C]-0.2804[/C][C]0.390061[/C][/ROW]
[ROW][C]2[/C][C]-0.017558[/C][C]-0.1349[/C][C]0.446587[/C][/ROW]
[ROW][C]3[/C][C]-0.050778[/C][C]-0.39[/C][C]0.348957[/C][/ROW]
[ROW][C]4[/C][C]0.082708[/C][C]0.6353[/C][C]0.263848[/C][/ROW]
[ROW][C]5[/C][C]-0.117084[/C][C]-0.8993[/C][C]0.186063[/C][/ROW]
[ROW][C]6[/C][C]0.064636[/C][C]0.4965[/C][C]0.310702[/C][/ROW]
[ROW][C]7[/C][C]-0.110687[/C][C]-0.8502[/C][C]0.199326[/C][/ROW]
[ROW][C]8[/C][C]0.051851[/C][C]0.3983[/C][C]0.345932[/C][/ROW]
[ROW][C]9[/C][C]-0.082591[/C][C]-0.6344[/C][C]0.264138[/C][/ROW]
[ROW][C]10[/C][C]-0.025676[/C][C]-0.1972[/C][C]0.422166[/C][/ROW]
[ROW][C]11[/C][C]0.112159[/C][C]0.8615[/C][C]0.196222[/C][/ROW]
[ROW][C]12[/C][C]0.306809[/C][C]2.3566[/C][C]0.01089[/C][/ROW]
[ROW][C]13[/C][C]-0.018836[/C][C]-0.1447[/C][C]0.442727[/C][/ROW]
[ROW][C]14[/C][C]8.3e-05[/C][C]6e-04[/C][C]0.499747[/C][/ROW]
[ROW][C]15[/C][C]0.00624[/C][C]0.0479[/C][C]0.480966[/C][/ROW]
[ROW][C]16[/C][C]0.03715[/C][C]0.2854[/C][C]0.388185[/C][/ROW]
[ROW][C]17[/C][C]-0.128736[/C][C]-0.9888[/C][C]0.163389[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294072&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294072&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	-0.03651	-0.2804	0.390061
2	-0.017558	-0.1349	0.446587
3	-0.050778	-0.39	0.348957
4	0.082708	0.6353	0.263848
5	-0.117084	-0.8993	0.186063
6	0.064636	0.4965	0.310702
7	-0.110687	-0.8502	0.199326
8	0.051851	0.3983	0.345932
9	-0.082591	-0.6344	0.264138
10	-0.025676	-0.1972	0.422166
11	0.112159	0.8615	0.196222
12	0.306809	2.3566	0.01089
13	-0.018836	-0.1447	0.442727
14	8.3e-05	6e-04	0.499747
15	0.00624	0.0479	0.480966
16	0.03715	0.2854	0.388185
17	-0.128736	-0.9888	0.163389

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.03651	-0.2804	0.390061
2	-0.018917	-0.1453	0.442484
3	-0.052211	-0.401	0.344921
4	0.078844	0.6056	0.273548
5	-0.11444	-0.879	0.191475
6	0.059692	0.4585	0.324139
7	-0.107782	-0.8279	0.205536
8	0.035176	0.2702	0.393979
9	-0.067395	-0.5177	0.303313
10	-0.058601	-0.4501	0.327135
11	0.146045	1.1218	0.133248
12	0.282297	2.1684	0.017088
13	0.040158	0.3085	0.379409
14	0.002895	0.0222	0.491167
15	0.017789	0.1366	0.445891
16	0.014448	0.111	0.456005
17	-0.099578	-0.7649	0.223699

