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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 28 Nov 2015 11:09:15 +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/2015/Nov/28/t1448708969p1yzvsr3ctpps43.htm/, Retrieved Mon, 13 May 2024 21:04:59 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284366, Retrieved Mon, 13 May 2024 21:04:59 +0000

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No (this computation is public)

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Estimated Impact

118

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-       [(Partial) Autocorrelation Function] [Autocorrelation v...] [2015-11-28 11:09:15] [8acc4c3875a0c63009483cc7dfb4f316] [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	'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284366&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284366&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284366&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	'Sir Maurice George Kendall' @ kendall.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.7457	5.7762	0
2	0.491399	3.8064	0.000167
3	0.237099	1.8366	0.035615
4	0.257014	1.9908	0.02553
5	0.276929	2.1451	0.018002
6	0.296845	2.2993	0.012491
7	0.240126	1.86	0.033894
8	0.183406	1.4207	0.080296
9	0.126687	0.9813	0.165189
10	0.099117	0.7678	0.22282
11	0.071548	0.5542	0.290749
12	0.043978	0.3406	0.367279
13	-0.070349	-0.5449	0.293914
14	-0.184675	-1.4305	0.078882
15	-0.299002	-2.3161	0.011995
16	-0.271583	-2.1037	0.019804
17	-0.244164	-1.8913	0.031708

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.7457 & 5.7762 & 0 \tabularnewline
2 & 0.491399 & 3.8064 & 0.000167 \tabularnewline
3 & 0.237099 & 1.8366 & 0.035615 \tabularnewline
4 & 0.257014 & 1.9908 & 0.02553 \tabularnewline
5 & 0.276929 & 2.1451 & 0.018002 \tabularnewline
6 & 0.296845 & 2.2993 & 0.012491 \tabularnewline
7 & 0.240126 & 1.86 & 0.033894 \tabularnewline
8 & 0.183406 & 1.4207 & 0.080296 \tabularnewline
9 & 0.126687 & 0.9813 & 0.165189 \tabularnewline
10 & 0.099117 & 0.7678 & 0.22282 \tabularnewline
11 & 0.071548 & 0.5542 & 0.290749 \tabularnewline
12 & 0.043978 & 0.3406 & 0.367279 \tabularnewline
13 & -0.070349 & -0.5449 & 0.293914 \tabularnewline
14 & -0.184675 & -1.4305 & 0.078882 \tabularnewline
15 & -0.299002 & -2.3161 & 0.011995 \tabularnewline
16 & -0.271583 & -2.1037 & 0.019804 \tabularnewline
17 & -0.244164 & -1.8913 & 0.031708 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284366&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]0.7457[/C][C]5.7762[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.491399[/C][C]3.8064[/C][C]0.000167[/C][/ROW]
[ROW][C]3[/C][C]0.237099[/C][C]1.8366[/C][C]0.035615[/C][/ROW]
[ROW][C]4[/C][C]0.257014[/C][C]1.9908[/C][C]0.02553[/C][/ROW]
[ROW][C]5[/C][C]0.276929[/C][C]2.1451[/C][C]0.018002[/C][/ROW]
[ROW][C]6[/C][C]0.296845[/C][C]2.2993[/C][C]0.012491[/C][/ROW]
[ROW][C]7[/C][C]0.240126[/C][C]1.86[/C][C]0.033894[/C][/ROW]
[ROW][C]8[/C][C]0.183406[/C][C]1.4207[/C][C]0.080296[/C][/ROW]
[ROW][C]9[/C][C]0.126687[/C][C]0.9813[/C][C]0.165189[/C][/ROW]
[ROW][C]10[/C][C]0.099117[/C][C]0.7678[/C][C]0.22282[/C][/ROW]
[ROW][C]11[/C][C]0.071548[/C][C]0.5542[/C][C]0.290749[/C][/ROW]
[ROW][C]12[/C][C]0.043978[/C][C]0.3406[/C][C]0.367279[/C][/ROW]
[ROW][C]13[/C][C]-0.070349[/C][C]-0.5449[/C][C]0.293914[/C][/ROW]
[ROW][C]14[/C][C]-0.184675[/C][C]-1.4305[/C][C]0.078882[/C][/ROW]
[ROW][C]15[/C][C]-0.299002[/C][C]-2.3161[/C][C]0.011995[/C][/ROW]
[ROW][C]16[/C][C]-0.271583[/C][C]-2.1037[/C][C]0.019804[/C][/ROW]
[ROW][C]17[/C][C]-0.244164[/C][C]-1.8913[/C][C]0.031708[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284366&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284366&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	0.7457	5.7762	0
2	0.491399	3.8064	0.000167
3	0.237099	1.8366	0.035615
4	0.257014	1.9908	0.02553
5	0.276929	2.1451	0.018002
6	0.296845	2.2993	0.012491
7	0.240126	1.86	0.033894
8	0.183406	1.4207	0.080296
9	0.126687	0.9813	0.165189
10	0.099117	0.7678	0.22282
11	0.071548	0.5542	0.290749
12	0.043978	0.3406	0.367279
13	-0.070349	-0.5449	0.293914
14	-0.184675	-1.4305	0.078882
15	-0.299002	-2.3161	0.011995
16	-0.271583	-2.1037	0.019804
17	-0.244164	-1.8913	0.031708

