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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 02 Dec 2011 05:58:37 -0500

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/2011/Dec/02/t13228235776l299u6k6jtgrxm.htm/, Retrieved Sun, 28 Apr 2024 23:54:27 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=150096, Retrieved Sun, 28 Apr 2024 23:54:27 +0000

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105

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-       [(Partial) Autocorrelation Function] [] [2011-12-02 10:58:37] [13d85cac30d4a10947636c080219d4f4] [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	2 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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150096&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]2 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=150096&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150096&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	2 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.176736	-1.2245	0.113377
2	-0.049668	-0.3441	0.366132
3	0.027838	0.1929	0.423938
4	-0.132901	-0.9208	0.180888
5	0.228402	1.5824	0.060061
6	-0.013086	-0.0907	0.464069
7	-0.318036	-2.2034	0.016198
8	-0.084752	-0.5872	0.279917
9	0.054677	0.3788	0.353249
10	-0.151878	-1.0522	0.148978
11	0.012657	0.0877	0.465245
12	-0.116019	-0.8038	0.212737
13	-0.056265	-0.3898	0.3492
14	0.116626	0.808	0.211537
15	0.015995	0.1108	0.456113
16	-0.089611	-0.6208	0.26882
17	0.180572	1.251	0.108491

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.176736 & -1.2245 & 0.113377 \tabularnewline
2 & -0.049668 & -0.3441 & 0.366132 \tabularnewline
3 & 0.027838 & 0.1929 & 0.423938 \tabularnewline
4 & -0.132901 & -0.9208 & 0.180888 \tabularnewline
5 & 0.228402 & 1.5824 & 0.060061 \tabularnewline
6 & -0.013086 & -0.0907 & 0.464069 \tabularnewline
7 & -0.318036 & -2.2034 & 0.016198 \tabularnewline
8 & -0.084752 & -0.5872 & 0.279917 \tabularnewline
9 & 0.054677 & 0.3788 & 0.353249 \tabularnewline
10 & -0.151878 & -1.0522 & 0.148978 \tabularnewline
11 & 0.012657 & 0.0877 & 0.465245 \tabularnewline
12 & -0.116019 & -0.8038 & 0.212737 \tabularnewline
13 & -0.056265 & -0.3898 & 0.3492 \tabularnewline
14 & 0.116626 & 0.808 & 0.211537 \tabularnewline
15 & 0.015995 & 0.1108 & 0.456113 \tabularnewline
16 & -0.089611 & -0.6208 & 0.26882 \tabularnewline
17 & 0.180572 & 1.251 & 0.108491 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150096&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]-0.176736[/C][C]-1.2245[/C][C]0.113377[/C][/ROW]
[ROW][C]2[/C][C]-0.049668[/C][C]-0.3441[/C][C]0.366132[/C][/ROW]
[ROW][C]3[/C][C]0.027838[/C][C]0.1929[/C][C]0.423938[/C][/ROW]
[ROW][C]4[/C][C]-0.132901[/C][C]-0.9208[/C][C]0.180888[/C][/ROW]
[ROW][C]5[/C][C]0.228402[/C][C]1.5824[/C][C]0.060061[/C][/ROW]
[ROW][C]6[/C][C]-0.013086[/C][C]-0.0907[/C][C]0.464069[/C][/ROW]
[ROW][C]7[/C][C]-0.318036[/C][C]-2.2034[/C][C]0.016198[/C][/ROW]
[ROW][C]8[/C][C]-0.084752[/C][C]-0.5872[/C][C]0.279917[/C][/ROW]
[ROW][C]9[/C][C]0.054677[/C][C]0.3788[/C][C]0.353249[/C][/ROW]
[ROW][C]10[/C][C]-0.151878[/C][C]-1.0522[/C][C]0.148978[/C][/ROW]
[ROW][C]11[/C][C]0.012657[/C][C]0.0877[/C][C]0.465245[/C][/ROW]
[ROW][C]12[/C][C]-0.116019[/C][C]-0.8038[/C][C]0.212737[/C][/ROW]
[ROW][C]13[/C][C]-0.056265[/C][C]-0.3898[/C][C]0.3492[/C][/ROW]
[ROW][C]14[/C][C]0.116626[/C][C]0.808[/C][C]0.211537[/C][/ROW]
[ROW][C]15[/C][C]0.015995[/C][C]0.1108[/C][C]0.456113[/C][/ROW]
[ROW][C]16[/C][C]-0.089611[/C][C]-0.6208[/C][C]0.26882[/C][/ROW]
[ROW][C]17[/C][C]0.180572[/C][C]1.251[/C][C]0.108491[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150096&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150096&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	-0.176736	-1.2245	0.113377
2	-0.049668	-0.3441	0.366132
3	0.027838	0.1929	0.423938
4	-0.132901	-0.9208	0.180888
5	0.228402	1.5824	0.060061
6	-0.013086	-0.0907	0.464069
7	-0.318036	-2.2034	0.016198
8	-0.084752	-0.5872	0.279917
9	0.054677	0.3788	0.353249
10	-0.151878	-1.0522	0.148978
11	0.012657	0.0877	0.465245
12	-0.116019	-0.8038	0.212737
13	-0.056265	-0.3898	0.3492
14	0.116626	0.808	0.211537
15	0.015995	0.1108	0.456113
16	-0.089611	-0.6208	0.26882
17	0.180572	1.251	0.108491

