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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 06 Dec 2017 17:53:31 +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/06/t151257930027sgyfcyx6qv9z1.htm/, Retrieved Tue, 14 May 2024 10:00:04 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308624, Retrieved Tue, 14 May 2024 10:00:04 +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] [autocorrelation (...] [2017-12-06 16:53:31] [33956d13de8d8b5d5d1b78ead3554acb] [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=308624&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=308624&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308624&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	0.719942	10.4825	0
2	0.621897	9.055	0
3	0.743487	10.8253	0
4	0.618181	9.0008	0
5	0.66663	9.7063	0
6	0.816523	11.8888	0
7	0.6262	9.1176	0
8	0.568511	8.2776	0
9	0.637362	9.2801	0
10	0.496341	7.2268	0
11	0.585909	8.531	0
12	0.766235	11.1566	0
13	0.555402	8.0868	0
14	0.459059	6.684	0
15	0.559602	8.1479	0
16	0.469369	6.8341	0
17	0.509738	7.4219	0
18	0.64684	9.4181	0
19	0.479675	6.9842	0
20	0.433075	6.3057	0
21	0.49306	7.1791	0
22	0.371442	5.4083	0
23	0.46362	6.7504	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.719942 & 10.4825 & 0 \tabularnewline
2 & 0.621897 & 9.055 & 0 \tabularnewline
3 & 0.743487 & 10.8253 & 0 \tabularnewline
4 & 0.618181 & 9.0008 & 0 \tabularnewline
5 & 0.66663 & 9.7063 & 0 \tabularnewline
6 & 0.816523 & 11.8888 & 0 \tabularnewline
7 & 0.6262 & 9.1176 & 0 \tabularnewline
8 & 0.568511 & 8.2776 & 0 \tabularnewline
9 & 0.637362 & 9.2801 & 0 \tabularnewline
10 & 0.496341 & 7.2268 & 0 \tabularnewline
11 & 0.585909 & 8.531 & 0 \tabularnewline
12 & 0.766235 & 11.1566 & 0 \tabularnewline
13 & 0.555402 & 8.0868 & 0 \tabularnewline
14 & 0.459059 & 6.684 & 0 \tabularnewline
15 & 0.559602 & 8.1479 & 0 \tabularnewline
16 & 0.469369 & 6.8341 & 0 \tabularnewline
17 & 0.509738 & 7.4219 & 0 \tabularnewline
18 & 0.64684 & 9.4181 & 0 \tabularnewline
19 & 0.479675 & 6.9842 & 0 \tabularnewline
20 & 0.433075 & 6.3057 & 0 \tabularnewline
21 & 0.49306 & 7.1791 & 0 \tabularnewline
22 & 0.371442 & 5.4083 & 0 \tabularnewline
23 & 0.46362 & 6.7504 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308624&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]0.719942[/C][C]10.4825[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.621897[/C][C]9.055[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.743487[/C][C]10.8253[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.618181[/C][C]9.0008[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.66663[/C][C]9.7063[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.816523[/C][C]11.8888[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.6262[/C][C]9.1176[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.568511[/C][C]8.2776[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.637362[/C][C]9.2801[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.496341[/C][C]7.2268[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.585909[/C][C]8.531[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.766235[/C][C]11.1566[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.555402[/C][C]8.0868[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.459059[/C][C]6.684[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.559602[/C][C]8.1479[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.469369[/C][C]6.8341[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.509738[/C][C]7.4219[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.64684[/C][C]9.4181[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.479675[/C][C]6.9842[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.433075[/C][C]6.3057[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.49306[/C][C]7.1791[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]0.371442[/C][C]5.4083[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]0.46362[/C][C]6.7504[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308624&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308624&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	0.719942	10.4825	0
2	0.621897	9.055	0
3	0.743487	10.8253	0
4	0.618181	9.0008	0
5	0.66663	9.7063	0
6	0.816523	11.8888	0
7	0.6262	9.1176	0
8	0.568511	8.2776	0
9	0.637362	9.2801	0
10	0.496341	7.2268	0
11	0.585909	8.531	0
12	0.766235	11.1566	0
13	0.555402	8.0868	0
14	0.459059	6.684	0
15	0.559602	8.1479	0
16	0.469369	6.8341	0
17	0.509738	7.4219	0
18	0.64684	9.4181	0
19	0.479675	6.9842	0
20	0.433075	6.3057	0
21	0.49306	7.1791	0
22	0.371442	5.4083	0
23	0.46362	6.7504	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.719942	10.4825	0
2	0.215037	3.131	0.000994
3	0.516362	7.5183	0
4	-0.128922	-1.8771	0.030937
5	0.436112	6.3499	0
6	0.344387	5.0144	1e-06
7	-0.18883	-2.7494	0.003243
8	-0.05084	-0.7402	0.229988
9	-0.141253	-2.0567	0.020471
10	-0.212612	-3.0957	0.001114
11	0.231185	3.3661	0.000453
12	0.383527	5.5842	0
13	-0.138951	-2.0232	0.022156
14	-0.291721	-4.2475	1.6e-05
15	-0.000462	-0.0067	0.497317
16	0.131901	1.9205	0.028068
17	-0.01355	-0.1973	0.421892
18	0.037335	0.5436	0.293643
19	-0.073328	-1.0677	0.143442
20	0.078116	1.1374	0.12833
21	-0.026694	-0.3887	0.348955
22	-0.02698	-0.3928	0.347416
23	0.077941	1.1348	0.128861

