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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 17 Dec 2016 15:54:51 +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/2016/Dec/17/t1481986520qlfd6zwzk61enst.htm/, Retrieved Thu, 02 May 2024 05:54:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300835, Retrieved Thu, 02 May 2024 05:54:36 +0000

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-       [(Partial) Autocorrelation Function] [""N2582"" autocorr 1] [2016-12-17 14:54:51] [afe7f6443461a2cd6ee0b843643e84a9] [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	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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300835&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]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300835&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300835&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	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.976868	10.5212	0
2	0.953846	10.2732	0
3	0.931107	10.0283	0
4	0.908173	9.7813	0
5	0.883336	9.5138	0
6	0.858716	9.2486	0
7	0.834229	8.9849	0
8	0.809435	8.7179	0
9	0.783937	8.4433	0
10	0.758781	8.1723	0
11	0.734361	7.9093	0
12	0.710297	7.6501	0
13	0.684997	7.3776	0
14	0.659303	7.1009	0
15	0.633821	6.8265	0
16	0.608645	6.5553	0
17	0.581915	6.2674	0
18	0.555895	5.9872	0
19	0.53047	5.7133	0
20	0.504682	5.4356	0
21	0.478486	5.1535	1e-06

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.976868 & 10.5212 & 0 \tabularnewline
2 & 0.953846 & 10.2732 & 0 \tabularnewline
3 & 0.931107 & 10.0283 & 0 \tabularnewline
4 & 0.908173 & 9.7813 & 0 \tabularnewline
5 & 0.883336 & 9.5138 & 0 \tabularnewline
6 & 0.858716 & 9.2486 & 0 \tabularnewline
7 & 0.834229 & 8.9849 & 0 \tabularnewline
8 & 0.809435 & 8.7179 & 0 \tabularnewline
9 & 0.783937 & 8.4433 & 0 \tabularnewline
10 & 0.758781 & 8.1723 & 0 \tabularnewline
11 & 0.734361 & 7.9093 & 0 \tabularnewline
12 & 0.710297 & 7.6501 & 0 \tabularnewline
13 & 0.684997 & 7.3776 & 0 \tabularnewline
14 & 0.659303 & 7.1009 & 0 \tabularnewline
15 & 0.633821 & 6.8265 & 0 \tabularnewline
16 & 0.608645 & 6.5553 & 0 \tabularnewline
17 & 0.581915 & 6.2674 & 0 \tabularnewline
18 & 0.555895 & 5.9872 & 0 \tabularnewline
19 & 0.53047 & 5.7133 & 0 \tabularnewline
20 & 0.504682 & 5.4356 & 0 \tabularnewline
21 & 0.478486 & 5.1535 & 1e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300835&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]0.976868[/C][C]10.5212[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.953846[/C][C]10.2732[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.931107[/C][C]10.0283[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.908173[/C][C]9.7813[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.883336[/C][C]9.5138[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.858716[/C][C]9.2486[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.834229[/C][C]8.9849[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.809435[/C][C]8.7179[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.783937[/C][C]8.4433[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.758781[/C][C]8.1723[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.734361[/C][C]7.9093[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.710297[/C][C]7.6501[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.684997[/C][C]7.3776[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.659303[/C][C]7.1009[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.633821[/C][C]6.8265[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.608645[/C][C]6.5553[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.581915[/C][C]6.2674[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.555895[/C][C]5.9872[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.53047[/C][C]5.7133[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.504682[/C][C]5.4356[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.478486[/C][C]5.1535[/C][C]1e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300835&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300835&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	0.976868	10.5212	0
2	0.953846	10.2732	0
3	0.931107	10.0283	0
4	0.908173	9.7813	0
5	0.883336	9.5138	0
6	0.858716	9.2486	0
7	0.834229	8.9849	0
8	0.809435	8.7179	0
9	0.783937	8.4433	0
10	0.758781	8.1723	0
11	0.734361	7.9093	0
12	0.710297	7.6501	0
13	0.684997	7.3776	0
14	0.659303	7.1009	0
15	0.633821	6.8265	0
16	0.608645	6.5553	0
17	0.581915	6.2674	0
18	0.555895	5.9872	0
19	0.53047	5.7133	0
20	0.504682	5.4356	0
21	0.478486	5.1535	1e-06

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.976868	10.5212	0
2	-0.009322	-0.1004	0.460098
3	-0.005568	-0.06	0.476142
4	-0.016012	-0.1725	0.43169
5	-0.053636	-0.5777	0.2823
6	-0.008715	-0.0939	0.462689
7	-0.01081	-0.1164	0.453756
8	-0.019712	-0.2123	0.416119
9	-0.027526	-0.2965	0.383702
10	-0.007354	-0.0792	0.468501
11	0.001538	0.0166	0.493407
12	-0.005409	-0.0583	0.476821
13	-0.03991	-0.4298	0.334053
14	-0.024581	-0.2647	0.395838
15	-0.012543	-0.1351	0.446386
16	-0.009053	-0.0975	0.461248
17	-0.047407	-0.5106	0.305303
18	-0.001329	-0.0143	0.494301
19	-0.004987	-0.0537	0.478629
20	-0.02435	-0.2623	0.396793
21	-0.022314	-0.2403	0.405251

