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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 16 Dec 2016 09:46:12 +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/Dec/16/t1481878051jr96bp2c5gus5kh.htm/, Retrieved Fri, 03 May 2024 01:54:53 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300134, Retrieved Fri, 03 May 2024 01:54:53 +0000

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

-       [(Partial) Autocorrelation Function] [] [2016-12-16 08:46:12] [94ac3c9a028ddd47e8862e80eac9f626] [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	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300134&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

2 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300134&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300134&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	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.003724	-0.0396	0.484245
2	-0.266696	-2.835	0.002715
3	-0.336161	-3.5734	0.00026
4	-0.36141	-3.8418	0.000101
5	0.325125	3.4561	0.000386
6	0.374751	3.9837	6e-05
7	0.288014	3.0616	0.001376
8	-0.264895	-2.8159	0.002871
9	-0.337151	-3.584	0.00025
10	-0.269825	-2.8683	0.002463
11	0.04497	0.478	0.316774
12	0.718473	7.6375	0
13	0.07578	0.8056	0.211096
14	-0.232675	-2.4734	0.007436
15	-0.349881	-3.7193	0.000156
16	-0.3155	-3.3538	0.000543
17	0.303498	3.2262	0.000821
18	0.318515	3.3859	0.000488
19	0.223477	2.3756	0.009602
20	-0.215602	-2.2919	0.011882

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.003724 & -0.0396 & 0.484245 \tabularnewline
2 & -0.266696 & -2.835 & 0.002715 \tabularnewline
3 & -0.336161 & -3.5734 & 0.00026 \tabularnewline
4 & -0.36141 & -3.8418 & 0.000101 \tabularnewline
5 & 0.325125 & 3.4561 & 0.000386 \tabularnewline
6 & 0.374751 & 3.9837 & 6e-05 \tabularnewline
7 & 0.288014 & 3.0616 & 0.001376 \tabularnewline
8 & -0.264895 & -2.8159 & 0.002871 \tabularnewline
9 & -0.337151 & -3.584 & 0.00025 \tabularnewline
10 & -0.269825 & -2.8683 & 0.002463 \tabularnewline
11 & 0.04497 & 0.478 & 0.316774 \tabularnewline
12 & 0.718473 & 7.6375 & 0 \tabularnewline
13 & 0.07578 & 0.8056 & 0.211096 \tabularnewline
14 & -0.232675 & -2.4734 & 0.007436 \tabularnewline
15 & -0.349881 & -3.7193 & 0.000156 \tabularnewline
16 & -0.3155 & -3.3538 & 0.000543 \tabularnewline
