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

Sat, 16 Dec 2017 14:56:01 +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/16/t1513432577i0lta049sthbtzu.htm/, Retrieved Wed, 15 May 2024 11:34:04 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=309885, Retrieved Wed, 15 May 2024 11:34:04 +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] [] [2017-12-16 13:56:01] [deec28e763260dad9f228be262d61467] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

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=309885&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=309885&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309885&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	-0.552546	-7.7946	0
2	-0.104434	-1.4732	0.071136
3	0.360877	5.0908	0
4	-0.271695	-3.8327	8.5e-05
5	0.029139	0.4111	0.340737
6	0.213296	3.0089	0.00148
7	-0.282403	-3.9838	4.8e-05
8	0.054506	0.7689	0.221432
9	0.237659	3.3526	0.000479
10	-0.258248	-3.643	0.000172
11	0.166808	2.3531	0.009796
12	-0.048844	-0.689	0.245802
13	-0.174574	-2.4627	0.00732
14	0.254368	3.5883	0.00021
15	-0.020245	-0.2856	0.387746
16	-0.285556	-4.0283	4e-05
17	0.245805	3.4675	0.000322
18	0.064407	0.9086	0.182338
19	-0.260186	-3.6704	0.000156
20	0.250396	3.5323	0.000256
21	-0.053552	-0.7554	0.225436
22	-0.280705	-3.9598	5.2e-05
23	0.462959	6.5308	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.552546 & -7.7946 & 0 \tabularnewline
2 & -0.104434 & -1.4732 & 0.071136 \tabularnewline
3 & 0.360877 & 5.0908 & 0 \tabularnewline
4 & -0.271695 & -3.8327 & 8.5e-05 \tabularnewline
5 & 0.029139 & 0.4111 & 0.340737 \tabularnewline
6 & 0.213296 & 3.0089 & 0.00148 \tabularnewline
7 & -0.282403 & -3.9838 & 4.8e-05 \tabularnewline
8 & 0.054506 & 0.7689 & 0.221432 \tabularnewline
9 & 0.237659 & 3.3526 & 0.000479 \tabularnewline
10 & -0.258248 & -3.643 & 0.000172 \tabularnewline
11 & 0.166808 & 2.3531 & 0.009796 \tabularnewline
12 & -0.048844 & -0.689 & 0.245802 \tabularnewline
13 & -0.174574 & -2.4627 & 0.00732 \tabularnewline
14 & 0.254368 & 3.5883 & 0.00021 \tabularnewline
15 & -0.020245 & -0.2856 & 0.387746 \tabularnewline
16 & -0.285556 & -4.0283 & 4e-05 \tabularnewline
17 & 0.245805 & 3.4675 & 0.000322 \tabularnewline
18 & 0.064407 & 0.9086 & 0.182338 \tabularnewline
19 & -0.260186 & -3.6704 & 0.000156 \tabularnewline
20 & 0.250396 & 3.5323 & 0.000256 \tabularnewline
21 & -0.053552 & -0.7554 & 0.225436 \tabularnewline
22 & -0.280705 & -3.9598 & 5.2e-05 \tabularnewline
23 & 0.462959 & 6.5308 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309885&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]-0.552546[/C][C]-7.7946[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.104434[/C][C]-1.4732[/C][C]0.071136[/C][/ROW]
[ROW][C]3[/C][C]0.360877[/C][C]5.0908[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]-0.271695[/C][C]-3.8327[/C][C]8.5e-05[/C][/ROW]
[ROW][C]5[/C][C]0.029139[/C][C]0.4111[/C][C]0.340737[/C][/ROW]
[ROW][C]6[/C][C]0.213296[/C][C]3.0089[/C][C]0.00148[/C][/ROW]
[ROW][C]7[/C][C]-0.282403[/C][C]-3.9838[/C][C]4.8e-05[/C][/ROW]
[ROW][C]8[/C][C]0.054506[/C][C]0.7689[/C][C]0.221432[/C][/ROW]
