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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 15 Dec 2016 20:54:47 +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/2016/Dec/15/t1481831852w9agfdvc0nzf03v.htm/, Retrieved Fri, 03 May 2024 06:26:00 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299987, Retrieved Fri, 03 May 2024 06:26:00 +0000

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-       [(Partial) Autocorrelation Function] [ACF N2142 d=D=0] [2016-12-15 19:54:47] [31f526a885cd288e1bc58dc4a6a7fb1f] [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=299987&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=299987&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299987&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	0.878596	9.8622	0
2	0.795213	8.9262	0
3	0.731177	8.2074	0
4	0.692789	7.7765	0
5	0.673405	7.5589	0
6	0.611123	6.8598	0
7	0.588195	6.6025	0
8	0.525393	5.8975	0
9	0.493042	5.5344	0
10	0.490822	5.5095	0
11	0.486441	5.4603	0
12	0.495065	5.5571	0
13	0.440435	4.9439	1e-06
14	0.375576	4.2158	2.4e-05
15	0.323482	3.6311	0.000205
16	0.282046	3.166	0.000969
17	0.287194	3.2238	0.000806
18	0.258839	2.9055	0.002166
19	0.255078	2.8632	0.002456
20	0.213876	2.4008	0.008912
21	0.186103	2.089	0.01936

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.878596 & 9.8622 & 0 \tabularnewline
2 & 0.795213 & 8.9262 & 0 \tabularnewline
3 & 0.731177 & 8.2074 & 0 \tabularnewline
4 & 0.692789 & 7.7765 & 0 \tabularnewline
5 & 0.673405 & 7.5589 & 0 \tabularnewline
6 & 0.611123 & 6.8598 & 0 \tabularnewline
7 & 0.588195 & 6.6025 & 0 \tabularnewline
8 & 0.525393 & 5.8975 & 0 \tabularnewline
9 & 0.493042 & 5.5344 & 0 \tabularnewline
10 & 0.490822 & 5.5095 & 0 \tabularnewline
11 & 0.486441 & 5.4603 & 0 \tabularnewline
12 & 0.495065 & 5.5571 & 0 \tabularnewline
13 & 0.440435 & 4.9439 & 1e-06 \tabularnewline
14 & 0.375576 & 4.2158 & 2.4e-05 \tabularnewline
15 & 0.323482 & 3.6311 & 0.000205 \tabularnewline
16 & 0.282046 & 3.166 & 0.000969 \tabularnewline
17 & 0.287194 & 3.2238 & 0.000806 \tabularnewline
18 & 0.258839 & 2.9055 & 0.002166 \tabularnewline
19 & 0.255078 & 2.8632 & 0.002456 \tabularnewline
20 & 0.213876 & 2.4008 & 0.008912 \tabularnewline
21 & 0.186103 & 2.089 & 0.01936 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299987&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]0.878596[/C][C]9.8622[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.795213[/C][C]8.9262[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.731177[/C][C]8.2074[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.692789[/C][C]7.7765[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.673405[/C][C]7.5589[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.611123[/C][C]6.8598[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.588195[/C][C]6.6025[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.525393[/C][C]5.8975[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.493042[/C][C]5.5344[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.490822[/C][C]5.5095[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.486441[/C][C]5.4603[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.495065[/C][C]5.5571[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.440435[/C][C]4.9439[/C][C]1e-06[/C][/ROW]
[ROW][C]14[/C][C]0.375576[/C][C]4.2158[/C][C]2.4e-05[/C][/ROW]
[ROW][C]15[/C][C]0.323482[/C][C]3.6311[/C][C]0.000205[/C][/ROW]
[ROW][C]16[/C][C]0.282046[/C][C]3.166[/C][C]0.000969[/C][/ROW]
[ROW][C]17[/C][C]0.287194[/C][C]3.2238[/C][C]0.000806[/C][/ROW]
[ROW][C]18[/C][C]0.258839[/C][C]2.9055[/C][C]0.002166[/C][/ROW]
[ROW][C]19[/C][C]0.255078[/C][C]2.8632[/C][C]0.002456[/C][/ROW]
[ROW][C]20[/C][C]0.213876[/C][C]2.4008[/C][C]0.008912[/C][/ROW]
[ROW][C]21[/C][C]0.186103[/C][C]2.089[/C][C]0.01936[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299987&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299987&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	0.878596	9.8622	0
2	0.795213	8.9262	0
3	0.731177	8.2074	0
4	0.692789	7.7765	0
5	0.673405	7.5589	0
6	0.611123	6.8598	0
7	0.588195	6.6025	0
8	0.525393	5.8975	0
9	0.493042	5.5344	0
10	0.490822	5.5095	0
11	0.486441	5.4603	0
12	0.495065	5.5571	0
13	0.440435	4.9439	1e-06
14	0.375576	4.2158	2.4e-05
15	0.323482	3.6311	0.000205
16	0.282046	3.166	0.000969
17	0.287194	3.2238	0.000806
18	0.258839	2.9055	0.002166
19	0.255078	2.8632	0.002456
20	0.213876	2.4008	0.008912
21	0.186103	2.089	0.01936

