Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 19 Dec 2017 07:50:32 +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/2017/Dec/19/t1513666538yvdnarnkdedf1ff.htm/, Retrieved Wed, 15 May 2024 05:44:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310265, Retrieved Wed, 15 May 2024 05:44:29 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

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

-       [(Partial) Autocorrelation Function] [] [2017-12-19 06:50:32] [1ea4e9c673228daef4af35aa2d91fd76] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

19.2
15.5
8.8
9.6
6.1
1.1
4.7
6.1
9.7
17.5
18.1
18.3
16
14.2
8.5
5.3
4.5
4.8
9.6
10.1
10.2
13.5
19.4
19
16.5
13.1
10.3
6.6
3.3
3.5
4.3
8.8
13.6
16.5
16.2
19.3
16.5
13.5
12.4
9.3
6.6
6.1
6.1
6.4
12.8
14.8
18.6
20.2
15.8
11.1
9
3
1.4
2.1
5.1
7.1
11.1
14.5
19.2
17.3
15.4

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=310265&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=310265&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310265&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	0.792497	6.1896	0
2	0.419555	3.2768	0.000867
3	-0.009339	-0.0729	0.471047
4	-0.453432	-3.5414	0.000385
5	-0.747431	-5.8376	0
6	-0.803808	-6.2779	0
7	-0.679088	-5.3038	1e-06
8	-0.355462	-2.7762	0.003646
9	0.054835	0.4283	0.334979
10	0.384738	3.0049	0.001926
11	0.604253	4.7194	7e-06
12	0.671236	5.2425	1e-06
13	0.552498	4.3151	3e-05
14	0.277458	2.167	0.017074
15	-0.051622	-0.4032	0.344111
16	-0.364096	-2.8437	0.00303
17	-0.566498	-4.4245	2e-05

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.792497 & 6.1896 & 0 \tabularnewline
2 & 0.419555 & 3.2768 & 0.000867 \tabularnewline
3 & -0.009339 & -0.0729 & 0.471047 \tabularnewline
4 & -0.453432 & -3.5414 & 0.000385 \tabularnewline
5 & -0.747431 & -5.8376 & 0 \tabularnewline
6 & -0.803808 & -6.2779 & 0 \tabularnewline
7 & -0.679088 & -5.3038 & 1e-06 \tabularnewline
8 & -0.355462 & -2.7762 & 0.003646 \tabularnewline
9 & 0.054835 & 0.4283 & 0.334979 \tabularnewline
10 & 0.384738 & 3.0049 & 0.001926 \tabularnewline
11 & 0.604253 & 4.7194 & 7e-06 \tabularnewline
12 & 0.671236 & 5.2425 & 1e-06 \tabularnewline
13 & 0.552498 & 4.3151 & 3e-05 \tabularnewline
14 & 0.277458 & 2.167 & 0.017074 \tabularnewline
15 & -0.051622 & -0.4032 & 0.344111 \tabularnewline
16 & -0.364096 & -2.8437 & 0.00303 \tabularnewline
17 & -0.566498 & -4.4245 & 2e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310265&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]0.792497[/C][C]6.1896[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.419555[/C][C]3.2768[/C][C]0.000867[/C][/ROW]
[ROW][C]3[/C][C]-0.009339[/C][C]-0.0729[/C][C]0.471047[/C][/ROW]
[ROW][C]4[/C][C]-0.453432[/C][C]-3.5414[/C][C]0.000385[/C][/ROW]
[ROW][C]5[/C][C]-0.747431[/C][C]-5.8376[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]-0.803808[/C][C]-6.2779[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]-0.679088[/C][C]-5.3038[/C][C]1e-06[/C][/ROW]
[ROW][C]8[/C][C]-0.355462[/C][C]-2.7762[/C][C]0.003646[/C][/ROW]
[ROW][C]9[/C][C]0.054835[/C][C]0.4283[/C][C]0.334979[/C][/ROW]
[ROW][C]10[/C][C]0.384738[/C][C]3.0049[/C][C]0.001926[/C][/ROW]
[ROW][C]11[/C][C]0.604253[/C][C]4.7194[/C][C]7e-06[/C][/ROW]
[ROW][C]12[/C][C]0.671236[/C][C]5.2425[/C][C]1e-06[/C][/ROW]
[ROW][C]13[/C][C]0.552498[/C][C]4.3151[/C][C]3e-05[/C][/ROW]
[ROW][C]14[/C][C]0.277458[/C][C]2.167[/C][C]0.017074[/C][/ROW]
[ROW][C]15[/C][C]-0.051622[/C][C]-0.4032[/C][C]0.344111[/C][/ROW]
[ROW][C]16[/C][C]-0.364096[/C][C]-2.8437[/C][C]0.00303[/C][/ROW]
[ROW][C]17[/C][C]-0.566498[/C][C]-4.4245[/C][C]2e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310265&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310265&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	0.792497	6.1896	0
2	0.419555	3.2768	0.000867
3	-0.009339	-0.0729	0.471047
4	-0.453432	-3.5414	0.000385
5	-0.747431	-5.8376	0
6	-0.803808	-6.2779	0
7	-0.679088	-5.3038	1e-06
8	-0.355462	-2.7762	0.003646
9	0.054835	0.4283	0.334979
10	0.384738	3.0049	0.001926
11	0.604253	4.7194	7e-06
12	0.671236	5.2425	1e-06
13	0.552498	4.3151	3e-05
14	0.277458	2.167	0.017074
15	-0.051622	-0.4032	0.344111
16	-0.364096	-2.8437	0.00303
17	-0.566498	-4.4245	2e-05

