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*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 18 Dec 2016 22:04:57 +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/18/t1482095108l7ywvyhwf4x2usr.htm/, Retrieved Thu, 09 May 2024 01:21:01 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301243, Retrieved Thu, 09 May 2024 01:21:01 +0000

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Estimated Impact

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

-     [Spectral Analysis] [] [2016-12-16 13:29:44] [683f400e1b95307fc738e729f07c4fce]
- R P   [Spectral Analysis] [] [2016-12-18 18:43:40] [683f400e1b95307fc738e729f07c4fce]
- RMP       [(Partial) Autocorrelation Function] [] [2016-12-18 21:04:57] [404ac5ee4f7301873f6a96ef36861981] [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=301243&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=301243&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301243&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	0.573724	6.1792	0
2	0.610249	6.5726	0
3	0.555742	5.9855	0
4	0.523644	5.6398	0
5	0.414862	4.4682	9e-06
6	0.359779	3.8749	8.9e-05
7	0.324992	3.5003	0.00033
8	0.253007	2.725	0.003713
9	0.166035	1.7882	0.038173
10	0.23623	2.5443	0.006132
11	0.115961	1.2489	0.107101
12	0.049147	0.5293	0.298794
13	0.087583	0.9433	0.173743
14	0.045937	0.4948	0.310855
15	-0.002038	-0.022	0.491262
16	-0.010422	-0.1122	0.45541
17	-0.060942	-0.6564	0.256445
18	-0.061844	-0.6661	0.25334
19	-0.124842	-1.3446	0.09069
20	-0.096689	-1.0414	0.149933

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.573724 & 6.1792 & 0 \tabularnewline
2 & 0.610249 & 6.5726 & 0 \tabularnewline
3 & 0.555742 & 5.9855 & 0 \tabularnewline
4 & 0.523644 & 5.6398 & 0 \tabularnewline
5 & 0.414862 & 4.4682 & 9e-06 \tabularnewline
6 & 0.359779 & 3.8749 & 8.9e-05 \tabularnewline
7 & 0.324992 & 3.5003 & 0.00033 \tabularnewline
8 & 0.253007 & 2.725 & 0.003713 \tabularnewline
9 & 0.166035 & 1.7882 & 0.038173 \tabularnewline
10 & 0.23623 & 2.5443 & 0.006132 \tabularnewline
11 & 0.115961 & 1.2489 & 0.107101 \tabularnewline
12 & 0.049147 & 0.5293 & 0.298794 \tabularnewline
13 & 0.087583 & 0.9433 & 0.173743 \tabularnewline
14 & 0.045937 & 0.4948 & 0.310855 \tabularnewline
15 & -0.002038 & -0.022 & 0.491262 \tabularnewline
16 & -0.010422 & -0.1122 & 0.45541 \tabularnewline
