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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 21 Dec 2016 17:03:56 +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/t14823362663o2a9az4grwzx5i.htm/, Retrieved Mon, 06 May 2024 19:43:14 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302404, Retrieved Mon, 06 May 2024 19:43:14 +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] [] [2016-12-21 16:03:56] [2802fcbee976b89d2ab84425d3d65dcf] [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=302404&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=302404&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302404&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	0.279359	3.1233	0.001111
2	0.135145	1.511	0.066661
3	0.246136	2.7519	0.003404
4	0.158907	1.7766	0.03903
5	0.030839	0.3448	0.365415
6	0.02635	0.2946	0.384392
7	0.068742	0.7686	0.221804
8	-0.002114	-0.0236	0.49059
9	-0.031845	-0.356	0.361206
10	0.011633	0.1301	0.448365
11	0.112188	1.2543	0.106037
12	0.205322	2.2956	0.011683
13	0.138039	1.5433	0.06264
14	0.024006	0.2684	0.394417
15	0.080191	0.8966	0.185838
16	-0.001014	-0.0113	0.495488
17	-0.072938	-0.8155	0.208175
18	0.033188	0.371	0.355615
19	-0.036853	-0.412	0.340513
20	-0.098119	-1.097	0.137373

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.279359 & 3.1233 & 0.001111 \tabularnewline
2 & 0.135145 & 1.511 & 0.066661 \tabularnewline
3 & 0.246136 & 2.7519 & 0.003404 \tabularnewline
4 & 0.158907 & 1.7766 & 0.03903 \tabularnewline
5 & 0.030839 & 0.3448 & 0.365415 \tabularnewline
6 & 0.02635 & 0.2946 & 0.384392 \tabularnewline
7 & 0.068742 & 0.7686 & 0.221804 \tabularnewline
8 & -0.002114 & -0.0236 & 0.49059 \tabularnewline
9 & -0.031845 & -0.356 & 0.361206 \tabularnewline
10 & 0.011633 & 0.1301 & 0.448365 \tabularnewline
11 & 0.112188 & 1.2543 & 0.106037 \tabularnewline
12 & 0.205322 & 2.2956 & 0.011683 \tabularnewline
13 & 0.138039 & 1.5433 & 0.06264 \tabularnewline
14 & 0.024006 & 0.2684 & 0.394417 \tabularnewline
15 & 0.080191 & 0.8966 & 0.185838 \tabularnewline
16 & -0.001014 & -0.0113 & 0.495488 \tabularnewline
17 & -0.072938 & -0.8155 & 0.208175 \tabularnewline
18 & 0.033188 & 0.371 & 0.355615 \tabularnewline
