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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 17 Oct 2014 13:15:58 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Oct/17/t1413548263m1z7sbhd0alh4uo.htm/, Retrieved Fri, 10 May 2024 20:50:55 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=243250, Retrieved Fri, 10 May 2024 20:50:55 +0000

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-       [(Partial) Autocorrelation Function] [] [2014-10-17 12:15:58] [f1a1c306ccf782003dcf1365fad9efec] [Current]
-   P     [(Partial) Autocorrelation Function] [] [2014-12-16 13:12:54] [b5b39717209e06ff52ecfc643c6cbf41] 

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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=243250&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=243250&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243250&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	0.169883	1.4315	0.078343
2	0.063859	0.5381	0.2961
3	0.055589	0.4684	0.320466
4	0.12171	1.0255	0.154293
5	0.116413	0.9809	0.164982
6	0.108768	0.9165	0.181255
7	0.046761	0.394	0.347375
8	0.043903	0.3699	0.356266
9	0.233887	1.9708	0.026325
10	0.080721	0.6802	0.249306
11	0.182301	1.5361	0.06448
12	0.244306	2.0586	0.021604
13	-0.110846	-0.934	0.176733
14	-0.064229	-0.5412	0.295031
15	-0.109184	-0.92	0.180343
16	-0.059215	-0.499	0.309676
17	-0.033857	-0.2853	0.388129
18	-0.007381	-0.0622	0.475292

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.169883 & 1.4315 & 0.078343 \tabularnewline
2 & 0.063859 & 0.5381 & 0.2961 \tabularnewline
3 & 0.055589 & 0.4684 & 0.320466 \tabularnewline
4 & 0.12171 & 1.0255 & 0.154293 \tabularnewline
5 & 0.116413 & 0.9809 & 0.164982 \tabularnewline
6 & 0.108768 & 0.9165 & 0.181255 \tabularnewline
7 & 0.046761 & 0.394 & 0.347375 \tabularnewline
8 & 0.043903 & 0.3699 & 0.356266 \tabularnewline
9 & 0.233887 & 1.9708 & 0.026325 \tabularnewline
10 & 0.080721 & 0.6802 & 0.249306 \tabularnewline
11 & 0.182301 & 1.5361 & 0.06448 \tabularnewline
12 & 0.244306 & 2.0586 & 0.021604 \tabularnewline
13 & -0.110846 & -0.934 & 0.176733 \tabularnewline
14 & -0.064229 & -0.5412 & 0.295031 \tabularnewline
15 & -0.109184 & -0.92 & 0.180343 \tabularnewline
16 & -0.059215 & -0.499 & 0.309676 \tabularnewline
17 & -0.033857 & -0.2853 & 0.388129 \tabularnewline
18 & -0.007381 & -0.0622 & 0.475292 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243250&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]0.169883[/C][C]1.4315[/C][C]0.078343[/C][/ROW]
[ROW][C]2[/C][C]0.063859[/C][C]0.5381[/C][C]0.2961[/C][/ROW]
[ROW][C]3[/C][C]0.055589[/C][C]0.4684[/C][C]0.320466[/C][/ROW]
[ROW][C]4[/C][C]0.12171[/C][C]1.0255[/C][C]0.154293[/C][/ROW]
[ROW][C]5[/C][C]0.116413[/C][C]0.9809[/C][C]0.164982[/C][/ROW]
[ROW][C]6[/C][C]0.108768[/C][C]0.9165[/C][C]0.181255[/C][/ROW]
[ROW][C]7[/C][C]0.046761[/C][C]0.394[/C][C]0.347375[/C][/ROW]
[ROW][C]8[/C][C]0.043903[/C][C]0.3699[/C][C]0.356266[/C][/ROW]
[ROW][C]9[/C][C]0.233887[/C][C]1.9708[/C][C]0.026325[/C][/ROW]
[ROW][C]10[/C][C]0.080721[/C][C]0.6802[/C][C]0.249306[/C][/ROW]
[ROW][C]11[/C][C]0.182301[/C][C]1.5361[/C][C]0.06448[/C][/ROW]
[ROW][C]12[/C][C]0.244306[/C][C]2.0586[/C][C]0.021604[/C][/ROW]
[ROW][C]13[/C][C]-0.110846[/C][C]-0.934[/C][C]0.176733[/C][/ROW]
[ROW][C]14[/C][C]-0.064229[/C][C]-0.5412[/C][C]0.295031[/C][/ROW]
[ROW][C]15[/C][C]-0.109184[/C][C]-0.92[/C][C]0.180343[/C][/ROW]
[ROW][C]16[/C][C]-0.059215[/C][C]-0.499[/C][C]0.309676[/C][/ROW]
[ROW][C]17[/C][C]-0.033857[/C][C]-0.2853[/C][C]0.388129[/C][/ROW]
[ROW][C]18[/C][C]-0.007381[/C][C]-0.0622[/C][C]0.475292[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243250&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243250&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	0.169883	1.4315	0.078343
2	0.063859	0.5381	0.2961
3	0.055589	0.4684	0.320466
4	0.12171	1.0255	0.154293
5	0.116413	0.9809	0.164982
6	0.108768	0.9165	0.181255
7	0.046761	0.394	0.347375
8	0.043903	0.3699	0.356266
9	0.233887	1.9708	0.026325
10	0.080721	0.6802	0.249306
11	0.182301	1.5361	0.06448
12	0.244306	2.0586	0.021604
13	-0.110846	-0.934	0.176733
14	-0.064229	-0.5412	0.295031
15	-0.109184	-0.92	0.180343
16	-0.059215	-0.499	0.309676
17	-0.033857	-0.2853	0.388129
18	-0.007381	-0.0622	0.475292