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.976868 & 10.5212 & 0 \tabularnewline
2 & -0.009322 & -0.1004 & 0.460098 \tabularnewline
3 & -0.005568 & -0.06 & 0.476142 \tabularnewline
4 & -0.016012 & -0.1725 & 0.43169 \tabularnewline
5 & -0.053636 & -0.5777 & 0.2823 \tabularnewline
6 & -0.008715 & -0.0939 & 0.462689 \tabularnewline
7 & -0.01081 & -0.1164 & 0.453756 \tabularnewline
8 & -0.019712 & -0.2123 & 0.416119 \tabularnewline
9 & -0.027526 & -0.2965 & 0.383702 \tabularnewline
10 & -0.007354 & -0.0792 & 0.468501 \tabularnewline
11 & 0.001538 & 0.0166 & 0.493407 \tabularnewline
12 & -0.005409 & -0.0583 & 0.476821 \tabularnewline
13 & -0.03991 & -0.4298 & 0.334053 \tabularnewline
14 & -0.024581 & -0.2647 & 0.395838 \tabularnewline
15 & -0.012543 & -0.1351 & 0.446386 \tabularnewline
16 & -0.009053 & -0.0975 & 0.461248 \tabularnewline
17 & -0.047407 & -0.5106 & 0.305303 \tabularnewline
18 & -0.001329 & -0.0143 & 0.494301 \tabularnewline
19 & -0.004987 & -0.0537 & 0.478629 \tabularnewline
20 & -0.02435 & -0.2623 & 0.396793 \tabularnewline
21 & -0.022314 & -0.2403 & 0.405251 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300835&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]0.976868[/C][C]10.5212[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.009322[/C][C]-0.1004[/C][C]0.460098[/C][/ROW]
[ROW][C]3[/C][C]-0.005568[/C][C]-0.06[/C][C]0.476142[/C][/ROW]
[ROW][C]4[/C][C]-0.016012[/C][C]-0.1725[/C][C]0.43169[/C][/ROW]
[ROW][C]5[/C][C]-0.053636[/C][C]-0.5777[/C][C]0.2823[/C][/ROW]
[ROW][C]6[/C][C]-0.008715[/C][C]-0.0939[/C][C]0.462689[/C][/ROW]
[ROW][C]7[/C][C]-0.01081[/C][C]-0.1164[/C][C]0.453756[/C][/ROW]
[ROW][C]8[/C][C]-0.019712[/C][C]-0.2123[/C][C]0.416119[/C][/ROW]
[ROW][C]9[/C][C]-0.027526[/C][C]-0.2965[/C][C]0.383702[/C][/ROW]
[ROW][C]10[/C][C]-0.007354[/C][C]-0.0792[/C][C]0.468501[/C][/ROW]
[ROW][C]11[/C][C]0.001538[/C][C]0.0166[/C][C]0.493407[/C][/ROW]
[ROW][C]12[/C][C]-0.005409[/C][C]-0.0583[/C][C]0.476821[/C][/ROW]
[ROW][C]13[/C][C]-0.03991[/C][C]-0.4298[/C][C]0.334053[/C][/ROW]
[ROW][C]14[/C][C]-0.024581[/C][C]-0.2647[/C][C]0.395838[/C][/ROW]
[ROW][C]15[/C][C]-0.012543[/C][C]-0.1351[/C][C]0.446386[/C][/ROW]
[ROW][C]16[/C][C]-0.009053[/C][C]-0.0975[/C][C]0.461248[/C][/ROW]
[ROW][C]17[/C][C]-0.047407[/C][C]-0.5106[/C][C]0.305303[/C][/ROW]
[ROW][C]18[/C][C]-0.001329[/C][C]-0.0143[/C][C]0.494301[/C][/ROW]
[ROW][C]19[/C][C]-0.004987[/C][C]-0.0537[/C][C]0.478629[/C][/ROW]
[ROW][C]20[/C][C]-0.02435[/C][C]-0.2623[/C][C]0.396793[/C][/ROW]
[ROW][C]21[/C][C]-0.022314[/C][C]-0.2403[/C][C]0.405251[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300835&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300835&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	0.976868	10.5212	0
2	-0.009322	-0.1004	0.460098
3	-0.005568	-0.06	0.476142
4	-0.016012	-0.1725	0.43169
5	-0.053636	-0.5777	0.2823
6	-0.008715	-0.0939	0.462689
7	-0.01081	-0.1164	0.453756
8	-0.019712	-0.2123	0.416119
9	-0.027526	-0.2965	0.383702
10	-0.007354	-0.0792	0.468501
11	0.001538	0.0166	0.493407
12	-0.005409	-0.0583	0.476821
13	-0.03991	-0.4298	0.334053
14	-0.024581	-0.2647	0.395838
15	-0.012543	-0.1351	0.446386
16	-0.009053	-0.0975	0.461248
17	-0.047407	-0.5106	0.305303
18	-0.001329	-0.0143	0.494301
19	-0.004987	-0.0537	0.478629
20	-0.02435	-0.2623	0.396793
21	-0.022314	-0.2403	0.405251

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 = 2.0 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 2.0 ; 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)
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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code