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.03651 & -0.2804 & 0.390061 \tabularnewline
2 & -0.018917 & -0.1453 & 0.442484 \tabularnewline
3 & -0.052211 & -0.401 & 0.344921 \tabularnewline
4 & 0.078844 & 0.6056 & 0.273548 \tabularnewline
5 & -0.11444 & -0.879 & 0.191475 \tabularnewline
6 & 0.059692 & 0.4585 & 0.324139 \tabularnewline
7 & -0.107782 & -0.8279 & 0.205536 \tabularnewline
8 & 0.035176 & 0.2702 & 0.393979 \tabularnewline
9 & -0.067395 & -0.5177 & 0.303313 \tabularnewline
10 & -0.058601 & -0.4501 & 0.327135 \tabularnewline
11 & 0.146045 & 1.1218 & 0.133248 \tabularnewline
12 & 0.282297 & 2.1684 & 0.017088 \tabularnewline
13 & 0.040158 & 0.3085 & 0.379409 \tabularnewline
14 & 0.002895 & 0.0222 & 0.491167 \tabularnewline
15 & 0.017789 & 0.1366 & 0.445891 \tabularnewline
16 & 0.014448 & 0.111 & 0.456005 \tabularnewline
17 & -0.099578 & -0.7649 & 0.223699 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294072&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]-0.03651[/C][C]-0.2804[/C][C]0.390061[/C][/ROW]
[ROW][C]2[/C][C]-0.018917[/C][C]-0.1453[/C][C]0.442484[/C][/ROW]
[ROW][C]3[/C][C]-0.052211[/C][C]-0.401[/C][C]0.344921[/C][/ROW]
[ROW][C]4[/C][C]0.078844[/C][C]0.6056[/C][C]0.273548[/C][/ROW]
[ROW][C]5[/C][C]-0.11444[/C][C]-0.879[/C][C]0.191475[/C][/ROW]
[ROW][C]6[/C][C]0.059692[/C][C]0.4585[/C][C]0.324139[/C][/ROW]
[ROW][C]7[/C][C]-0.107782[/C][C]-0.8279[/C][C]0.205536[/C][/ROW]
[ROW][C]8[/C][C]0.035176[/C][C]0.2702[/C][C]0.393979[/C][/ROW]
[ROW][C]9[/C][C]-0.067395[/C][C]-0.5177[/C][C]0.303313[/C][/ROW]
[ROW][C]10[/C][C]-0.058601[/C][C]-0.4501[/C][C]0.327135[/C][/ROW]
[ROW][C]11[/C][C]0.146045[/C][C]1.1218[/C][C]0.133248[/C][/ROW]
[ROW][C]12[/C][C]0.282297[/C][C]2.1684[/C][C]0.017088[/C][/ROW]
[ROW][C]13[/C][C]0.040158[/C][C]0.3085[/C][C]0.379409[/C][/ROW]
[ROW][C]14[/C][C]0.002895[/C][C]0.0222[/C][C]0.491167[/C][/ROW]
[ROW][C]15[/C][C]0.017789[/C][C]0.1366[/C][C]0.445891[/C][/ROW]
[ROW][C]16[/C][C]0.014448[/C][C]0.111[/C][C]0.456005[/C][/ROW]
[ROW][C]17[/C][C]-0.099578[/C][C]-0.7649[/C][C]0.223699[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294072&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294072&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	-0.03651	-0.2804	0.390061
2	-0.018917	-0.1453	0.442484
3	-0.052211	-0.401	0.344921
4	0.078844	0.6056	0.273548
5	-0.11444	-0.879	0.191475
6	0.059692	0.4585	0.324139
7	-0.107782	-0.8279	0.205536
8	0.035176	0.2702	0.393979
9	-0.067395	-0.5177	0.303313
10	-0.058601	-0.4501	0.327135
11	0.146045	1.1218	0.133248
12	0.282297	2.1684	0.017088
13	0.040158	0.3085	0.379409
14	0.002895	0.0222	0.491167
15	0.017789	0.1366	0.445891
16	0.014448	0.111	0.456005
17	-0.099578	-0.7649	0.223699

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)
x <- na.omit(x)
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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Input Parameters & R Code