[ROW][C]9[/C][C]0.237659[/C][C]3.3526[/C][C]0.000479[/C][/ROW]
[ROW][C]10[/C][C]-0.258248[/C][C]-3.643[/C][C]0.000172[/C][/ROW]
[ROW][C]11[/C][C]0.166808[/C][C]2.3531[/C][C]0.009796[/C][/ROW]
[ROW][C]12[/C][C]-0.048844[/C][C]-0.689[/C][C]0.245802[/C][/ROW]
[ROW][C]13[/C][C]-0.174574[/C][C]-2.4627[/C][C]0.00732[/C][/ROW]
[ROW][C]14[/C][C]0.254368[/C][C]3.5883[/C][C]0.00021[/C][/ROW]
[ROW][C]15[/C][C]-0.020245[/C][C]-0.2856[/C][C]0.387746[/C][/ROW]
[ROW][C]16[/C][C]-0.285556[/C][C]-4.0283[/C][C]4e-05[/C][/ROW]
[ROW][C]17[/C][C]0.245805[/C][C]3.4675[/C][C]0.000322[/C][/ROW]
[ROW][C]18[/C][C]0.064407[/C][C]0.9086[/C][C]0.182338[/C][/ROW]
[ROW][C]19[/C][C]-0.260186[/C][C]-3.6704[/C][C]0.000156[/C][/ROW]
[ROW][C]20[/C][C]0.250396[/C][C]3.5323[/C][C]0.000256[/C][/ROW]
[ROW][C]21[/C][C]-0.053552[/C][C]-0.7554[/C][C]0.225436[/C][/ROW]
[ROW][C]22[/C][C]-0.280705[/C][C]-3.9598[/C][C]5.2e-05[/C][/ROW]
[ROW][C]23[/C][C]0.462959[/C][C]6.5308[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309885&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309885&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	-0.552546	-7.7946	0
2	-0.104434	-1.4732	0.071136
3	0.360877	5.0908	0
4	-0.271695	-3.8327	8.5e-05
5	0.029139	0.4111	0.340737
6	0.213296	3.0089	0.00148
7	-0.282403	-3.9838	4.8e-05
8	0.054506	0.7689	0.221432
9	0.237659	3.3526	0.000479
10	-0.258248	-3.643	0.000172
11	0.166808	2.3531	0.009796
12	-0.048844	-0.689	0.245802
13	-0.174574	-2.4627	0.00732
14	0.254368	3.5883	0.00021
15	-0.020245	-0.2856	0.387746
16	-0.285556	-4.0283	4e-05
17	0.245805	3.4675	0.000322
18	0.064407	0.9086	0.182338
19	-0.260186	-3.6704	0.000156
20	0.250396	3.5323	0.000256
21	-0.053552	-0.7554	0.225436
22	-0.280705	-3.9598	5.2e-05
23	0.462959	6.5308	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.552546	-7.7946	0
2	-0.589815	-8.3204	0
3	-0.125298	-1.7675	0.039335
4	-0.157741	-2.2252	0.013595
5	-0.134538	-1.8979	0.029579
6	0.108492	1.5305	0.063745
7	-0.03533	-0.4984	0.30938
8	-0.201237	-2.8388	0.002499
9	0.029719	0.4192	0.337749
10	0.058775	0.8291	0.204012
11	0.280992	3.9639	5.1e-05
12	0.129284	1.8238	0.034843
13	-0.163614	-2.3081	0.011012
14	-0.145396	-2.0511	0.020786
15	0.109506	1.5448	0.061995
16	-0.087658	-1.2366	0.108853
17	-0.203109	-2.8652	0.002307
18	0.051167	0.7218	0.235634
19	-0.023948	-0.3378	0.367923
20	-0.050779	-0.7163	0.237314
21	0.129787	1.8309	0.034308
22	-0.158507	-2.236	0.01323
23	0.156878	2.213	0.014016

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.552546 & -7.7946 & 0 \tabularnewline
2 & -0.589815 & -8.3204 & 0 \tabularnewline
3 & -0.125298 & -1.7675 & 0.039335 \tabularnewline
4 & -0.157741 & -2.2252 & 0.013595 \tabularnewline
5 & -0.134538 & -1.8979 & 0.029579 \tabularnewline
6 & 0.108492 & 1.5305 & 0.063745 \tabularnewline
7 & -0.03533 & -0.4984 & 0.30938 \tabularnewline
8 & -0.201237 & -2.8388 & 0.002499 \tabularnewline
9 & 0.029719 & 0.4192 & 0.337749 \tabularnewline
10 & 0.058775 & 0.8291 & 0.204012 \tabularnewline
11 & 0.280992 & 3.9639 & 5.1e-05 \tabularnewline
12 & 0.129284 & 1.8238 & 0.034843 \tabularnewline
