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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 21 Dec 2016 15:08:08 +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/21/t1482329314xl30hbkgeawk4y4.htm/, Retrieved Mon, 06 May 2024 12:53:32 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302310, Retrieved Mon, 06 May 2024 12:53:32 +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] [n1731] [2016-12-21 14:08:08] [0fbc99f8be9cad246c7cf6558103ab95] [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=302310&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=302310&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302310&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	0.153002	1.4991	0.068564
2	0.013227	0.1296	0.448578
3	0.072826	0.7135	0.238619
4	0.180413	1.7677	0.040146
5	0.13288	1.302	0.098023
6	-0.046926	-0.4598	0.323358
7	-0.096871	-0.9491	0.172468
8	-0.14198	-1.3911	0.083703
9	0.012987	0.1272	0.449506
10	0.098436	0.9645	0.168615
11	0.065983	0.6465	0.259749
12	-0.381231	-3.7353	0.000159
13	0.061066	0.5983	0.275516
14	0.099426	0.9742	0.166211
15	0.030564	0.2995	0.382618
16	-0.032514	-0.3186	0.375371
17	-0.077014	-0.7546	0.226174
18	0.0644	0.631	0.264773
19	-0.014983	-0.1468	0.441799
20	-0.022468	-0.2201	0.413114

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.153002 & 1.4991 & 0.068564 \tabularnewline
2 & 0.013227 & 0.1296 & 0.448578 \tabularnewline
3 & 0.072826 & 0.7135 & 0.238619 \tabularnewline
4 & 0.180413 & 1.7677 & 0.040146 \tabularnewline
5 & 0.13288 & 1.302 & 0.098023 \tabularnewline
6 & -0.046926 & -0.4598 & 0.323358 \tabularnewline
7 & -0.096871 & -0.9491 & 0.172468 \tabularnewline
8 & -0.14198 & -1.3911 & 0.083703 \tabularnewline
9 & 0.012987 & 0.1272 & 0.449506 \tabularnewline
10 & 0.098436 & 0.9645 & 0.168615 \tabularnewline
11 & 0.065983 & 0.6465 & 0.259749 \tabularnewline
12 & -0.381231 & -3.7353 & 0.000159 \tabularnewline
13 & 0.061066 & 0.5983 & 0.275516 \tabularnewline
14 & 0.099426 & 0.9742 & 0.166211 \tabularnewline
15 & 0.030564 & 0.2995 & 0.382618 \tabularnewline
16 & -0.032514 & -0.3186 & 0.375371 \tabularnewline
17 & -0.077014 & -0.7546 & 0.226174 \tabularnewline
18 & 0.0644 & 0.631 & 0.264773 \tabularnewline
