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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 24 Jan 2018 10:28:07 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2018/Jan/24/t151678617368eel83mhtej2rc.htm/, Retrieved Sun, 05 May 2024 22:28:45 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=312244, Retrieved Sun, 05 May 2024 22:28:45 +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] [] [2018-01-24 09:28:07] [602332dda9db4b5112abd453c5515d3f] [Current]

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2.80030819572237
0.546110929167911
-1.08882457056234
1.85116612407754
1.81431171737364
1.10336738027983
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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	6 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 time6 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=312244&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]

6 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=312244&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=312244&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	6 seconds
R Server	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.000545	-0.0073	0.497095
2	-0.058756	-0.7861	0.216423
3	-0.043071	-0.5762	0.282587
4	-0.056156	-0.7513	0.226725
5	0.032217	0.431	0.333482
6	0.054201	0.7252	0.234651
7	-0.09031	-1.2083	0.114269
8	-0.144761	-1.9368	0.027174
9	-0.066601	-0.8911	0.187047
10	-0.031827	-0.4258	0.335377
11	-0.005756	-0.077	0.469352
12	-0.000527	-0.0071	0.497191
13	0.018765	0.2511	0.401031
14	-0.076742	-1.0267	0.152965
15	-0.10233	-1.3691	0.086345
16	0.038953	0.5212	0.301453
17	-0.021592	-0.2889	0.386502
18	-0.101432	-1.3571	0.088235
19	0.088998	1.1907	0.117671
20	0.075682	1.0126	0.156319
21	-0.001381	-0.0185	0.492639
22	0.060329	0.8071	0.210327

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.000545 & -0.0073 & 0.497095 \tabularnewline
2 & -0.058756 & -0.7861 & 0.216423 \tabularnewline
3 & -0.043071 & -0.5762 & 0.282587 \tabularnewline
4 & -0.056156 & -0.7513 & 0.226725 \tabularnewline
5 & 0.032217 & 0.431 & 0.333482 \tabularnewline
6 & 0.054201 & 0.7252 & 0.234651 \tabularnewline
7 & -0.09031 & -1.2083 & 0.114269 \tabularnewline
8 & -0.144761 & -1.9368 & 0.027174 \tabularnewline
9 & -0.066601 & -0.8911 & 0.187047 \tabularnewline
10 & -0.031827 & -0.4258 & 0.335377 \tabularnewline
11 & -0.005756 & -0.077 & 0.469352 \tabularnewline
12 & -0.000527 & -0.0071 & 0.497191 \tabularnewline
13 & 0.018765 & 0.2511 & 0.401031 \tabularnewline
14 & -0.076742 & -1.0267 & 0.152965 \tabularnewline
15 & -0.10233 & -1.3691 & 0.086345 \tabularnewline