17 & 0.303498 & 3.2262 & 0.000821 \tabularnewline
18 & 0.318515 & 3.3859 & 0.000488 \tabularnewline
19 & 0.223477 & 2.3756 & 0.009602 \tabularnewline
20 & -0.215602 & -2.2919 & 0.011882 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300134&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]-0.003724[/C][C]-0.0396[/C][C]0.484245[/C][/ROW]
[ROW][C]2[/C][C]-0.266696[/C][C]-2.835[/C][C]0.002715[/C][/ROW]
[ROW][C]3[/C][C]-0.336161[/C][C]-3.5734[/C][C]0.00026[/C][/ROW]
[ROW][C]4[/C][C]-0.36141[/C][C]-3.8418[/C][C]0.000101[/C][/ROW]
[ROW][C]5[/C][C]0.325125[/C][C]3.4561[/C][C]0.000386[/C][/ROW]
[ROW][C]6[/C][C]0.374751[/C][C]3.9837[/C][C]6e-05[/C][/ROW]
[ROW][C]7[/C][C]0.288014[/C][C]3.0616[/C][C]0.001376[/C][/ROW]
[ROW][C]8[/C][C]-0.264895[/C][C]-2.8159[/C][C]0.002871[/C][/ROW]
[ROW][C]9[/C][C]-0.337151[/C][C]-3.584[/C][C]0.00025[/C][/ROW]
[ROW][C]10[/C][C]-0.269825[/C][C]-2.8683[/C][C]0.002463[/C][/ROW]
[ROW][C]11[/C][C]0.04497[/C][C]0.478[/C][C]0.316774[/C][/ROW]
[ROW][C]12[/C][C]0.718473[/C][C]7.6375[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.07578[/C][C]0.8056[/C][C]0.211096[/C][/ROW]
[ROW][C]14[/C][C]-0.232675[/C][C]-2.4734[/C][C]0.007436[/C][/ROW]
[ROW][C]15[/C][C]-0.349881[/C][C]-3.7193[/C][C]0.000156[/C][/ROW]
[ROW][C]16[/C][C]-0.3155[/C][C]-3.3538[/C][C]0.000543[/C][/ROW]
[ROW][C]17[/C][C]0.303498[/C][C]3.2262[/C][C]0.000821[/C][/ROW]
[ROW][C]18[/C][C]0.318515[/C][C]3.3859[/C][C]0.000488[/C][/ROW]
[ROW][C]19[/C][C]0.223477[/C][C]2.3756[/C][C]0.009602[/C][/ROW]
[ROW][C]20[/C][C]-0.215602[/C][C]-2.2919[/C][C]0.011882[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300134&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300134&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	-0.003724	-0.0396	0.484245
2	-0.266696	-2.835	0.002715
3	-0.336161	-3.5734	0.00026
4	-0.36141	-3.8418	0.000101
5	0.325125	3.4561	0.000386
6	0.374751	3.9837	6e-05
7	0.288014	3.0616	0.001376
8	-0.264895	-2.8159	0.002871
9	-0.337151	-3.584	0.00025
10	-0.269825	-2.8683	0.002463
11	0.04497	0.478	0.316774
12	0.718473	7.6375	0
13	0.07578	0.8056	0.211096
14	-0.232675	-2.4734	0.007436
15	-0.349881	-3.7193	0.000156
16	-0.3155	-3.3538	0.000543
17	0.303498	3.2262	0.000821
18	0.318515	3.3859	0.000488
19	0.223477	2.3756	0.009602
20	-0.215602	-2.2919	0.011882

