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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 18 Oct 2016 12:13:07 +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/2016/Oct/18/t1476789321nr950o15o77ll5s.htm/, Retrieved Sat, 27 Apr 2024 23:42:55 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sat, 27 Apr 2024 23:42:55 +0200

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

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

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.028826	-0.1976	0.422097
2	-0.30101	-2.0636	0.0223
3	0.218697	1.4993	0.070241
4	0.107774	0.7389	0.231833
5	-0.30086	-2.0626	0.022351
6	-0.30504	-2.0912	0.020969
7	-0.151657	-1.0397	0.151897
8	0.02607	0.1787	0.429459
9	0.080746	0.5536	0.291249
10	-0.220952	-1.5148	0.068264
11	0.076115	0.5218	0.302125
12	0.649938	4.4558	2.6e-05
13	-0.055519	-0.3806	0.352601
14	-0.192744	-1.3214	0.096385
15	0.228478	1.5664	0.061986
16	0.075776	0.5195	0.302927

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.028826 & -0.1976 & 0.422097 \tabularnewline
2 & -0.30101 & -2.0636 & 0.0223 \tabularnewline
3 & 0.218697 & 1.4993 & 0.070241 \tabularnewline
4 & 0.107774 & 0.7389 & 0.231833 \tabularnewline
5 & -0.30086 & -2.0626 & 0.022351 \tabularnewline
6 & -0.30504 & -2.0912 & 0.020969 \tabularnewline
7 & -0.151657 & -1.0397 & 0.151897 \tabularnewline
8 & 0.02607 & 0.1787 & 0.429459 \tabularnewline
9 & 0.080746 & 0.5536 & 0.291249 \tabularnewline
10 & -0.220952 & -1.5148 & 0.068264 \tabularnewline
11 & 0.076115 & 0.5218 & 0.302125 \tabularnewline
12 & 0.649938 & 4.4558 & 2.6e-05 \tabularnewline
13 & -0.055519 & -0.3806 & 0.352601 \tabularnewline
14 & -0.192744 & -1.3214 & 0.096385 \tabularnewline
15 & 0.228478 & 1.5664 & 0.061986 \tabularnewline
16 & 0.075776 & 0.5195 & 0.302927 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]-0.028826[/C][C]-0.1976[/C][C]0.422097[/C][/ROW]
[ROW][C]2[/C][C]-0.30101[/C][C]-2.0636[/C][C]0.0223[/C][/ROW]
[ROW][C]3[/C][C]0.218697[/C][C]1.4993[/C][C]0.070241[/C][/ROW]
[ROW][C]4[/C][C]0.107774[/C][C]0.7389[/C][C]0.231833[/C][/ROW]
[ROW][C]5[/C][C]-0.30086[/C][C]-2.0626[/C][C]0.022351[/C][/ROW]
[ROW][C]6[/C][C]-0.30504[/C][C]-2.0912[/C][C]0.020969[/C][/ROW]
[ROW][C]7[/C][C]-0.151657[/C][C]-1.0397[/C][C]0.151897[/C][/ROW]
[ROW][C]8[/C][C]0.02607[/C][C]0.1787[/C][C]0.429459[/C][/ROW]
[ROW][C]9[/C][C]0.080746[/C][C]0.5536[/C][C]0.291249[/C][/ROW]
[ROW][C]10[/C][C]-0.220952[/C][C]-1.5148[/C][C]0.068264[/C][/ROW]
[ROW][C]11[/C][C]0.076115[/C][C]0.5218[/C][C]0.302125[/C][/ROW]
[ROW][C]12[/C][C]0.649938[/C][C]4.4558[/C][C]2.6e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.055519[/C][C]-0.3806[/C][C]0.352601[/C][/ROW]
[ROW][C]14[/C][C]-0.192744[/C][C]-1.3214[/C][C]0.096385[/C][/ROW]
[ROW][C]15[/C][C]0.228478[/C][C]1.5664[/C][C]0.061986[/C][/ROW]
[ROW][C]16[/C][C]0.075776[/C][C]0.5195[/C][C]0.302927[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	-0.028826	-0.1976	0.422097
2	-0.30101	-2.0636	0.0223
3	0.218697	1.4993	0.070241
4	0.107774	0.7389	0.231833
5	-0.30086	-2.0626	0.022351
6	-0.30504	-2.0912	0.020969
7	-0.151657	-1.0397	0.151897
8	0.02607	0.1787	0.429459
9	0.080746	0.5536	0.291249
10	-0.220952	-1.5148	0.068264
11	0.076115	0.5218	0.302125
12	0.649938	4.4558	2.6e-05
13	-0.055519	-0.3806	0.352601
14	-0.192744	-1.3214	0.096385
15	0.228478	1.5664	0.061986
16	0.075776	0.5195	0.302927