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.719942 & 10.4825 & 0 \tabularnewline
2 & 0.215037 & 3.131 & 0.000994 \tabularnewline
3 & 0.516362 & 7.5183 & 0 \tabularnewline
4 & -0.128922 & -1.8771 & 0.030937 \tabularnewline
5 & 0.436112 & 6.3499 & 0 \tabularnewline
6 & 0.344387 & 5.0144 & 1e-06 \tabularnewline
7 & -0.18883 & -2.7494 & 0.003243 \tabularnewline
8 & -0.05084 & -0.7402 & 0.229988 \tabularnewline
9 & -0.141253 & -2.0567 & 0.020471 \tabularnewline
10 & -0.212612 & -3.0957 & 0.001114 \tabularnewline
11 & 0.231185 & 3.3661 & 0.000453 \tabularnewline
12 & 0.383527 & 5.5842 & 0 \tabularnewline
13 & -0.138951 & -2.0232 & 0.022156 \tabularnewline
14 & -0.291721 & -4.2475 & 1.6e-05 \tabularnewline
15 & -0.000462 & -0.0067 & 0.497317 \tabularnewline
16 & 0.131901 & 1.9205 & 0.028068 \tabularnewline
17 & -0.01355 & -0.1973 & 0.421892 \tabularnewline
18 & 0.037335 & 0.5436 & 0.293643 \tabularnewline
19 & -0.073328 & -1.0677 & 0.143442 \tabularnewline
20 & 0.078116 & 1.1374 & 0.12833 \tabularnewline
21 & -0.026694 & -0.3887 & 0.348955 \tabularnewline
22 & -0.02698 & -0.3928 & 0.347416 \tabularnewline
23 & 0.077941 & 1.1348 & 0.128861 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308624&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]0.719942[/C][C]10.4825[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.215037[/C][C]3.131[/C][C]0.000994[/C][/ROW]
[ROW][C]3[/C][C]0.516362[/C][C]7.5183[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]-0.128922[/C][C]-1.8771[/C][C]0.030937[/C][/ROW]
[ROW][C]5[/C][C]0.436112[/C][C]6.3499[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.344387[/C][C]5.0144[/C][C]1e-06[/C][/ROW]
[ROW][C]7[/C][C]-0.18883[/C][C]-2.7494[/C][C]0.003243[/C][/ROW]
[ROW][C]8[/C][C]-0.05084[/C][C]-0.7402[/C][C]0.229988[/C][/ROW]
[ROW][C]9[/C][C]-0.141253[/C][C]-2.0567[/C][C]0.020471[/C][/ROW]
[ROW][C]10[/C][C]-0.212612[/C][C]-3.0957[/C][C]0.001114[/C][/ROW]
[ROW][C]11[/C][C]0.231185[/C][C]3.3661[/C][C]0.000453[/C][/ROW]
[ROW][C]12[/C][C]0.383527[/C][C]5.5842[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.138951[/C][C]-2.0232[/C][C]0.022156[/C][/ROW]
[ROW][C]14[/C][C]-0.291721[/C][C]-4.2475[/C][C]1.6e-05[/C][/ROW]
[ROW][C]15[/C][C]-0.000462[/C][C]-0.0067[/C][C]0.497317[/C][/ROW]
[ROW][C]16[/C][C]0.131901[/C][C]1.9205[/C][C]0.028068[/C][/ROW]
[ROW][C]17[/C][C]-0.01355[/C][C]-0.1973[/C][C]0.421892[/C][/ROW]
[ROW][C]18[/C][C]0.037335[/C][C]0.5436[/C][C]0.293643[/C][/ROW]
[ROW][C]19[/C][C]-0.073328[/C][C]-1.0677[/C][C]0.143442[/C][/ROW]
[ROW][C]20[/C][C]0.078116[/C][C]1.1374[/C][C]0.12833[/C][/ROW]
[ROW][C]21[/C][C]-0.026694[/C][C]-0.3887[/C][C]0.348955[/C][/ROW]
[ROW][C]22[/C][C]-0.02698[/C][C]-0.3928[/C][C]0.347416[/C][/ROW]
[ROW][C]23[/C][C]0.077941[/C][C]1.1348[/C][C]0.128861[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308624&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308624&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	0.719942	10.4825	0
2	0.215037	3.131	0.000994
3	0.516362	7.5183	0
4	-0.128922	-1.8771	0.030937
5	0.436112	6.3499	0
6	0.344387	5.0144	1e-06
7	-0.18883	-2.7494	0.003243
8	-0.05084	-0.7402	0.229988
9	-0.141253	-2.0567	0.020471
10	-0.212612	-3.0957	0.001114
11	0.231185	3.3661	0.000453
12	0.383527	5.5842	0
13	-0.138951	-2.0232	0.022156
14	-0.291721	-4.2475	1.6e-05
15	-0.000462	-0.0067	0.497317
16	0.131901	1.9205	0.028068
17	-0.01355	-0.1973	0.421892
18	0.037335	0.5436	0.293643
19	-0.073328	-1.0677	0.143442
20	0.078116	1.1374	0.12833
21	-0.026694	-0.3887	0.348955
22	-0.02698	-0.3928	0.347416
23	0.077941	1.1348	0.128861

Figure 1

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Postscript link

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Figure 2

PNG link

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Figure 3

PNG link

Postscript link

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