19 & -0.014983 & -0.1468 & 0.441799 \tabularnewline
20 & -0.022468 & -0.2201 & 0.413114 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302310&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]0.153002[/C][C]1.4991[/C][C]0.068564[/C][/ROW]
[ROW][C]2[/C][C]0.013227[/C][C]0.1296[/C][C]0.448578[/C][/ROW]
[ROW][C]3[/C][C]0.072826[/C][C]0.7135[/C][C]0.238619[/C][/ROW]
[ROW][C]4[/C][C]0.180413[/C][C]1.7677[/C][C]0.040146[/C][/ROW]
[ROW][C]5[/C][C]0.13288[/C][C]1.302[/C][C]0.098023[/C][/ROW]
[ROW][C]6[/C][C]-0.046926[/C][C]-0.4598[/C][C]0.323358[/C][/ROW]
[ROW][C]7[/C][C]-0.096871[/C][C]-0.9491[/C][C]0.172468[/C][/ROW]
[ROW][C]8[/C][C]-0.14198[/C][C]-1.3911[/C][C]0.083703[/C][/ROW]
[ROW][C]9[/C][C]0.012987[/C][C]0.1272[/C][C]0.449506[/C][/ROW]
[ROW][C]10[/C][C]0.098436[/C][C]0.9645[/C][C]0.168615[/C][/ROW]
[ROW][C]11[/C][C]0.065983[/C][C]0.6465[/C][C]0.259749[/C][/ROW]
[ROW][C]12[/C][C]-0.381231[/C][C]-3.7353[/C][C]0.000159[/C][/ROW]
[ROW][C]13[/C][C]0.061066[/C][C]0.5983[/C][C]0.275516[/C][/ROW]
[ROW][C]14[/C][C]0.099426[/C][C]0.9742[/C][C]0.166211[/C][/ROW]
[ROW][C]15[/C][C]0.030564[/C][C]0.2995[/C][C]0.382618[/C][/ROW]
[ROW][C]16[/C][C]-0.032514[/C][C]-0.3186[/C][C]0.375371[/C][/ROW]
[ROW][C]17[/C][C]-0.077014[/C][C]-0.7546[/C][C]0.226174[/C][/ROW]
[ROW][C]18[/C][C]0.0644[/C][C]0.631[/C][C]0.264773[/C][/ROW]
[ROW][C]19[/C][C]-0.014983[/C][C]-0.1468[/C][C]0.441799[/C][/ROW]
[ROW][C]20[/C][C]-0.022468[/C][C]-0.2201[/C][C]0.413114[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302310&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302310&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	0.153002	1.4991	0.068564
2	0.013227	0.1296	0.448578
3	0.072826	0.7135	0.238619
4	0.180413	1.7677	0.040146
5	0.13288	1.302	0.098023
6	-0.046926	-0.4598	0.323358
7	-0.096871	-0.9491	0.172468
8	-0.14198	-1.3911	0.083703
9	0.012987	0.1272	0.449506
10	0.098436	0.9645	0.168615
11	0.065983	0.6465	0.259749
12	-0.381231	-3.7353	0.000159
13	0.061066	0.5983	0.275516
14	0.099426	0.9742	0.166211
15	0.030564	0.2995	0.382618
16	-0.032514	-0.3186	0.375371
17	-0.077014	-0.7546	0.226174
18	0.0644	0.631	0.264773
19	-0.014983	-0.1468	0.441799
20	-0.022468	-0.2201	0.413114