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.169883	1.4315	0.078343
2	0.036039	0.3037	0.381134
3	0.040221	0.3389	0.36784
4	0.107376	0.9048	0.184324
5	0.07943	0.6693	0.252742
6	0.071168	0.5997	0.275316
7	0.005343	0.045	0.482107
8	0.013302	0.1121	0.455535
9	0.210863	1.7768	0.039946
10	-0.010986	-0.0926	0.463252
11	0.154174	1.2991	0.099058
12	0.197209	1.6617	0.05049
13	-0.255112	-2.1496	0.017497
14	-0.077031	-0.6491	0.259192
15	-0.183253	-1.5441	0.063502
16	-0.129857	-1.0942	0.138783
17	-0.03652	-0.3077	0.379597
18	-0.059474	-0.5011	0.308913

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.169883 & 1.4315 & 0.078343 \tabularnewline
2 & 0.036039 & 0.3037 & 0.381134 \tabularnewline
3 & 0.040221 & 0.3389 & 0.36784 \tabularnewline
4 & 0.107376 & 0.9048 & 0.184324 \tabularnewline
5 & 0.07943 & 0.6693 & 0.252742 \tabularnewline
6 & 0.071168 & 0.5997 & 0.275316 \tabularnewline
7 & 0.005343 & 0.045 & 0.482107 \tabularnewline
8 & 0.013302 & 0.1121 & 0.455535 \tabularnewline
9 & 0.210863 & 1.7768 & 0.039946 \tabularnewline
10 & -0.010986 & -0.0926 & 0.463252 \tabularnewline
11 & 0.154174 & 1.2991 & 0.099058 \tabularnewline
12 & 0.197209 & 1.6617 & 0.05049 \tabularnewline
13 & -0.255112 & -2.1496 & 0.017497 \tabularnewline
14 & -0.077031 & -0.6491 & 0.259192 \tabularnewline
15 & -0.183253 & -1.5441 & 0.063502 \tabularnewline
16 & -0.129857 & -1.0942 & 0.138783 \tabularnewline
17 & -0.03652 & -0.3077 & 0.379597 \tabularnewline
18 & -0.059474 & -0.5011 & 0.308913 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243250&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]0.169883[/C][C]1.4315[/C][C]0.078343[/C][/ROW]
[ROW][C]2[/C][C]0.036039[/C][C]0.3037[/C][C]0.381134[/C][/ROW]
[ROW][C]3[/C][C]0.040221[/C][C]0.3389[/C][C]0.36784[/C][/ROW]
[ROW][C]4[/C][C]0.107376[/C][C]0.9048[/C][C]0.184324[/C][/ROW]
[ROW][C]5[/C][C]0.07943[/C][C]0.6693[/C][C]0.252742[/C][/ROW]
[ROW][C]6[/C][C]0.071168[/C][C]0.5997[/C][C]0.275316[/C][/ROW]
[ROW][C]7[/C][C]0.005343[/C][C]0.045[/C][C]0.482107[/C][/ROW]
[ROW][C]8[/C][C]0.013302[/C][C]0.1121[/C][C]0.455535[/C][/ROW]
[ROW][C]9[/C][C]0.210863[/C][C]1.7768[/C][C]0.039946[/C][/ROW]
[ROW][C]10[/C][C]-0.010986[/C][C]-0.0926[/C][C]0.463252[/C][/ROW]
[ROW][C]11[/C][C]0.154174[/C][C]1.2991[/C][C]0.099058[/C][/ROW]
[ROW][C]12[/C][C]0.197209[/C][C]1.6617[/C][C]0.05049[/C][/ROW]
[ROW][C]13[/C][C]-0.255112[/C][C]-2.1496[/C][C]0.017497[/C][/ROW]
[ROW][C]14[/C][C]-0.077031[/C][C]-0.6491[/C][C]0.259192[/C][/ROW]
[ROW][C]15[/C][C]-0.183253[/C][C]-1.5441[/C][C]0.063502[/C][/ROW]
[ROW][C]16[/C][C]-0.129857[/C][C]-1.0942[/C][C]0.138783[/C][/ROW]
[ROW][C]17[/C][C]-0.03652[/C][C]-0.3077[/C][C]0.379597[/C][/ROW]
[ROW][C]18[/C][C]-0.059474[/C][C]-0.5011[/C][C]0.308913[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243250&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243250&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	0.169883	1.4315	0.078343
2	0.036039	0.3037	0.381134
3	0.040221	0.3389	0.36784
4	0.107376	0.9048	0.184324
5	0.07943	0.6693	0.252742
6	0.071168	0.5997	0.275316
7	0.005343	0.045	0.482107
8	0.013302	0.1121	0.455535
9	0.210863	1.7768	0.039946
10	-0.010986	-0.0926	0.463252
11	0.154174	1.2991	0.099058
12	0.197209	1.6617	0.05049
13	-0.255112	-2.1496	0.017497
14	-0.077031	-0.6491	0.259192
15	-0.183253	-1.5441	0.063502
16	-0.129857	-1.0942	0.138783
17	-0.03652	-0.3077	0.379597
18	-0.059474	-0.5011	0.308913

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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code