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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 27 Dec 2010 21:59:40 +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/27/t12934870761uf3v07h23zfogm.htm/, Retrieved Mon, 06 May 2024 14:55:50 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116157, Retrieved Mon, 06 May 2024 14:55:50 +0000

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102

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

-     [Spectral Analysis] [] [2010-12-27 20:46:00] [f57e4c4cbbe8f12a19647529ae7266aa]
- RMP     [(Partial) Autocorrelation Function] [] [2010-12-27 21:59:40] [c984196f1244e05baf3e7c2e52d47a33] [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	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116157&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116157&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116157&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.799764	5.5983	0
2	0.75768	5.3038	1e-06
3	0.695969	4.8718	6e-06
4	0.52213	3.6549	0.000313
5	0.455864	3.1911	0.001237
6	0.323326	2.2633	0.014042
7	0.150928	1.0565	0.147961
8	0.121436	0.8501	0.199715
9	0.001918	0.0134	0.494671
10	-0.080583	-0.5641	0.287636
11	-0.095247	-0.6667	0.254036
12	-0.154932	-1.0845	0.14172
13	-0.157819	-1.1047	0.137335
14	-0.129987	-0.9099	0.183662
15	-0.125037	-0.8753	0.192851
16	-0.120761	-0.8453	0.201019
17	-0.100888	-0.7062	0.241698

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.799764 & 5.5983 & 0 \tabularnewline
2 & 0.75768 & 5.3038 & 1e-06 \tabularnewline
3 & 0.695969 & 4.8718 & 6e-06 \tabularnewline
4 & 0.52213 & 3.6549 & 0.000313 \tabularnewline
5 & 0.455864 & 3.1911 & 0.001237 \tabularnewline
6 & 0.323326 & 2.2633 & 0.014042 \tabularnewline
7 & 0.150928 & 1.0565 & 0.147961 \tabularnewline
8 & 0.121436 & 0.8501 & 0.199715 \tabularnewline
9 & 0.001918 & 0.0134 & 0.494671 \tabularnewline
10 & -0.080583 & -0.5641 & 0.287636 \tabularnewline
11 & -0.095247 & -0.6667 & 0.254036 \tabularnewline
12 & -0.154932 & -1.0845 & 0.14172 \tabularnewline
13 & -0.157819 & -1.1047 & 0.137335 \tabularnewline
14 & -0.129987 & -0.9099 & 0.183662 \tabularnewline
15 & -0.125037 & -0.8753 & 0.192851 \tabularnewline
16 & -0.120761 & -0.8453 & 0.201019 \tabularnewline
17 & -0.100888 & -0.7062 & 0.241698 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116157&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]0.799764[/C][C]5.5983[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.75768[/C][C]5.3038[/C][C]1e-06[/C][/ROW]
[ROW][C]3[/C][C]0.695969[/C][C]4.8718[/C][C]6e-06[/C][/ROW]
[ROW][C]4[/C][C]0.52213[/C][C]3.6549[/C][C]0.000313[/C][/ROW]
[ROW][C]5[/C][C]0.455864[/C][C]3.1911[/C][C]0.001237[/C][/ROW]
[ROW][C]6[/C][C]0.323326[/C][C]2.2633[/C][C]0.014042[/C][/ROW]
[ROW][C]7[/C][C]0.150928[/C][C]1.0565[/C][C]0.147961[/C][/ROW]
[ROW][C]8[/C][C]0.121436[/C][C]0.8501[/C][C]0.199715[/C][/ROW]
[ROW][C]9[/C][C]0.001918[/C][C]0.0134[/C][C]0.494671[/C][/ROW]
[ROW][C]10[/C][C]-0.080583[/C][C]-0.5641[/C][C]0.287636[/C][/ROW]
[ROW][C]11[/C][C]-0.095247[/C][C]-0.6667[/C][C]0.254036[/C][/ROW]
[ROW][C]12[/C][C]-0.154932[/C][C]-1.0845[/C][C]0.14172[/C][/ROW]
[ROW][C]13[/C][C]-0.157819[/C][C]-1.1047[/C][C]0.137335[/C][/ROW]
[ROW][C]14[/C][C]-0.129987[/C][C]-0.9099[/C][C]0.183662[/C][/ROW]
[ROW][C]15[/C][C]-0.125037[/C][C]-0.8753[/C][C]0.192851[/C][/ROW]
[ROW][C]16[/C][C]-0.120761[/C][C]-0.8453[/C][C]0.201019[/C][/ROW]
[ROW][C]17[/C][C]-0.100888[/C][C]-0.7062[/C][C]0.241698[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116157&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116157&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	0.799764	5.5983	0
2	0.75768	5.3038	1e-06
3	0.695969	4.8718	6e-06
4	0.52213	3.6549	0.000313
5	0.455864	3.1911	0.001237
6	0.323326	2.2633	0.014042
7	0.150928	1.0565	0.147961
8	0.121436	0.8501	0.199715
9	0.001918	0.0134	0.494671
10	-0.080583	-0.5641	0.287636
11	-0.095247	-0.6667	0.254036
12	-0.154932	-1.0845	0.14172
13	-0.157819	-1.1047	0.137335
14	-0.129987	-0.9099	0.183662
15	-0.125037	-0.8753	0.192851
16	-0.120761	-0.8453	0.201019
17	-0.100888	-0.7062	0.241698