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.153002	1.4991	0.068564
2	-0.010427	-0.1022	0.459421
3	0.07412	0.7262	0.234735
4	0.162747	1.5946	0.057045
5	0.087597	0.8583	0.196441
6	-0.084272	-0.8257	0.205513
7	-0.105447	-1.0332	0.152062
8	-0.170205	-1.6677	0.049321
9	0.022426	0.2197	0.413275
10	0.130201	1.2757	0.102569
11	0.129361	1.2675	0.104026
12	-0.381267	-3.7356	0.000159
13	0.190391	1.8654	0.032587
14	-0.013011	-0.1275	0.449412
15	0.004348	0.0426	0.483055
16	0.05025	0.4924	0.311798
17	-0.012716	-0.1246	0.450553
18	0.016363	0.1603	0.436482
19	-0.080103	-0.7848	0.217238
20	-0.12565	-1.2311	0.110644

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.153002 & 1.4991 & 0.068564 \tabularnewline
2 & -0.010427 & -0.1022 & 0.459421 \tabularnewline
3 & 0.07412 & 0.7262 & 0.234735 \tabularnewline
4 & 0.162747 & 1.5946 & 0.057045 \tabularnewline
5 & 0.087597 & 0.8583 & 0.196441 \tabularnewline
6 & -0.084272 & -0.8257 & 0.205513 \tabularnewline
7 & -0.105447 & -1.0332 & 0.152062 \tabularnewline
8 & -0.170205 & -1.6677 & 0.049321 \tabularnewline
9 & 0.022426 & 0.2197 & 0.413275 \tabularnewline
10 & 0.130201 & 1.2757 & 0.102569 \tabularnewline
11 & 0.129361 & 1.2675 & 0.104026 \tabularnewline
12 & -0.381267 & -3.7356 & 0.000159 \tabularnewline
13 & 0.190391 & 1.8654 & 0.032587 \tabularnewline
14 & -0.013011 & -0.1275 & 0.449412 \tabularnewline
15 & 0.004348 & 0.0426 & 0.483055 \tabularnewline
16 & 0.05025 & 0.4924 & 0.311798 \tabularnewline
17 & -0.012716 & -0.1246 & 0.450553 \tabularnewline
18 & 0.016363 & 0.1603 & 0.436482 \tabularnewline
19 & -0.080103 & -0.7848 & 0.217238 \tabularnewline
20 & -0.12565 & -1.2311 & 0.110644 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302310&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]0.153002[/C][C]1.4991[/C][C]0.068564[/C][/ROW]
[ROW][C]2[/C][C]-0.010427[/C][C]-0.1022[/C][C]0.459421[/C][/ROW]
[ROW][C]3[/C][C]0.07412[/C][C]0.7262[/C][C]0.234735[/C][/ROW]
[ROW][C]4[/C][C]0.162747[/C][C]1.5946[/C][C]0.057045[/C][/ROW]
[ROW][C]5[/C][C]0.087597[/C][C]0.8583[/C][C]0.196441[/C][/ROW]
[ROW][C]6[/C][C]-0.084272[/C][C]-0.8257[/C][C]0.205513[/C][/ROW]
[ROW][C]7[/C][C]-0.105447[/C][C]-1.0332[/C][C]0.152062[/C][/ROW]
[ROW][C]8[/C][C]-0.170205[/C][C]-1.6677[/C][C]0.049321[/C][/ROW]
[ROW][C]9[/C][C]0.022426[/C][C]0.2197[/C][C]0.413275[/C][/ROW]
[ROW][C]10[/C][C]0.130201[/C][C]1.2757[/C][C]0.102569[/C][/ROW]
[ROW][C]11[/C][C]0.129361[/C][C]1.2675[/C][C]0.104026[/C][/ROW]
[ROW][C]12[/C][C]-0.381267[/C][C]-3.7356[/C][C]0.000159[/C][/ROW]
[ROW][C]13[/C][C]0.190391[/C][C]1.8654[/C][C]0.032587[/C][/ROW]
[ROW][C]14[/C][C]-0.013011[/C][C]-0.1275[/C][C]0.449412[/C][/ROW]
[ROW][C]15[/C][C]0.004348[/C][C]0.0426[/C][C]0.483055[/C][/ROW]
[ROW][C]16[/C][C]0.05025[/C][C]0.4924[/C][C]0.311798[/C][/ROW]
[ROW][C]17[/C][C]-0.012716[/C][C]-0.1246[/C][C]0.450553[/C][/ROW]
[ROW][C]18[/C][C]0.016363[/C][C]0.1603[/C][C]0.436482[/C][/ROW]
[ROW][C]19[/C][C]-0.080103[/C][C]-0.7848[/C][C]0.217238[/C][/ROW]
[ROW][C]20[/C][C]-0.12565[/C][C]-1.2311[/C][C]0.110644[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302310&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302310&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	0.153002	1.4991	0.068564
2	-0.010427	-0.1022	0.459421
3	0.07412	0.7262	0.234735
4	0.162747	1.5946	0.057045
5	0.087597	0.8583	0.196441
6	-0.084272	-0.8257	0.205513
7	-0.105447	-1.0332	0.152062
8	-0.170205	-1.6677	0.049321
9	0.022426	0.2197	0.413275
10	0.130201	1.2757	0.102569
11	0.129361	1.2675	0.104026
12	-0.381267	-3.7356	0.000159
13	0.190391	1.8654	0.032587
14	-0.013011	-0.1275	0.449412
15	0.004348	0.0426	0.483055
16	0.05025	0.4924	0.311798
17	-0.012716	-0.1246	0.450553
18	0.016363	0.1603	0.436482
19	-0.080103	-0.7848	0.217238
20	-0.12565	-1.2311	0.110644

Figure 1

PNG link

Postscript link

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Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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