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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 28 Nov 2015 11:07:56 +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/t1448708897veu3k1hhsef9lkx.htm/, Retrieved Tue, 14 May 2024 12:17:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284365, Retrieved Tue, 14 May 2024 12:17:29 +0000

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No (this computation is public)

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Estimated Impact

118

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

-       [(Partial) Autocorrelation Function] [Autocorrelation M...] [2015-11-28 11:07:56] [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	'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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284365&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284365&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284365&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	'George Udny Yule' @ yule.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.834072	6.4607	0
2	0.668143	5.1754	1e-06
3	0.502215	3.8901	0.000127
4	0.464628	3.599	0.000324
5	0.427041	3.3078	0.000796
6	0.389455	3.0167	0.001872
7	0.347308	2.6902	0.004617
8	0.305162	2.3638	0.010673
9	0.263015	2.0373	0.023019
10	0.268896	2.0829	0.020767
11	0.274776	2.1284	0.01871
12	0.280657	2.174	0.016832
13	0.196436	1.5216	0.066683
14	0.112215	0.8692	0.194097
15	0.027994	0.2168	0.414534
16	-0.014264	-0.1105	0.456195
17	-0.056522	-0.4378	0.331545

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.834072 & 6.4607 & 0 \tabularnewline
2 & 0.668143 & 5.1754 & 1e-06 \tabularnewline
3 & 0.502215 & 3.8901 & 0.000127 \tabularnewline
4 & 0.464628 & 3.599 & 0.000324 \tabularnewline
5 & 0.427041 & 3.3078 & 0.000796 \tabularnewline
6 & 0.389455 & 3.0167 & 0.001872 \tabularnewline
7 & 0.347308 & 2.6902 & 0.004617 \tabularnewline
8 & 0.305162 & 2.3638 & 0.010673 \tabularnewline
9 & 0.263015 & 2.0373 & 0.023019 \tabularnewline
10 & 0.268896 & 2.0829 & 0.020767 \tabularnewline
11 & 0.274776 & 2.1284 & 0.01871 \tabularnewline
12 & 0.280657 & 2.174 & 0.016832 \tabularnewline
13 & 0.196436 & 1.5216 & 0.066683 \tabularnewline
14 & 0.112215 & 0.8692 & 0.194097 \tabularnewline
15 & 0.027994 & 0.2168 & 0.414534 \tabularnewline
16 & -0.014264 & -0.1105 & 0.456195 \tabularnewline
17 & -0.056522 & -0.4378 & 0.331545 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284365&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]0.834072[/C][C]6.4607[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.668143[/C][C]5.1754[/C][C]1e-06[/C][/ROW]
[ROW][C]3[/C][C]0.502215[/C][C]3.8901[/C][C]0.000127[/C][/ROW]
[ROW][C]4[/C][C]0.464628[/C][C]3.599[/C][C]0.000324[/C][/ROW]
[ROW][C]5[/C][C]0.427041[/C][C]3.3078[/C][C]0.000796[/C][/ROW]
[ROW][C]6[/C][C]0.389455[/C][C]3.0167[/C][C]0.001872[/C][/ROW]
[ROW][C]7[/C][C]0.347308[/C][C]2.6902[/C][C]0.004617[/C][/ROW]
[ROW][C]8[/C][C]0.305162[/C][C]2.3638[/C][C]0.010673[/C][/ROW]
[ROW][C]9[/C][C]0.263015[/C][C]2.0373[/C][C]0.023019[/C][/ROW]
[ROW][C]10[/C][C]0.268896[/C][C]2.0829[/C][C]0.020767[/C][/ROW]
[ROW][C]11[/C][C]0.274776[/C][C]2.1284[/C][C]0.01871[/C][/ROW]
[ROW][C]12[/C][C]0.280657[/C][C]2.174[/C][C]0.016832[/C][/ROW]
[ROW][C]13[/C][C]0.196436[/C][C]1.5216[/C][C]0.066683[/C][/ROW]
[ROW][C]14[/C][C]0.112215[/C][C]0.8692[/C][C]0.194097[/C][/ROW]
[ROW][C]15[/C][C]0.027994[/C][C]0.2168[/C][C]0.414534[/C][/ROW]
[ROW][C]16[/C][C]-0.014264[/C][C]-0.1105[/C][C]0.456195[/C][/ROW]
[ROW][C]17[/C][C]-0.056522[/C][C]-0.4378[/C][C]0.331545[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284365&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284365&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	0.834072	6.4607	0
2	0.668143	5.1754	1e-06
3	0.502215	3.8901	0.000127
4	0.464628	3.599	0.000324
5	0.427041	3.3078	0.000796
6	0.389455	3.0167	0.001872
7	0.347308	2.6902	0.004617
8	0.305162	2.3638	0.010673
9	0.263015	2.0373	0.023019
10	0.268896	2.0829	0.020767
11	0.274776	2.1284	0.01871
12	0.280657	2.174	0.016832
13	0.196436	1.5216	0.066683
14	0.112215	0.8692	0.194097
15	0.027994	0.2168	0.414534
16	-0.014264	-0.1105	0.456195
17	-0.056522	-0.4378	0.331545

