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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

Wed, 30 Nov 2016 14:26:25 +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/Nov/30/t1480512618xpj764w8nm11v96.htm/, Retrieved Sun, 19 May 2024 00:38:45 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=297403, Retrieved Sun, 19 May 2024 00:38:45 +0000

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-       [(Partial) Autocorrelation Function] [] [2016-11-30 13:26:25] [d06ec19b175650a2a09ee5879d174acf] [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=297403&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=297403&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297403&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	0.973095	10.4806	0
2	0.946077	10.1896	0
3	0.918941	9.8973	0
4	0.891847	9.6055	0
5	0.864849	9.3147	0
6	0.838003	9.0256	0
7	0.811243	8.7374	0
8	0.784549	8.4499	0
9	0.758036	8.1643	0
10	0.731769	7.8814	0
11	0.705765	7.6013	0
12	0.680081	7.3247	0
13	0.654684	7.0512	0
14	0.629536	6.7803	0
15	0.604635	6.5121	0
16	0.579909	6.2458	0
17	0.55539	5.9817	0
18	0.53102	5.7193	0
19	0.506804	5.4584	0
20	0.482741	5.1993	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.973095 & 10.4806 & 0 \tabularnewline
2 & 0.946077 & 10.1896 & 0 \tabularnewline
3 & 0.918941 & 9.8973 & 0 \tabularnewline
4 & 0.891847 & 9.6055 & 0 \tabularnewline
5 & 0.864849 & 9.3147 & 0 \tabularnewline
6 & 0.838003 & 9.0256 & 0 \tabularnewline
7 & 0.811243 & 8.7374 & 0 \tabularnewline
8 & 0.784549 & 8.4499 & 0 \tabularnewline
9 & 0.758036 & 8.1643 & 0 \tabularnewline
10 & 0.731769 & 7.8814 & 0 \tabularnewline
11 & 0.705765 & 7.6013 & 0 \tabularnewline
12 & 0.680081 & 7.3247 & 0 \tabularnewline
13 & 0.654684 & 7.0512 & 0 \tabularnewline
14 & 0.629536 & 6.7803 & 0 \tabularnewline
15 & 0.604635 & 6.5121 & 0 \tabularnewline
16 & 0.579909 & 6.2458 & 0 \tabularnewline
17 & 0.55539 & 5.9817 & 0 \tabularnewline
18 & 0.53102 & 5.7193 & 0 \tabularnewline
19 & 0.506804 & 5.4584 & 0 \tabularnewline
20 & 0.482741 & 5.1993 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297403&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]0.973095[/C][C]10.4806[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.946077[/C][C]10.1896[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.918941[/C][C]9.8973[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.891847[/C][C]9.6055[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.864849[/C][C]9.3147[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.838003[/C][C]9.0256[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.811243[/C][C]8.7374[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.784549[/C][C]8.4499[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.758036[/C][C]8.1643[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.731769[/C][C]7.8814[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.705765[/C][C]7.6013[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.680081[/C][C]7.3247[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.654684[/C][C]7.0512[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.629536[/C][C]6.7803[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.604635[/C][C]6.5121[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.579909[/C][C]6.2458[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.55539[/C][C]5.9817[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.53102[/C][C]5.7193[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.506804[/C][C]5.4584[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.482741[/C][C]5.1993[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297403&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297403&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	0.973095	10.4806	0
2	0.946077	10.1896	0
3	0.918941	9.8973	0
4	0.891847	9.6055	0
5	0.864849	9.3147	0
6	0.838003	9.0256	0
7	0.811243	8.7374	0
8	0.784549	8.4499	0
9	0.758036	8.1643	0
10	0.731769	7.8814	0
11	0.705765	7.6013	0
12	0.680081	7.3247	0
13	0.654684	7.0512	0
14	0.629536	6.7803	0
15	0.604635	6.5121	0
16	0.579909	6.2458	0
17	0.55539	5.9817	0
18	0.53102	5.7193	0
19	0.506804	5.4584	0
20	0.482741	5.1993	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.973095	10.4806	0
2	-0.015783	-0.17	0.43266
3	-0.016081	-0.1732	0.431399
4	-0.013359	-0.1439	0.442923
5	-0.012496	-0.1346	0.446587
6	-0.011624	-0.1252	0.450294
7	-0.013006	-0.1401	0.444421
8	-0.013552	-0.146	0.442103
9	-0.011544	-0.1243	0.450632
10	-0.010455	-0.1126	0.455272
11	-0.010228	-0.1102	0.456237
12	-0.009234	-0.0994	0.460476
13	-0.009928	-0.1069	0.457516
14	-0.010646	-0.1147	0.454455
15	-0.010802	-0.1163	0.453793
16	-0.012221	-0.1316	0.447756
17	-0.011746	-0.1265	0.449773
18	-0.012905	-0.139	0.444848
19	-0.013	-0.14	0.444446
20	-0.013112	-0.1412	0.443968