16 & 0.038953 & 0.5212 & 0.301453 \tabularnewline
17 & -0.021592 & -0.2889 & 0.386502 \tabularnewline
18 & -0.101432 & -1.3571 & 0.088235 \tabularnewline
19 & 0.088998 & 1.1907 & 0.117671 \tabularnewline
20 & 0.075682 & 1.0126 & 0.156319 \tabularnewline
21 & -0.001381 & -0.0185 & 0.492639 \tabularnewline
22 & 0.060329 & 0.8071 & 0.210327 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=312244&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]-0.000545[/C][C]-0.0073[/C][C]0.497095[/C][/ROW]
[ROW][C]2[/C][C]-0.058756[/C][C]-0.7861[/C][C]0.216423[/C][/ROW]
[ROW][C]3[/C][C]-0.043071[/C][C]-0.5762[/C][C]0.282587[/C][/ROW]
[ROW][C]4[/C][C]-0.056156[/C][C]-0.7513[/C][C]0.226725[/C][/ROW]
[ROW][C]5[/C][C]0.032217[/C][C]0.431[/C][C]0.333482[/C][/ROW]
[ROW][C]6[/C][C]0.054201[/C][C]0.7252[/C][C]0.234651[/C][/ROW]
[ROW][C]7[/C][C]-0.09031[/C][C]-1.2083[/C][C]0.114269[/C][/ROW]
[ROW][C]8[/C][C]-0.144761[/C][C]-1.9368[/C][C]0.027174[/C][/ROW]
[ROW][C]9[/C][C]-0.066601[/C][C]-0.8911[/C][C]0.187047[/C][/ROW]
[ROW][C]10[/C][C]-0.031827[/C][C]-0.4258[/C][C]0.335377[/C][/ROW]
[ROW][C]11[/C][C]-0.005756[/C][C]-0.077[/C][C]0.469352[/C][/ROW]
[ROW][C]12[/C][C]-0.000527[/C][C]-0.0071[/C][C]0.497191[/C][/ROW]
[ROW][C]13[/C][C]0.018765[/C][C]0.2511[/C][C]0.401031[/C][/ROW]
[ROW][C]14[/C][C]-0.076742[/C][C]-1.0267[/C][C]0.152965[/C][/ROW]
[ROW][C]15[/C][C]-0.10233[/C][C]-1.3691[/C][C]0.086345[/C][/ROW]
[ROW][C]16[/C][C]0.038953[/C][C]0.5212[/C][C]0.301453[/C][/ROW]
[ROW][C]17[/C][C]-0.021592[/C][C]-0.2889[/C][C]0.386502[/C][/ROW]
[ROW][C]18[/C][C]-0.101432[/C][C]-1.3571[/C][C]0.088235[/C][/ROW]
[ROW][C]19[/C][C]0.088998[/C][C]1.1907[/C][C]0.117671[/C][/ROW]
[ROW][C]20[/C][C]0.075682[/C][C]1.0126[/C][C]0.156319[/C][/ROW]
[ROW][C]21[/C][C]-0.001381[/C][C]-0.0185[/C][C]0.492639[/C][/ROW]
[ROW][C]22[/C][C]0.060329[/C][C]0.8071[/C][C]0.210327[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=312244&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=312244&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	-0.000545	-0.0073	0.497095
2	-0.058756	-0.7861	0.216423
3	-0.043071	-0.5762	0.282587
4	-0.056156	-0.7513	0.226725
5	0.032217	0.431	0.333482
6	0.054201	0.7252	0.234651
7	-0.09031	-1.2083	0.114269
8	-0.144761	-1.9368	0.027174
9	-0.066601	-0.8911	0.187047
10	-0.031827	-0.4258	0.335377
11	-0.005756	-0.077	0.469352
12	-0.000527	-0.0071	0.497191
13	0.018765	0.2511	0.401031
14	-0.076742	-1.0267	0.152965
15	-0.10233	-1.3691	0.086345
16	0.038953	0.5212	0.301453
17	-0.021592	-0.2889	0.386502
18	-0.101432	-1.3571	0.088235
19	0.088998	1.1907	0.117671
20	0.075682	1.0126	0.156319
21	-0.001381	-0.0185	0.492639
22	0.060329	0.8071	0.210327