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.834072	6.4607	0
2	-0.09047	-0.7008	0.243075
3	-0.099469	-0.7705	0.222018
4	0.319	2.471	0.008166
5	-0.051356	-0.3978	0.346094
6	-0.054136	-0.4193	0.338234
7	0.111621	0.8646	0.195349
8	-0.043264	-0.3351	0.369351
9	-0.045221	-0.3503	0.363679
10	0.205811	1.5942	0.058072
11	-0.029784	-0.2307	0.409165
12	-0.030698	-0.2378	0.406428
13	-0.178704	-1.3842	0.085706
14	-0.044057	-0.3413	0.367048
15	-0.046088	-0.357	0.361174
16	-0.076651	-0.5937	0.277461
17	-0.05374	-0.4163	0.339351

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.834072 & 6.4607 & 0 \tabularnewline
2 & -0.09047 & -0.7008 & 0.243075 \tabularnewline
3 & -0.099469 & -0.7705 & 0.222018 \tabularnewline
4 & 0.319 & 2.471 & 0.008166 \tabularnewline
5 & -0.051356 & -0.3978 & 0.346094 \tabularnewline
6 & -0.054136 & -0.4193 & 0.338234 \tabularnewline
7 & 0.111621 & 0.8646 & 0.195349 \tabularnewline
8 & -0.043264 & -0.3351 & 0.369351 \tabularnewline
9 & -0.045221 & -0.3503 & 0.363679 \tabularnewline
10 & 0.205811 & 1.5942 & 0.058072 \tabularnewline
11 & -0.029784 & -0.2307 & 0.409165 \tabularnewline
12 & -0.030698 & -0.2378 & 0.406428 \tabularnewline
13 & -0.178704 & -1.3842 & 0.085706 \tabularnewline
14 & -0.044057 & -0.3413 & 0.367048 \tabularnewline
15 & -0.046088 & -0.357 & 0.361174 \tabularnewline
16 & -0.076651 & -0.5937 & 0.277461 \tabularnewline
17 & -0.05374 & -0.4163 & 0.339351 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284365&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]0.834072[/C][C]6.4607[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.09047[/C][C]-0.7008[/C][C]0.243075[/C][/ROW]
[ROW][C]3[/C][C]-0.099469[/C][C]-0.7705[/C][C]0.222018[/C][/ROW]
[ROW][C]4[/C][C]0.319[/C][C]2.471[/C][C]0.008166[/C][/ROW]
[ROW][C]5[/C][C]-0.051356[/C][C]-0.3978[/C][C]0.346094[/C][/ROW]
[ROW][C]6[/C][C]-0.054136[/C][C]-0.4193[/C][C]0.338234[/C][/ROW]
[ROW][C]7[/C][C]0.111621[/C][C]0.8646[/C][C]0.195349[/C][/ROW]
[ROW][C]8[/C][C]-0.043264[/C][C]-0.3351[/C][C]0.369351[/C][/ROW]
[ROW][C]9[/C][C]-0.045221[/C][C]-0.3503[/C][C]0.363679[/C][/ROW]
[ROW][C]10[/C][C]0.205811[/C][C]1.5942[/C][C]0.058072[/C][/ROW]
[ROW][C]11[/C][C]-0.029784[/C][C]-0.2307[/C][C]0.409165[/C][/ROW]
[ROW][C]12[/C][C]-0.030698[/C][C]-0.2378[/C][C]0.406428[/C][/ROW]
[ROW][C]13[/C][C]-0.178704[/C][C]-1.3842[/C][C]0.085706[/C][/ROW]
[ROW][C]14[/C][C]-0.044057[/C][C]-0.3413[/C][C]0.367048[/C][/ROW]
[ROW][C]15[/C][C]-0.046088[/C][C]-0.357[/C][C]0.361174[/C][/ROW]
[ROW][C]16[/C][C]-0.076651[/C][C]-0.5937[/C][C]0.277461[/C][/ROW]
[ROW][C]17[/C][C]-0.05374[/C][C]-0.4163[/C][C]0.339351[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284365&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284365&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	0.834072	6.4607	0
2	-0.09047	-0.7008	0.243075
3	-0.099469	-0.7705	0.222018
4	0.319	2.471	0.008166
5	-0.051356	-0.3978	0.346094
6	-0.054136	-0.4193	0.338234
7	0.111621	0.8646	0.195349
8	-0.043264	-0.3351	0.369351
9	-0.045221	-0.3503	0.363679
10	0.205811	1.5942	0.058072
11	-0.029784	-0.2307	0.409165
12	-0.030698	-0.2378	0.406428
13	-0.178704	-1.3842	0.085706
14	-0.044057	-0.3413	0.367048
15	-0.046088	-0.357	0.361174
16	-0.076651	-0.5937	0.277461
17	-0.05374	-0.4163	0.339351

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