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.973095 & 10.4806 & 0 \tabularnewline
2 & -0.015783 & -0.17 & 0.43266 \tabularnewline
3 & -0.016081 & -0.1732 & 0.431399 \tabularnewline
4 & -0.013359 & -0.1439 & 0.442923 \tabularnewline
5 & -0.012496 & -0.1346 & 0.446587 \tabularnewline
6 & -0.011624 & -0.1252 & 0.450294 \tabularnewline
7 & -0.013006 & -0.1401 & 0.444421 \tabularnewline
8 & -0.013552 & -0.146 & 0.442103 \tabularnewline
9 & -0.011544 & -0.1243 & 0.450632 \tabularnewline
10 & -0.010455 & -0.1126 & 0.455272 \tabularnewline
11 & -0.010228 & -0.1102 & 0.456237 \tabularnewline
12 & -0.009234 & -0.0994 & 0.460476 \tabularnewline
13 & -0.009928 & -0.1069 & 0.457516 \tabularnewline
14 & -0.010646 & -0.1147 & 0.454455 \tabularnewline
15 & -0.010802 & -0.1163 & 0.453793 \tabularnewline
16 & -0.012221 & -0.1316 & 0.447756 \tabularnewline
17 & -0.011746 & -0.1265 & 0.449773 \tabularnewline
18 & -0.012905 & -0.139 & 0.444848 \tabularnewline
19 & -0.013 & -0.14 & 0.444446 \tabularnewline
20 & -0.013112 & -0.1412 & 0.443968 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297403&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]0.973095[/C][C]10.4806[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.015783[/C][C]-0.17[/C][C]0.43266[/C][/ROW]
[ROW][C]3[/C][C]-0.016081[/C][C]-0.1732[/C][C]0.431399[/C][/ROW]
[ROW][C]4[/C][C]-0.013359[/C][C]-0.1439[/C][C]0.442923[/C][/ROW]
[ROW][C]5[/C][C]-0.012496[/C][C]-0.1346[/C][C]0.446587[/C][/ROW]
[ROW][C]6[/C][C]-0.011624[/C][C]-0.1252[/C][C]0.450294[/C][/ROW]
[ROW][C]7[/C][C]-0.013006[/C][C]-0.1401[/C][C]0.444421[/C][/ROW]
[ROW][C]8[/C][C]-0.013552[/C][C]-0.146[/C][C]0.442103[/C][/ROW]
[ROW][C]9[/C][C]-0.011544[/C][C]-0.1243[/C][C]0.450632[/C][/ROW]
[ROW][C]10[/C][C]-0.010455[/C][C]-0.1126[/C][C]0.455272[/C][/ROW]
[ROW][C]11[/C][C]-0.010228[/C][C]-0.1102[/C][C]0.456237[/C][/ROW]
[ROW][C]12[/C][C]-0.009234[/C][C]-0.0994[/C][C]0.460476[/C][/ROW]
[ROW][C]13[/C][C]-0.009928[/C][C]-0.1069[/C][C]0.457516[/C][/ROW]
[ROW][C]14[/C][C]-0.010646[/C][C]-0.1147[/C][C]0.454455[/C][/ROW]
[ROW][C]15[/C][C]-0.010802[/C][C]-0.1163[/C][C]0.453793[/C][/ROW]
[ROW][C]16[/C][C]-0.012221[/C][C]-0.1316[/C][C]0.447756[/C][/ROW]
[ROW][C]17[/C][C]-0.011746[/C][C]-0.1265[/C][C]0.449773[/C][/ROW]
[ROW][C]18[/C][C]-0.012905[/C][C]-0.139[/C][C]0.444848[/C][/ROW]
[ROW][C]19[/C][C]-0.013[/C][C]-0.14[/C][C]0.444446[/C][/ROW]
[ROW][C]20[/C][C]-0.013112[/C][C]-0.1412[/C][C]0.443968[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297403&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297403&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	0.973095	10.4806	0
2	-0.015783	-0.17	0.43266
3	-0.016081	-0.1732	0.431399
4	-0.013359	-0.1439	0.442923
5	-0.012496	-0.1346	0.446587
6	-0.011624	-0.1252	0.450294
7	-0.013006	-0.1401	0.444421
8	-0.013552	-0.146	0.442103
9	-0.011544	-0.1243	0.450632
10	-0.010455	-0.1126	0.455272
11	-0.010228	-0.1102	0.456237
12	-0.009234	-0.0994	0.460476
13	-0.009928	-0.1069	0.457516
14	-0.010646	-0.1147	0.454455
15	-0.010802	-0.1163	0.453793
16	-0.012221	-0.1316	0.447756
17	-0.011746	-0.1265	0.449773
18	-0.012905	-0.139	0.444848
19	-0.013	-0.14	0.444446
20	-0.013112	-0.1412	0.443968

Figure 1

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Postscript link

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Figure 2

PNG link

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Figure 3

PNG link

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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')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code