19 & -0.036853 & -0.412 & 0.340513 \tabularnewline
20 & -0.098119 & -1.097 & 0.137373 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302404&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]0.279359[/C][C]3.1233[/C][C]0.001111[/C][/ROW]
[ROW][C]2[/C][C]0.135145[/C][C]1.511[/C][C]0.066661[/C][/ROW]
[ROW][C]3[/C][C]0.246136[/C][C]2.7519[/C][C]0.003404[/C][/ROW]
[ROW][C]4[/C][C]0.158907[/C][C]1.7766[/C][C]0.03903[/C][/ROW]
[ROW][C]5[/C][C]0.030839[/C][C]0.3448[/C][C]0.365415[/C][/ROW]
[ROW][C]6[/C][C]0.02635[/C][C]0.2946[/C][C]0.384392[/C][/ROW]
[ROW][C]7[/C][C]0.068742[/C][C]0.7686[/C][C]0.221804[/C][/ROW]
[ROW][C]8[/C][C]-0.002114[/C][C]-0.0236[/C][C]0.49059[/C][/ROW]
[ROW][C]9[/C][C]-0.031845[/C][C]-0.356[/C][C]0.361206[/C][/ROW]
[ROW][C]10[/C][C]0.011633[/C][C]0.1301[/C][C]0.448365[/C][/ROW]
[ROW][C]11[/C][C]0.112188[/C][C]1.2543[/C][C]0.106037[/C][/ROW]
[ROW][C]12[/C][C]0.205322[/C][C]2.2956[/C][C]0.011683[/C][/ROW]
[ROW][C]13[/C][C]0.138039[/C][C]1.5433[/C][C]0.06264[/C][/ROW]
[ROW][C]14[/C][C]0.024006[/C][C]0.2684[/C][C]0.394417[/C][/ROW]
[ROW][C]15[/C][C]0.080191[/C][C]0.8966[/C][C]0.185838[/C][/ROW]
[ROW][C]16[/C][C]-0.001014[/C][C]-0.0113[/C][C]0.495488[/C][/ROW]
[ROW][C]17[/C][C]-0.072938[/C][C]-0.8155[/C][C]0.208175[/C][/ROW]
[ROW][C]18[/C][C]0.033188[/C][C]0.371[/C][C]0.355615[/C][/ROW]
[ROW][C]19[/C][C]-0.036853[/C][C]-0.412[/C][C]0.340513[/C][/ROW]
[ROW][C]20[/C][C]-0.098119[/C][C]-1.097[/C][C]0.137373[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302404&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302404&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	0.279359	3.1233	0.001111
2	0.135145	1.511	0.066661
3	0.246136	2.7519	0.003404
4	0.158907	1.7766	0.03903
5	0.030839	0.3448	0.365415
6	0.02635	0.2946	0.384392
7	0.068742	0.7686	0.221804
8	-0.002114	-0.0236	0.49059
9	-0.031845	-0.356	0.361206
10	0.011633	0.1301	0.448365
11	0.112188	1.2543	0.106037
12	0.205322	2.2956	0.011683
13	0.138039	1.5433	0.06264
14	0.024006	0.2684	0.394417
15	0.080191	0.8966	0.185838
16	-0.001014	-0.0113	0.495488
17	-0.072938	-0.8155	0.208175
18	0.033188	0.371	0.355615
19	-0.036853	-0.412	0.340513
20	-0.098119	-1.097	0.137373