13 & -0.163614 & -2.3081 & 0.011012 \tabularnewline
14 & -0.145396 & -2.0511 & 0.020786 \tabularnewline
15 & 0.109506 & 1.5448 & 0.061995 \tabularnewline
16 & -0.087658 & -1.2366 & 0.108853 \tabularnewline
17 & -0.203109 & -2.8652 & 0.002307 \tabularnewline
18 & 0.051167 & 0.7218 & 0.235634 \tabularnewline
19 & -0.023948 & -0.3378 & 0.367923 \tabularnewline
20 & -0.050779 & -0.7163 & 0.237314 \tabularnewline
21 & 0.129787 & 1.8309 & 0.034308 \tabularnewline
22 & -0.158507 & -2.236 & 0.01323 \tabularnewline
23 & 0.156878 & 2.213 & 0.014016 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309885&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]-0.552546[/C][C]-7.7946[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.589815[/C][C]-8.3204[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]-0.125298[/C][C]-1.7675[/C][C]0.039335[/C][/ROW]
[ROW][C]4[/C][C]-0.157741[/C][C]-2.2252[/C][C]0.013595[/C][/ROW]
[ROW][C]5[/C][C]-0.134538[/C][C]-1.8979[/C][C]0.029579[/C][/ROW]
[ROW][C]6[/C][C]0.108492[/C][C]1.5305[/C][C]0.063745[/C][/ROW]
[ROW][C]7[/C][C]-0.03533[/C][C]-0.4984[/C][C]0.30938[/C][/ROW]
[ROW][C]8[/C][C]-0.201237[/C][C]-2.8388[/C][C]0.002499[/C][/ROW]
[ROW][C]9[/C][C]0.029719[/C][C]0.4192[/C][C]0.337749[/C][/ROW]
[ROW][C]10[/C][C]0.058775[/C][C]0.8291[/C][C]0.204012[/C][/ROW]
[ROW][C]11[/C][C]0.280992[/C][C]3.9639[/C][C]5.1e-05[/C][/ROW]
[ROW][C]12[/C][C]0.129284[/C][C]1.8238[/C][C]0.034843[/C][/ROW]
[ROW][C]13[/C][C]-0.163614[/C][C]-2.3081[/C][C]0.011012[/C][/ROW]
[ROW][C]14[/C][C]-0.145396[/C][C]-2.0511[/C][C]0.020786[/C][/ROW]
[ROW][C]15[/C][C]0.109506[/C][C]1.5448[/C][C]0.061995[/C][/ROW]
[ROW][C]16[/C][C]-0.087658[/C][C]-1.2366[/C][C]0.108853[/C][/ROW]
[ROW][C]17[/C][C]-0.203109[/C][C]-2.8652[/C][C]0.002307[/C][/ROW]
[ROW][C]18[/C][C]0.051167[/C][C]0.7218[/C][C]0.235634[/C][/ROW]
[ROW][C]19[/C][C]-0.023948[/C][C]-0.3378[/C][C]0.367923[/C][/ROW]
[ROW][C]20[/C][C]-0.050779[/C][C]-0.7163[/C][C]0.237314[/C][/ROW]
[ROW][C]21[/C][C]0.129787[/C][C]1.8309[/C][C]0.034308[/C][/ROW]
[ROW][C]22[/C][C]-0.158507[/C][C]-2.236[/C][C]0.01323[/C][/ROW]
[ROW][C]23[/C][C]0.156878[/C][C]2.213[/C][C]0.014016[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309885&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309885&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	-0.552546	-7.7946	0
2	-0.589815	-8.3204	0
3	-0.125298	-1.7675	0.039335
4	-0.157741	-2.2252	0.013595
5	-0.134538	-1.8979	0.029579
6	0.108492	1.5305	0.063745
7	-0.03533	-0.4984	0.30938
8	-0.201237	-2.8388	0.002499
9	0.029719	0.4192	0.337749
10	0.058775	0.8291	0.204012
11	0.280992	3.9639	5.1e-05
12	0.129284	1.8238	0.034843
13	-0.163614	-2.3081	0.011012
14	-0.145396	-2.0511	0.020786
15	0.109506	1.5448	0.061995
16	-0.087658	-1.2366	0.108853
17	-0.203109	-2.8652	0.002307
18	0.051167	0.7218	0.235634
19	-0.023948	-0.3378	0.367923
20	-0.050779	-0.7163	0.237314
21	0.129787	1.8309	0.034308
22	-0.158507	-2.236	0.01323
23	0.156878	2.213	0.014016

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 = 2 ; par3 = TRUE ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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