17 & -0.060942 & -0.6564 & 0.256445 \tabularnewline
18 & -0.061844 & -0.6661 & 0.25334 \tabularnewline
19 & -0.124842 & -1.3446 & 0.09069 \tabularnewline
20 & -0.096689 & -1.0414 & 0.149933 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301243&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]0.573724[/C][C]6.1792[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.610249[/C][C]6.5726[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.555742[/C][C]5.9855[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.523644[/C][C]5.6398[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.414862[/C][C]4.4682[/C][C]9e-06[/C][/ROW]
[ROW][C]6[/C][C]0.359779[/C][C]3.8749[/C][C]8.9e-05[/C][/ROW]
[ROW][C]7[/C][C]0.324992[/C][C]3.5003[/C][C]0.00033[/C][/ROW]
[ROW][C]8[/C][C]0.253007[/C][C]2.725[/C][C]0.003713[/C][/ROW]
[ROW][C]9[/C][C]0.166035[/C][C]1.7882[/C][C]0.038173[/C][/ROW]
[ROW][C]10[/C][C]0.23623[/C][C]2.5443[/C][C]0.006132[/C][/ROW]
[ROW][C]11[/C][C]0.115961[/C][C]1.2489[/C][C]0.107101[/C][/ROW]
[ROW][C]12[/C][C]0.049147[/C][C]0.5293[/C][C]0.298794[/C][/ROW]
[ROW][C]13[/C][C]0.087583[/C][C]0.9433[/C][C]0.173743[/C][/ROW]
[ROW][C]14[/C][C]0.045937[/C][C]0.4948[/C][C]0.310855[/C][/ROW]
[ROW][C]15[/C][C]-0.002038[/C][C]-0.022[/C][C]0.491262[/C][/ROW]
[ROW][C]16[/C][C]-0.010422[/C][C]-0.1122[/C][C]0.45541[/C][/ROW]
[ROW][C]17[/C][C]-0.060942[/C][C]-0.6564[/C][C]0.256445[/C][/ROW]
[ROW][C]18[/C][C]-0.061844[/C][C]-0.6661[/C][C]0.25334[/C][/ROW]
[ROW][C]19[/C][C]-0.124842[/C][C]-1.3446[/C][C]0.09069[/C][/ROW]
[ROW][C]20[/C][C]-0.096689[/C][C]-1.0414[/C][C]0.149933[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301243&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301243&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	0.573724	6.1792	0
2	0.610249	6.5726	0
3	0.555742	5.9855	0
4	0.523644	5.6398	0
5	0.414862	4.4682	9e-06
6	0.359779	3.8749	8.9e-05
7	0.324992	3.5003	0.00033
8	0.253007	2.725	0.003713
9	0.166035	1.7882	0.038173
10	0.23623	2.5443	0.006132
11	0.115961	1.2489	0.107101
12	0.049147	0.5293	0.298794
13	0.087583	0.9433	0.173743
14	0.045937	0.4948	0.310855
15	-0.002038	-0.022	0.491262
16	-0.010422	-0.1122	0.45541
17	-0.060942	-0.6564	0.256445
18	-0.061844	-0.6661	0.25334
19	-0.124842	-1.3446	0.09069
20	-0.096689	-1.0414	0.149933