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.176736	-1.2245	0.113377
2	-0.083513	-0.5786	0.282785
3	0.003708	0.0257	0.489805
4	-0.136213	-0.9437	0.175021
5	0.191175	1.3245	0.095805
6	0.045662	0.3164	0.376553
7	-0.309319	-2.143	0.018605
8	-0.244548	-1.6943	0.048346
9	0.020626	0.1429	0.443484
10	-0.231016	-1.6005	0.058022
11	-0.182406	-1.2637	0.106212
12	-0.093833	-0.6501	0.259366
13	-0.072843	-0.5047	0.308049
14	-0.150791	-1.0447	0.150695
15	-0.082707	-0.573	0.284656
16	-0.189343	-1.3118	0.097913
17	-0.010002	-0.0693	0.472521

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.176736 & -1.2245 & 0.113377 \tabularnewline
2 & -0.083513 & -0.5786 & 0.282785 \tabularnewline
3 & 0.003708 & 0.0257 & 0.489805 \tabularnewline
4 & -0.136213 & -0.9437 & 0.175021 \tabularnewline
5 & 0.191175 & 1.3245 & 0.095805 \tabularnewline
6 & 0.045662 & 0.3164 & 0.376553 \tabularnewline
7 & -0.309319 & -2.143 & 0.018605 \tabularnewline
8 & -0.244548 & -1.6943 & 0.048346 \tabularnewline
9 & 0.020626 & 0.1429 & 0.443484 \tabularnewline
10 & -0.231016 & -1.6005 & 0.058022 \tabularnewline
11 & -0.182406 & -1.2637 & 0.106212 \tabularnewline
12 & -0.093833 & -0.6501 & 0.259366 \tabularnewline
13 & -0.072843 & -0.5047 & 0.308049 \tabularnewline
14 & -0.150791 & -1.0447 & 0.150695 \tabularnewline
15 & -0.082707 & -0.573 & 0.284656 \tabularnewline
16 & -0.189343 & -1.3118 & 0.097913 \tabularnewline
17 & -0.010002 & -0.0693 & 0.472521 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150096&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]-0.176736[/C][C]-1.2245[/C][C]0.113377[/C][/ROW]
[ROW][C]2[/C][C]-0.083513[/C][C]-0.5786[/C][C]0.282785[/C][/ROW]
[ROW][C]3[/C][C]0.003708[/C][C]0.0257[/C][C]0.489805[/C][/ROW]
[ROW][C]4[/C][C]-0.136213[/C][C]-0.9437[/C][C]0.175021[/C][/ROW]
[ROW][C]5[/C][C]0.191175[/C][C]1.3245[/C][C]0.095805[/C][/ROW]
[ROW][C]6[/C][C]0.045662[/C][C]0.3164[/C][C]0.376553[/C][/ROW]
[ROW][C]7[/C][C]-0.309319[/C][C]-2.143[/C][C]0.018605[/C][/ROW]
[ROW][C]8[/C][C]-0.244548[/C][C]-1.6943[/C][C]0.048346[/C][/ROW]
[ROW][C]9[/C][C]0.020626[/C][C]0.1429[/C][C]0.443484[/C][/ROW]
[ROW][C]10[/C][C]-0.231016[/C][C]-1.6005[/C][C]0.058022[/C][/ROW]
[ROW][C]11[/C][C]-0.182406[/C][C]-1.2637[/C][C]0.106212[/C][/ROW]
[ROW][C]12[/C][C]-0.093833[/C][C]-0.6501[/C][C]0.259366[/C][/ROW]
[ROW][C]13[/C][C]-0.072843[/C][C]-0.5047[/C][C]0.308049[/C][/ROW]
[ROW][C]14[/C][C]-0.150791[/C][C]-1.0447[/C][C]0.150695[/C][/ROW]
[ROW][C]15[/C][C]-0.082707[/C][C]-0.573[/C][C]0.284656[/C][/ROW]
[ROW][C]16[/C][C]-0.189343[/C][C]-1.3118[/C][C]0.097913[/C][/ROW]
[ROW][C]17[/C][C]-0.010002[/C][C]-0.0693[/C][C]0.472521[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150096&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150096&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	-0.176736	-1.2245	0.113377
2	-0.083513	-0.5786	0.282785
3	0.003708	0.0257	0.489805
4	-0.136213	-0.9437	0.175021
5	0.191175	1.3245	0.095805
6	0.045662	0.3164	0.376553
7	-0.309319	-2.143	0.018605
8	-0.244548	-1.6943	0.048346
9	0.020626	0.1429	0.443484
10	-0.231016	-1.6005	0.058022
11	-0.182406	-1.2637	0.106212
12	-0.093833	-0.6501	0.259366
13	-0.072843	-0.5047	0.308049
14	-0.150791	-1.0447	0.150695
15	-0.082707	-0.573	0.284656
16	-0.189343	-1.3118	0.097913
17	-0.010002	-0.0693	0.472521

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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Dataset

Tables (Output of Computation)

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Input Parameters & R Code