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.7457	5.7762	0
2	-0.145672	-1.1284	0.131827
3	-0.170511	-1.3208	0.095796
4	0.444425	3.4425	0.000528
5	-0.065584	-0.508	0.306653
6	-0.070188	-0.5437	0.294341
7	0.136808	1.0597	0.146761
8	-0.053294	-0.4128	0.340607
9	-0.056294	-0.4361	0.332181
10	0.043666	0.3382	0.368184
11	-0.051584	-0.3996	0.345447
12	-0.054389	-0.4213	0.337521
13	-0.244112	-1.8909	0.031736
14	-0.089519	-0.6934	0.245363
15	-0.098321	-0.7616	0.224644
16	0.040769	0.3158	0.376628
17	-0.090618	-0.7019	0.24272

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.7457 & 5.7762 & 0 \tabularnewline
2 & -0.145672 & -1.1284 & 0.131827 \tabularnewline
3 & -0.170511 & -1.3208 & 0.095796 \tabularnewline
4 & 0.444425 & 3.4425 & 0.000528 \tabularnewline
5 & -0.065584 & -0.508 & 0.306653 \tabularnewline
6 & -0.070188 & -0.5437 & 0.294341 \tabularnewline
7 & 0.136808 & 1.0597 & 0.146761 \tabularnewline
8 & -0.053294 & -0.4128 & 0.340607 \tabularnewline
9 & -0.056294 & -0.4361 & 0.332181 \tabularnewline
10 & 0.043666 & 0.3382 & 0.368184 \tabularnewline
11 & -0.051584 & -0.3996 & 0.345447 \tabularnewline
12 & -0.054389 & -0.4213 & 0.337521 \tabularnewline
13 & -0.244112 & -1.8909 & 0.031736 \tabularnewline
14 & -0.089519 & -0.6934 & 0.245363 \tabularnewline
15 & -0.098321 & -0.7616 & 0.224644 \tabularnewline
16 & 0.040769 & 0.3158 & 0.376628 \tabularnewline
17 & -0.090618 & -0.7019 & 0.24272 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284366&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]0.7457[/C][C]5.7762[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.145672[/C][C]-1.1284[/C][C]0.131827[/C][/ROW]
[ROW][C]3[/C][C]-0.170511[/C][C]-1.3208[/C][C]0.095796[/C][/ROW]
[ROW][C]4[/C][C]0.444425[/C][C]3.4425[/C][C]0.000528[/C][/ROW]
[ROW][C]5[/C][C]-0.065584[/C][C]-0.508[/C][C]0.306653[/C][/ROW]
[ROW][C]6[/C][C]-0.070188[/C][C]-0.5437[/C][C]0.294341[/C][/ROW]
[ROW][C]7[/C][C]0.136808[/C][C]1.0597[/C][C]0.146761[/C][/ROW]
[ROW][C]8[/C][C]-0.053294[/C][C]-0.4128[/C][C]0.340607[/C][/ROW]
[ROW][C]9[/C][C]-0.056294[/C][C]-0.4361[/C][C]0.332181[/C][/ROW]
[ROW][C]10[/C][C]0.043666[/C][C]0.3382[/C][C]0.368184[/C][/ROW]
[ROW][C]11[/C][C]-0.051584[/C][C]-0.3996[/C][C]0.345447[/C][/ROW]
[ROW][C]12[/C][C]-0.054389[/C][C]-0.4213[/C][C]0.337521[/C][/ROW]
[ROW][C]13[/C][C]-0.244112[/C][C]-1.8909[/C][C]0.031736[/C][/ROW]
[ROW][C]14[/C][C]-0.089519[/C][C]-0.6934[/C][C]0.245363[/C][/ROW]
[ROW][C]15[/C][C]-0.098321[/C][C]-0.7616[/C][C]0.224644[/C][/ROW]
[ROW][C]16[/C][C]0.040769[/C][C]0.3158[/C][C]0.376628[/C][/ROW]
[ROW][C]17[/C][C]-0.090618[/C][C]-0.7019[/C][C]0.24272[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284366&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284366&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	0.7457	5.7762	0
2	-0.145672	-1.1284	0.131827
3	-0.170511	-1.3208	0.095796
4	0.444425	3.4425	0.000528
5	-0.065584	-0.508	0.306653
6	-0.070188	-0.5437	0.294341
7	0.136808	1.0597	0.146761
8	-0.053294	-0.4128	0.340607
9	-0.056294	-0.4361	0.332181
10	0.043666	0.3382	0.368184
11	-0.051584	-0.3996	0.345447
12	-0.054389	-0.4213	0.337521
13	-0.244112	-1.8909	0.031736
14	-0.089519	-0.6934	0.245363
15	-0.098321	-0.7616	0.224644
16	0.040769	0.3158	0.376628
17	-0.090618	-0.7019	0.24272

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 = 0 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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