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.003724	-0.0396	0.484245
2	-0.266713	-2.8352	0.002714
3	-0.364335	-3.8729	9e-05
4	-0.58172	-6.1838	0
5	-0.086622	-0.9208	0.179557
6	0.016977	0.1805	0.428554
7	0.347116	3.6899	0.000173
8	-0.035187	-0.374	0.354536
9	0.183135	1.9468	0.027023
10	-0.227135	-2.4145	0.008682
11	-0.192805	-2.0495	0.021362
12	0.38392	4.0811	4.2e-05
13	0.1031	1.096	0.137712
14	-0.099673	-1.0595	0.145806
15	-0.109417	-1.1631	0.123617
16	-0.016163	-0.1718	0.431944
17	0.050094	0.5325	0.29771
18	-0.125425	-1.3333	0.09256
19	-0.101421	-1.0781	0.141637
20	-0.10696	-1.137	0.128971

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.003724 & -0.0396 & 0.484245 \tabularnewline
2 & -0.266713 & -2.8352 & 0.002714 \tabularnewline
3 & -0.364335 & -3.8729 & 9e-05 \tabularnewline
4 & -0.58172 & -6.1838 & 0 \tabularnewline
5 & -0.086622 & -0.9208 & 0.179557 \tabularnewline
6 & 0.016977 & 0.1805 & 0.428554 \tabularnewline
7 & 0.347116 & 3.6899 & 0.000173 \tabularnewline
8 & -0.035187 & -0.374 & 0.354536 \tabularnewline
9 & 0.183135 & 1.9468 & 0.027023 \tabularnewline
10 & -0.227135 & -2.4145 & 0.008682 \tabularnewline
11 & -0.192805 & -2.0495 & 0.021362 \tabularnewline
12 & 0.38392 & 4.0811 & 4.2e-05 \tabularnewline
13 & 0.1031 & 1.096 & 0.137712 \tabularnewline
14 & -0.099673 & -1.0595 & 0.145806 \tabularnewline
15 & -0.109417 & -1.1631 & 0.123617 \tabularnewline
16 & -0.016163 & -0.1718 & 0.431944 \tabularnewline
17 & 0.050094 & 0.5325 & 0.29771 \tabularnewline
18 & -0.125425 & -1.3333 & 0.09256 \tabularnewline
19 & -0.101421 & -1.0781 & 0.141637 \tabularnewline
20 & -0.10696 & -1.137 & 0.128971 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300134&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]-0.003724[/C][C]-0.0396[/C][C]0.484245[/C][/ROW]
[ROW][C]2[/C][C]-0.266713[/C][C]-2.8352[/C][C]0.002714[/C][/ROW]
[ROW][C]3[/C][C]-0.364335[/C][C]-3.8729[/C][C]9e-05[/C][/ROW]
[ROW][C]4[/C][C]-0.58172[/C][C]-6.1838[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]-0.086622[/C][C]-0.9208[/C][C]0.179557[/C][/ROW]
[ROW][C]6[/C][C]0.016977[/C][C]0.1805[/C][C]0.428554[/C][/ROW]
[ROW][C]7[/C][C]0.347116[/C][C]3.6899[/C][C]0.000173[/C][/ROW]
[ROW][C]8[/C][C]-0.035187[/C][C]-0.374[/C][C]0.354536[/C][/ROW]
[ROW][C]9[/C][C]0.183135[/C][C]1.9468[/C][C]0.027023[/C][/ROW]
[ROW][C]10[/C][C]-0.227135[/C][C]-2.4145[/C][C]0.008682[/C][/ROW]
[ROW][C]11[/C][C]-0.192805[/C][C]-2.0495[/C][C]0.021362[/C][/ROW]
[ROW][C]12[/C][C]0.38392[/C][C]4.0811[/C][C]4.2e-05[/C][/ROW]
[ROW][C]13[/C][C]0.1031[/C][C]1.096[/C][C]0.137712[/C][/ROW]
[ROW][C]14[/C][C]-0.099673[/C][C]-1.0595[/C][C]0.145806[/C][/ROW]
[ROW][C]15[/C][C]-0.109417[/C][C]-1.1631[/C][C]0.123617[/C][/ROW]
[ROW][C]16[/C][C]-0.016163[/C][C]-0.1718[/C][C]0.431944[/C][/ROW]
[ROW][C]17[/C][C]0.050094[/C][C]0.5325[/C][C]0.29771[/C][/ROW]
[ROW][C]18[/C][C]-0.125425[/C][C]-1.3333[/C][C]0.09256[/C][/ROW]
[ROW][C]19[/C][C]-0.101421[/C][C]-1.0781[/C][C]0.141637[/C][/ROW]
[ROW][C]20[/C][C]-0.10696[/C][C]-1.137[/C][C]0.128971[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300134&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300134&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	-0.003724	-0.0396	0.484245
2	-0.266713	-2.8352	0.002714
3	-0.364335	-3.8729	9e-05
4	-0.58172	-6.1838	0
5	-0.086622	-0.9208	0.179557
6	0.016977	0.1805	0.428554
7	0.347116	3.6899	0.000173
8	-0.035187	-0.374	0.354536
9	0.183135	1.9468	0.027023
10	-0.227135	-2.4145	0.008682
11	-0.192805	-2.0495	0.021362
12	0.38392	4.0811	4.2e-05
13	0.1031	1.096	0.137712
14	-0.099673	-1.0595	0.145806
15	-0.109417	-1.1631	0.123617
16	-0.016163	-0.1718	0.431944
17	0.050094	0.5325	0.29771
18	-0.125425	-1.3333	0.09256
19	-0.101421	-1.0781	0.141637
20	-0.10696	-1.137	0.128971

Figure 1

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Postscript link

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Figure 2

PNG link

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Figure 3

PNG link

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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,'ACF(k)',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,'PACF(k)',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