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.573724	6.1792	0
2	0.419011	4.5129	8e-06
3	0.202387	2.1798	0.015647
4	0.10347	1.1144	0.133705
5	-0.088891	-0.9574	0.170182
6	-0.095967	-1.0336	0.151738
7	-0.015019	-0.1618	0.43589
8	-0.042397	-0.4566	0.324396
9	-0.101734	-1.0957	0.137739
10	0.163927	1.7655	0.040051
11	-0.052671	-0.5673	0.285809
12	-0.148102	-1.5951	0.056705
13	0.072603	0.782	0.217917
14	0.002527	0.0272	0.489165
15	-0.044852	-0.4831	0.314978
16	0.020334	0.219	0.413517
17	-0.112335	-1.2099	0.114391
18	-0.024849	-0.2676	0.394728
19	-0.027021	-0.291	0.385778
20	-0.017814	-0.1919	0.424093

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.573724 & 6.1792 & 0 \tabularnewline
2 & 0.419011 & 4.5129 & 8e-06 \tabularnewline
3 & 0.202387 & 2.1798 & 0.015647 \tabularnewline
4 & 0.10347 & 1.1144 & 0.133705 \tabularnewline
5 & -0.088891 & -0.9574 & 0.170182 \tabularnewline
6 & -0.095967 & -1.0336 & 0.151738 \tabularnewline
7 & -0.015019 & -0.1618 & 0.43589 \tabularnewline
8 & -0.042397 & -0.4566 & 0.324396 \tabularnewline
9 & -0.101734 & -1.0957 & 0.137739 \tabularnewline
10 & 0.163927 & 1.7655 & 0.040051 \tabularnewline
11 & -0.052671 & -0.5673 & 0.285809 \tabularnewline
12 & -0.148102 & -1.5951 & 0.056705 \tabularnewline
13 & 0.072603 & 0.782 & 0.217917 \tabularnewline
14 & 0.002527 & 0.0272 & 0.489165 \tabularnewline
15 & -0.044852 & -0.4831 & 0.314978 \tabularnewline
16 & 0.020334 & 0.219 & 0.413517 \tabularnewline
17 & -0.112335 & -1.2099 & 0.114391 \tabularnewline
18 & -0.024849 & -0.2676 & 0.394728 \tabularnewline
19 & -0.027021 & -0.291 & 0.385778 \tabularnewline
20 & -0.017814 & -0.1919 & 0.424093 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301243&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]0.573724[/C][C]6.1792[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.419011[/C][C]4.5129[/C][C]8e-06[/C][/ROW]
[ROW][C]3[/C][C]0.202387[/C][C]2.1798[/C][C]0.015647[/C][/ROW]
[ROW][C]4[/C][C]0.10347[/C][C]1.1144[/C][C]0.133705[/C][/ROW]
[ROW][C]5[/C][C]-0.088891[/C][C]-0.9574[/C][C]0.170182[/C][/ROW]
[ROW][C]6[/C][C]-0.095967[/C][C]-1.0336[/C][C]0.151738[/C][/ROW]
[ROW][C]7[/C][C]-0.015019[/C][C]-0.1618[/C][C]0.43589[/C][/ROW]
[ROW][C]8[/C][C]-0.042397[/C][C]-0.4566[/C][C]0.324396[/C][/ROW]
[ROW][C]9[/C][C]-0.101734[/C][C]-1.0957[/C][C]0.137739[/C][/ROW]
[ROW][C]10[/C][C]0.163927[/C][C]1.7655[/C][C]0.040051[/C][/ROW]
[ROW][C]11[/C][C]-0.052671[/C][C]-0.5673[/C][C]0.285809[/C][/ROW]
[ROW][C]12[/C][C]-0.148102[/C][C]-1.5951[/C][C]0.056705[/C][/ROW]
[ROW][C]13[/C][C]0.072603[/C][C]0.782[/C][C]0.217917[/C][/ROW]
[ROW][C]14[/C][C]0.002527[/C][C]0.0272[/C][C]0.489165[/C][/ROW]
[ROW][C]15[/C][C]-0.044852[/C][C]-0.4831[/C][C]0.314978[/C][/ROW]
[ROW][C]16[/C][C]0.020334[/C][C]0.219[/C][C]0.413517[/C][/ROW]
[ROW][C]17[/C][C]-0.112335[/C][C]-1.2099[/C][C]0.114391[/C][/ROW]
[ROW][C]18[/C][C]-0.024849[/C][C]-0.2676[/C][C]0.394728[/C][/ROW]
[ROW][C]19[/C][C]-0.027021[/C][C]-0.291[/C][C]0.385778[/C][/ROW]
[ROW][C]20[/C][C]-0.017814[/C][C]-0.1919[/C][C]0.424093[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301243&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301243&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	0.573724	6.1792	0
2	0.419011	4.5129	8e-06
3	0.202387	2.1798	0.015647
4	0.10347	1.1144	0.133705
5	-0.088891	-0.9574	0.170182
6	-0.095967	-1.0336	0.151738
7	-0.015019	-0.1618	0.43589
8	-0.042397	-0.4566	0.324396
9	-0.101734	-1.0957	0.137739
10	0.163927	1.7655	0.040051
11	-0.052671	-0.5673	0.285809
12	-0.148102	-1.5951	0.056705
13	0.072603	0.782	0.217917
14	0.002527	0.0272	0.489165
15	-0.044852	-0.4831	0.314978
16	0.020334	0.219	0.413517
17	-0.112335	-1.2099	0.114391
18	-0.024849	-0.2676	0.394728
19	-0.027021	-0.291	0.385778
20	-0.017814	-0.1919	0.424093

Figure 1

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Postscript link

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Figure 2

PNG link

Postscript link

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Figure 3

PNG link

Postscript link

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Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code