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.279359	3.1233	0.001111
2	0.061937	0.6925	0.244961
3	0.210598	2.3546	0.010051
4	0.04315	0.4824	0.315173
5	-0.054722	-0.6118	0.270887
6	-0.029175	-0.3262	0.372414
7	0.034013	0.3803	0.352191
8	-0.029875	-0.334	0.369467
9	-0.024197	-0.2705	0.393601
10	0.011774	0.1316	0.447743
11	0.125396	1.402	0.081701
12	0.197861	2.2122	0.014386
13	0.052444	0.5863	0.279352
14	-0.106323	-1.1887	0.118401
15	-0.022348	-0.2499	0.401552
16	-0.09967	-1.1143	0.133636
17	-0.065491	-0.7322	0.232705
18	0.07441	0.8319	0.203516
19	-0.047956	-0.5362	0.296401
20	-0.02893	-0.3235	0.373447

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.279359 & 3.1233 & 0.001111 \tabularnewline
2 & 0.061937 & 0.6925 & 0.244961 \tabularnewline
3 & 0.210598 & 2.3546 & 0.010051 \tabularnewline
4 & 0.04315 & 0.4824 & 0.315173 \tabularnewline
5 & -0.054722 & -0.6118 & 0.270887 \tabularnewline
6 & -0.029175 & -0.3262 & 0.372414 \tabularnewline
7 & 0.034013 & 0.3803 & 0.352191 \tabularnewline
8 & -0.029875 & -0.334 & 0.369467 \tabularnewline
9 & -0.024197 & -0.2705 & 0.393601 \tabularnewline
10 & 0.011774 & 0.1316 & 0.447743 \tabularnewline
11 & 0.125396 & 1.402 & 0.081701 \tabularnewline
12 & 0.197861 & 2.2122 & 0.014386 \tabularnewline
13 & 0.052444 & 0.5863 & 0.279352 \tabularnewline
14 & -0.106323 & -1.1887 & 0.118401 \tabularnewline
15 & -0.022348 & -0.2499 & 0.401552 \tabularnewline
16 & -0.09967 & -1.1143 & 0.133636 \tabularnewline
17 & -0.065491 & -0.7322 & 0.232705 \tabularnewline
18 & 0.07441 & 0.8319 & 0.203516 \tabularnewline
19 & -0.047956 & -0.5362 & 0.296401 \tabularnewline
20 & -0.02893 & -0.3235 & 0.373447 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302404&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]0.279359[/C][C]3.1233[/C][C]0.001111[/C][/ROW]
[ROW][C]2[/C][C]0.061937[/C][C]0.6925[/C][C]0.244961[/C][/ROW]
[ROW][C]3[/C][C]0.210598[/C][C]2.3546[/C][C]0.010051[/C][/ROW]
[ROW][C]4[/C][C]0.04315[/C][C]0.4824[/C][C]0.315173[/C][/ROW]
[ROW][C]5[/C][C]-0.054722[/C][C]-0.6118[/C][C]0.270887[/C][/ROW]
[ROW][C]6[/C][C]-0.029175[/C][C]-0.3262[/C][C]0.372414[/C][/ROW]
[ROW][C]7[/C][C]0.034013[/C][C]0.3803[/C][C]0.352191[/C][/ROW]
[ROW][C]8[/C][C]-0.029875[/C][C]-0.334[/C][C]0.369467[/C][/ROW]
[ROW][C]9[/C][C]-0.024197[/C][C]-0.2705[/C][C]0.393601[/C][/ROW]
[ROW][C]10[/C][C]0.011774[/C][C]0.1316[/C][C]0.447743[/C][/ROW]
[ROW][C]11[/C][C]0.125396[/C][C]1.402[/C][C]0.081701[/C][/ROW]
[ROW][C]12[/C][C]0.197861[/C][C]2.2122[/C][C]0.014386[/C][/ROW]
[ROW][C]13[/C][C]0.052444[/C][C]0.5863[/C][C]0.279352[/C][/ROW]
[ROW][C]14[/C][C]-0.106323[/C][C]-1.1887[/C][C]0.118401[/C][/ROW]
[ROW][C]15[/C][C]-0.022348[/C][C]-0.2499[/C][C]0.401552[/C][/ROW]
[ROW][C]16[/C][C]-0.09967[/C][C]-1.1143[/C][C]0.133636[/C][/ROW]
[ROW][C]17[/C][C]-0.065491[/C][C]-0.7322[/C][C]0.232705[/C][/ROW]
[ROW][C]18[/C][C]0.07441[/C][C]0.8319[/C][C]0.203516[/C][/ROW]
[ROW][C]19[/C][C]-0.047956[/C][C]-0.5362[/C][C]0.296401[/C][/ROW]
[ROW][C]20[/C][C]-0.02893[/C][C]-0.3235[/C][C]0.373447[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302404&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302404&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	0.279359	3.1233	0.001111
2	0.061937	0.6925	0.244961
3	0.210598	2.3546	0.010051
4	0.04315	0.4824	0.315173
5	-0.054722	-0.6118	0.270887
6	-0.029175	-0.3262	0.372414
7	0.034013	0.3803	0.352191
8	-0.029875	-0.334	0.369467
9	-0.024197	-0.2705	0.393601
10	0.011774	0.1316	0.447743
11	0.125396	1.402	0.081701
12	0.197861	2.2122	0.014386
13	0.052444	0.5863	0.279352
14	-0.106323	-1.1887	0.118401
15	-0.022348	-0.2499	0.401552
16	-0.09967	-1.1143	0.133636
17	-0.065491	-0.7322	0.232705
18	0.07441	0.8319	0.203516
19	-0.047956	-0.5362	0.296401
20	-0.02893	-0.3235	0.373447

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

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PDF link

Parameters (Session):

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

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)
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