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.799764	5.5983	0
2	0.327595	2.2932	0.013084
3	0.082428	0.577	0.283293
4	-0.356457	-2.4952	0.008003
5	-0.03191	-0.2234	0.412088
6	-0.117799	-0.8246	0.2068
7	-0.240383	-1.6827	0.0494
8	0.158416	1.1089	0.136441
9	0.015382	0.1077	0.457346
10	-0.035199	-0.2464	0.403202
11	0.015224	0.1066	0.457784
12	0.057342	0.4014	0.344938
13	0.00207	0.0145	0.494248
14	0.033718	0.236	0.407197
15	0.099628	0.6974	0.244425
16	-0.168138	-1.177	0.122447
17	-0.094935	-0.6645	0.254728

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.799764 & 5.5983 & 0 \tabularnewline
2 & 0.327595 & 2.2932 & 0.013084 \tabularnewline
3 & 0.082428 & 0.577 & 0.283293 \tabularnewline
4 & -0.356457 & -2.4952 & 0.008003 \tabularnewline
5 & -0.03191 & -0.2234 & 0.412088 \tabularnewline
6 & -0.117799 & -0.8246 & 0.2068 \tabularnewline
7 & -0.240383 & -1.6827 & 0.0494 \tabularnewline
8 & 0.158416 & 1.1089 & 0.136441 \tabularnewline
9 & 0.015382 & 0.1077 & 0.457346 \tabularnewline
10 & -0.035199 & -0.2464 & 0.403202 \tabularnewline
11 & 0.015224 & 0.1066 & 0.457784 \tabularnewline
12 & 0.057342 & 0.4014 & 0.344938 \tabularnewline
13 & 0.00207 & 0.0145 & 0.494248 \tabularnewline
14 & 0.033718 & 0.236 & 0.407197 \tabularnewline
15 & 0.099628 & 0.6974 & 0.244425 \tabularnewline
16 & -0.168138 & -1.177 & 0.122447 \tabularnewline
17 & -0.094935 & -0.6645 & 0.254728 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116157&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]0.799764[/C][C]5.5983[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.327595[/C][C]2.2932[/C][C]0.013084[/C][/ROW]
[ROW][C]3[/C][C]0.082428[/C][C]0.577[/C][C]0.283293[/C][/ROW]
[ROW][C]4[/C][C]-0.356457[/C][C]-2.4952[/C][C]0.008003[/C][/ROW]
[ROW][C]5[/C][C]-0.03191[/C][C]-0.2234[/C][C]0.412088[/C][/ROW]
[ROW][C]6[/C][C]-0.117799[/C][C]-0.8246[/C][C]0.2068[/C][/ROW]
[ROW][C]7[/C][C]-0.240383[/C][C]-1.6827[/C][C]0.0494[/C][/ROW]
[ROW][C]8[/C][C]0.158416[/C][C]1.1089[/C][C]0.136441[/C][/ROW]
[ROW][C]9[/C][C]0.015382[/C][C]0.1077[/C][C]0.457346[/C][/ROW]
[ROW][C]10[/C][C]-0.035199[/C][C]-0.2464[/C][C]0.403202[/C][/ROW]
[ROW][C]11[/C][C]0.015224[/C][C]0.1066[/C][C]0.457784[/C][/ROW]
[ROW][C]12[/C][C]0.057342[/C][C]0.4014[/C][C]0.344938[/C][/ROW]
[ROW][C]13[/C][C]0.00207[/C][C]0.0145[/C][C]0.494248[/C][/ROW]
[ROW][C]14[/C][C]0.033718[/C][C]0.236[/C][C]0.407197[/C][/ROW]
[ROW][C]15[/C][C]0.099628[/C][C]0.6974[/C][C]0.244425[/C][/ROW]
[ROW][C]16[/C][C]-0.168138[/C][C]-1.177[/C][C]0.122447[/C][/ROW]
[ROW][C]17[/C][C]-0.094935[/C][C]-0.6645[/C][C]0.254728[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116157&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116157&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	0.799764	5.5983	0
2	0.327595	2.2932	0.013084
3	0.082428	0.577	0.283293
4	-0.356457	-2.4952	0.008003
5	-0.03191	-0.2234	0.412088
6	-0.117799	-0.8246	0.2068
7	-0.240383	-1.6827	0.0494
8	0.158416	1.1089	0.136441
9	0.015382	0.1077	0.457346
10	-0.035199	-0.2464	0.403202
11	0.015224	0.1066	0.457784
12	0.057342	0.4014	0.344938
13	0.00207	0.0145	0.494248
14	0.033718	0.236	0.407197
15	0.099628	0.6974	0.244425
16	-0.168138	-1.177	0.122447
17	-0.094935	-0.6645	0.254728

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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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Input Parameters & R Code