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.792497	6.1896	0
2	-0.560555	-4.3781	2.4e-05
3	-0.329233	-2.5714	0.006291
4	-0.520336	-4.064	7e-05
5	-0.177264	-1.3845	0.085628
6	-0.047441	-0.3705	0.356136
7	-0.208492	-1.6284	0.0543
8	0.115313	0.9006	0.185666
9	-0.051134	-0.3994	0.345508
10	-0.177549	-1.3867	0.085289
11	-0.022661	-0.177	0.430051
12	0.018931	0.1479	0.441472
13	0.118263	0.9237	0.17965
14	-0.174122	-1.3599	0.089427
15	-0.056187	-0.4388	0.331166
16	-0.108083	-0.8442	0.200942
17	-0.070072	-0.5473	0.293093

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.792497 & 6.1896 & 0 \tabularnewline
2 & -0.560555 & -4.3781 & 2.4e-05 \tabularnewline
3 & -0.329233 & -2.5714 & 0.006291 \tabularnewline
4 & -0.520336 & -4.064 & 7e-05 \tabularnewline
5 & -0.177264 & -1.3845 & 0.085628 \tabularnewline
6 & -0.047441 & -0.3705 & 0.356136 \tabularnewline
7 & -0.208492 & -1.6284 & 0.0543 \tabularnewline
8 & 0.115313 & 0.9006 & 0.185666 \tabularnewline
9 & -0.051134 & -0.3994 & 0.345508 \tabularnewline
10 & -0.177549 & -1.3867 & 0.085289 \tabularnewline
11 & -0.022661 & -0.177 & 0.430051 \tabularnewline
12 & 0.018931 & 0.1479 & 0.441472 \tabularnewline
13 & 0.118263 & 0.9237 & 0.17965 \tabularnewline
14 & -0.174122 & -1.3599 & 0.089427 \tabularnewline
15 & -0.056187 & -0.4388 & 0.331166 \tabularnewline
16 & -0.108083 & -0.8442 & 0.200942 \tabularnewline
17 & -0.070072 & -0.5473 & 0.293093 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310265&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]0.792497[/C][C]6.1896[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.560555[/C][C]-4.3781[/C][C]2.4e-05[/C][/ROW]
[ROW][C]3[/C][C]-0.329233[/C][C]-2.5714[/C][C]0.006291[/C][/ROW]
[ROW][C]4[/C][C]-0.520336[/C][C]-4.064[/C][C]7e-05[/C][/ROW]
[ROW][C]5[/C][C]-0.177264[/C][C]-1.3845[/C][C]0.085628[/C][/ROW]
[ROW][C]6[/C][C]-0.047441[/C][C]-0.3705[/C][C]0.356136[/C][/ROW]
[ROW][C]7[/C][C]-0.208492[/C][C]-1.6284[/C][C]0.0543[/C][/ROW]
[ROW][C]8[/C][C]0.115313[/C][C]0.9006[/C][C]0.185666[/C][/ROW]
[ROW][C]9[/C][C]-0.051134[/C][C]-0.3994[/C][C]0.345508[/C][/ROW]
[ROW][C]10[/C][C]-0.177549[/C][C]-1.3867[/C][C]0.085289[/C][/ROW]
[ROW][C]11[/C][C]-0.022661[/C][C]-0.177[/C][C]0.430051[/C][/ROW]
[ROW][C]12[/C][C]0.018931[/C][C]0.1479[/C][C]0.441472[/C][/ROW]
[ROW][C]13[/C][C]0.118263[/C][C]0.9237[/C][C]0.17965[/C][/ROW]
[ROW][C]14[/C][C]-0.174122[/C][C]-1.3599[/C][C]0.089427[/C][/ROW]
[ROW][C]15[/C][C]-0.056187[/C][C]-0.4388[/C][C]0.331166[/C][/ROW]
[ROW][C]16[/C][C]-0.108083[/C][C]-0.8442[/C][C]0.200942[/C][/ROW]
[ROW][C]17[/C][C]-0.070072[/C][C]-0.5473[/C][C]0.293093[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310265&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310265&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	0.792497	6.1896	0
2	-0.560555	-4.3781	2.4e-05
3	-0.329233	-2.5714	0.006291
4	-0.520336	-4.064	7e-05
5	-0.177264	-1.3845	0.085628
6	-0.047441	-0.3705	0.356136
7	-0.208492	-1.6284	0.0543
8	0.115313	0.9006	0.185666
9	-0.051134	-0.3994	0.345508
10	-0.177549	-1.3867	0.085289
11	-0.022661	-0.177	0.430051
12	0.018931	0.1479	0.441472
13	0.118263	0.9237	0.17965
14	-0.174122	-1.3599	0.089427
15	-0.056187	-0.4388	0.331166
16	-0.108083	-0.8442	0.200942
17	-0.070072	-0.5473	0.293093

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = 0 ; par3 = 0 ; par4 = 12 ;

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