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.028826	-0.1976	0.422097
2	-0.302092	-2.071	0.021936
3	0.218826	1.5002	0.070126
4	0.022409	0.1536	0.439279
5	-0.201672	-1.3826	0.086662
6	-0.365551	-2.5061	0.007864
7	-0.437191	-2.9972	0.002171
8	-0.193122	-1.324	0.095956
9	0.104699	0.7178	0.238224
10	-0.219763	-1.5066	0.0693
11	-0.160368	-1.0994	0.13859
12	0.393196	2.6956	0.004859
13	-0.061372	-0.4207	0.33793
14	0.049791	0.3413	0.367181
15	-0.091094	-0.6245	0.267657
16	-0.081457	-0.5584	0.289596

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.028826 & -0.1976 & 0.422097 \tabularnewline
2 & -0.302092 & -2.071 & 0.021936 \tabularnewline
3 & 0.218826 & 1.5002 & 0.070126 \tabularnewline
4 & 0.022409 & 0.1536 & 0.439279 \tabularnewline
5 & -0.201672 & -1.3826 & 0.086662 \tabularnewline
6 & -0.365551 & -2.5061 & 0.007864 \tabularnewline
7 & -0.437191 & -2.9972 & 0.002171 \tabularnewline
8 & -0.193122 & -1.324 & 0.095956 \tabularnewline
9 & 0.104699 & 0.7178 & 0.238224 \tabularnewline
10 & -0.219763 & -1.5066 & 0.0693 \tabularnewline
11 & -0.160368 & -1.0994 & 0.13859 \tabularnewline
12 & 0.393196 & 2.6956 & 0.004859 \tabularnewline
13 & -0.061372 & -0.4207 & 0.33793 \tabularnewline
14 & 0.049791 & 0.3413 & 0.367181 \tabularnewline
15 & -0.091094 & -0.6245 & 0.267657 \tabularnewline
16 & -0.081457 & -0.5584 & 0.289596 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]-0.028826[/C][C]-0.1976[/C][C]0.422097[/C][/ROW]
[ROW][C]2[/C][C]-0.302092[/C][C]-2.071[/C][C]0.021936[/C][/ROW]
[ROW][C]3[/C][C]0.218826[/C][C]1.5002[/C][C]0.070126[/C][/ROW]
[ROW][C]4[/C][C]0.022409[/C][C]0.1536[/C][C]0.439279[/C][/ROW]
[ROW][C]5[/C][C]-0.201672[/C][C]-1.3826[/C][C]0.086662[/C][/ROW]
[ROW][C]6[/C][C]-0.365551[/C][C]-2.5061[/C][C]0.007864[/C][/ROW]
[ROW][C]7[/C][C]-0.437191[/C][C]-2.9972[/C][C]0.002171[/C][/ROW]
[ROW][C]8[/C][C]-0.193122[/C][C]-1.324[/C][C]0.095956[/C][/ROW]
[ROW][C]9[/C][C]0.104699[/C][C]0.7178[/C][C]0.238224[/C][/ROW]
[ROW][C]10[/C][C]-0.219763[/C][C]-1.5066[/C][C]0.0693[/C][/ROW]
[ROW][C]11[/C][C]-0.160368[/C][C]-1.0994[/C][C]0.13859[/C][/ROW]
[ROW][C]12[/C][C]0.393196[/C][C]2.6956[/C][C]0.004859[/C][/ROW]
[ROW][C]13[/C][C]-0.061372[/C][C]-0.4207[/C][C]0.33793[/C][/ROW]
[ROW][C]14[/C][C]0.049791[/C][C]0.3413[/C][C]0.367181[/C][/ROW]
[ROW][C]15[/C][C]-0.091094[/C][C]-0.6245[/C][C]0.267657[/C][/ROW]
[ROW][C]16[/C][C]-0.081457[/C][C]-0.5584[/C][C]0.289596[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	-0.028826	-0.1976	0.422097
2	-0.302092	-2.071	0.021936
3	0.218826	1.5002	0.070126
4	0.022409	0.1536	0.439279
5	-0.201672	-1.3826	0.086662
6	-0.365551	-2.5061	0.007864
7	-0.437191	-2.9972	0.002171
8	-0.193122	-1.324	0.095956
9	0.104699	0.7178	0.238224
10	-0.219763	-1.5066	0.0693
11	-0.160368	-1.0994	0.13859
12	0.393196	2.6956	0.004859
13	-0.061372	-0.4207	0.33793
14	0.049791	0.3413	0.367181
15	-0.091094	-0.6245	0.267657
16	-0.081457	-0.5584	0.289596

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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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code