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.000545	-0.0073	0.497095
2	-0.058756	-0.7861	0.216422
3	-0.043286	-0.5791	0.281616
4	-0.060087	-0.8039	0.211257
5	0.026864	0.3594	0.359854
6	0.046036	0.6159	0.269367
7	-0.092306	-1.235	0.109229
8	-0.143115	-1.9147	0.02856
9	-0.074655	-0.9988	0.159618
10	-0.055028	-0.7362	0.23128
11	-0.043434	-0.5811	0.28095
12	-0.030478	-0.4078	0.341967
13	0.017386	0.2326	0.408164
14	-0.082649	-1.1058	0.135156
15	-0.136605	-1.8277	0.034633
16	-0.011354	-0.1519	0.439714
17	-0.074655	-0.9988	0.159615
18	-0.163324	-2.1851	0.015089
19	0.040715	0.5447	0.293307
20	0.065046	0.8703	0.192662
21	-0.024444	-0.327	0.372009
22	0.007402	0.099	0.460614

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.000545 & -0.0073 & 0.497095 \tabularnewline
2 & -0.058756 & -0.7861 & 0.216422 \tabularnewline
3 & -0.043286 & -0.5791 & 0.281616 \tabularnewline
4 & -0.060087 & -0.8039 & 0.211257 \tabularnewline
5 & 0.026864 & 0.3594 & 0.359854 \tabularnewline
6 & 0.046036 & 0.6159 & 0.269367 \tabularnewline
7 & -0.092306 & -1.235 & 0.109229 \tabularnewline
8 & -0.143115 & -1.9147 & 0.02856 \tabularnewline
9 & -0.074655 & -0.9988 & 0.159618 \tabularnewline
10 & -0.055028 & -0.7362 & 0.23128 \tabularnewline
11 & -0.043434 & -0.5811 & 0.28095 \tabularnewline
12 & -0.030478 & -0.4078 & 0.341967 \tabularnewline
13 & 0.017386 & 0.2326 & 0.408164 \tabularnewline
14 & -0.082649 & -1.1058 & 0.135156 \tabularnewline
15 & -0.136605 & -1.8277 & 0.034633 \tabularnewline
16 & -0.011354 & -0.1519 & 0.439714 \tabularnewline
17 & -0.074655 & -0.9988 & 0.159615 \tabularnewline
18 & -0.163324 & -2.1851 & 0.015089 \tabularnewline
19 & 0.040715 & 0.5447 & 0.293307 \tabularnewline
20 & 0.065046 & 0.8703 & 0.192662 \tabularnewline
21 & -0.024444 & -0.327 & 0.372009 \tabularnewline
22 & 0.007402 & 0.099 & 0.460614 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=312244&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]-0.000545[/C][C]-0.0073[/C][C]0.497095[/C][/ROW]
[ROW][C]2[/C][C]-0.058756[/C][C]-0.7861[/C][C]0.216422[/C][/ROW]
[ROW][C]3[/C][C]-0.043286[/C][C]-0.5791[/C][C]0.281616[/C][/ROW]
[ROW][C]4[/C][C]-0.060087[/C][C]-0.8039[/C][C]0.211257[/C][/ROW]
[ROW][C]5[/C][C]0.026864[/C][C]0.3594[/C][C]0.359854[/C][/ROW]
[ROW][C]6[/C][C]0.046036[/C][C]0.6159[/C][C]0.269367[/C][/ROW]
[ROW][C]7[/C][C]-0.092306[/C][C]-1.235[/C][C]0.109229[/C][/ROW]
[ROW][C]8[/C][C]-0.143115[/C][C]-1.9147[/C][C]0.02856[/C][/ROW]
[ROW][C]9[/C][C]-0.074655[/C][C]-0.9988[/C][C]0.159618[/C][/ROW]
[ROW][C]10[/C][C]-0.055028[/C][C]-0.7362[/C][C]0.23128[/C][/ROW]
[ROW][C]11[/C][C]-0.043434[/C][C]-0.5811[/C][C]0.28095[/C][/ROW]
[ROW][C]12[/C][C]-0.030478[/C][C]-0.4078[/C][C]0.341967[/C][/ROW]
[ROW][C]13[/C][C]0.017386[/C][C]0.2326[/C][C]0.408164[/C][/ROW]
[ROW][C]14[/C][C]-0.082649[/C][C]-1.1058[/C][C]0.135156[/C][/ROW]
[ROW][C]15[/C][C]-0.136605[/C][C]-1.8277[/C][C]0.034633[/C][/ROW]
[ROW][C]16[/C][C]-0.011354[/C][C]-0.1519[/C][C]0.439714[/C][/ROW]
[ROW][C]17[/C][C]-0.074655[/C][C]-0.9988[/C][C]0.159615[/C][/ROW]
[ROW][C]18[/C][C]-0.163324[/C][C]-2.1851[/C][C]0.015089[/C][/ROW]
[ROW][C]19[/C][C]0.040715[/C][C]0.5447[/C][C]0.293307[/C][/ROW]
[ROW][C]20[/C][C]0.065046[/C][C]0.8703[/C][C]0.192662[/C][/ROW]
[ROW][C]21[/C][C]-0.024444[/C][C]-0.327[/C][C]0.372009[/C][/ROW]
[ROW][C]22[/C][C]0.007402[/C][C]0.099[/C][C]0.460614[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=312244&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=312244&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	-0.000545	-0.0073	0.497095
2	-0.058756	-0.7861	0.216422
3	-0.043286	-0.5791	0.281616
4	-0.060087	-0.8039	0.211257
5	0.026864	0.3594	0.359854
6	0.046036	0.6159	0.269367
7	-0.092306	-1.235	0.109229
8	-0.143115	-1.9147	0.02856
9	-0.074655	-0.9988	0.159618
10	-0.055028	-0.7362	0.23128
11	-0.043434	-0.5811	0.28095
12	-0.030478	-0.4078	0.341967
13	0.017386	0.2326	0.408164
14	-0.082649	-1.1058	0.135156
15	-0.136605	-1.8277	0.034633
16	-0.011354	-0.1519	0.439714
17	-0.074655	-0.9988	0.159615
18	-0.163324	-2.1851	0.015089
19	0.040715	0.5447	0.293307
20	0.065046	0.8703	0.192662
21	-0.024444	-0.327	0.372009
22	0.007402	0.099	0.460614

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):

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