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.878596	9.8622	0
2	0.102083	1.1459	0.12701
3	0.062649	0.7032	0.241602
4	0.105498	1.1842	0.119279
5	0.110506	1.2404	0.10856
6	-0.14627	-1.6419	0.051555
7	0.130709	1.4672	0.072407
8	-0.158658	-1.7809	0.038667
9	0.069076	0.7754	0.219784
10	0.126432	1.4192	0.079155
11	0.063127	0.7086	0.239941
12	0.056006	0.6287	0.265353
13	-0.157755	-1.7708	0.039506
14	-0.180183	-2.0225	0.022618
15	-0.028213	-0.3167	0.376003
16	-0.044143	-0.4955	0.310553
17	0.140962	1.5823	0.058045
18	-0.013853	-0.1555	0.438337
19	0.118959	1.3353	0.09209
20	-0.114543	-1.2857	0.100446
21	0.018787	0.2109	0.416661

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.878596 & 9.8622 & 0 \tabularnewline
2 & 0.102083 & 1.1459 & 0.12701 \tabularnewline
3 & 0.062649 & 0.7032 & 0.241602 \tabularnewline
4 & 0.105498 & 1.1842 & 0.119279 \tabularnewline
5 & 0.110506 & 1.2404 & 0.10856 \tabularnewline
6 & -0.14627 & -1.6419 & 0.051555 \tabularnewline
7 & 0.130709 & 1.4672 & 0.072407 \tabularnewline
8 & -0.158658 & -1.7809 & 0.038667 \tabularnewline
9 & 0.069076 & 0.7754 & 0.219784 \tabularnewline
10 & 0.126432 & 1.4192 & 0.079155 \tabularnewline
11 & 0.063127 & 0.7086 & 0.239941 \tabularnewline
12 & 0.056006 & 0.6287 & 0.265353 \tabularnewline
13 & -0.157755 & -1.7708 & 0.039506 \tabularnewline
14 & -0.180183 & -2.0225 & 0.022618 \tabularnewline
15 & -0.028213 & -0.3167 & 0.376003 \tabularnewline
16 & -0.044143 & -0.4955 & 0.310553 \tabularnewline
17 & 0.140962 & 1.5823 & 0.058045 \tabularnewline
18 & -0.013853 & -0.1555 & 0.438337 \tabularnewline
19 & 0.118959 & 1.3353 & 0.09209 \tabularnewline
20 & -0.114543 & -1.2857 & 0.100446 \tabularnewline
21 & 0.018787 & 0.2109 & 0.416661 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299987&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]0.878596[/C][C]9.8622[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.102083[/C][C]1.1459[/C][C]0.12701[/C][/ROW]
[ROW][C]3[/C][C]0.062649[/C][C]0.7032[/C][C]0.241602[/C][/ROW]
[ROW][C]4[/C][C]0.105498[/C][C]1.1842[/C][C]0.119279[/C][/ROW]
[ROW][C]5[/C][C]0.110506[/C][C]1.2404[/C][C]0.10856[/C][/ROW]
[ROW][C]6[/C][C]-0.14627[/C][C]-1.6419[/C][C]0.051555[/C][/ROW]
[ROW][C]7[/C][C]0.130709[/C][C]1.4672[/C][C]0.072407[/C][/ROW]
[ROW][C]8[/C][C]-0.158658[/C][C]-1.7809[/C][C]0.038667[/C][/ROW]
[ROW][C]9[/C][C]0.069076[/C][C]0.7754[/C][C]0.219784[/C][/ROW]
[ROW][C]10[/C][C]0.126432[/C][C]1.4192[/C][C]0.079155[/C][/ROW]
[ROW][C]11[/C][C]0.063127[/C][C]0.7086[/C][C]0.239941[/C][/ROW]
[ROW][C]12[/C][C]0.056006[/C][C]0.6287[/C][C]0.265353[/C][/ROW]
[ROW][C]13[/C][C]-0.157755[/C][C]-1.7708[/C][C]0.039506[/C][/ROW]
[ROW][C]14[/C][C]-0.180183[/C][C]-2.0225[/C][C]0.022618[/C][/ROW]
[ROW][C]15[/C][C]-0.028213[/C][C]-0.3167[/C][C]0.376003[/C][/ROW]
[ROW][C]16[/C][C]-0.044143[/C][C]-0.4955[/C][C]0.310553[/C][/ROW]
[ROW][C]17[/C][C]0.140962[/C][C]1.5823[/C][C]0.058045[/C][/ROW]
[ROW][C]18[/C][C]-0.013853[/C][C]-0.1555[/C][C]0.438337[/C][/ROW]
[ROW][C]19[/C][C]0.118959[/C][C]1.3353[/C][C]0.09209[/C][/ROW]
[ROW][C]20[/C][C]-0.114543[/C][C]-1.2857[/C][C]0.100446[/C][/ROW]
[ROW][C]21[/C][C]0.018787[/C][C]0.2109[/C][C]0.416661[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299987&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299987&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	0.878596	9.8622	0
2	0.102083	1.1459	0.12701
3	0.062649	0.7032	0.241602
4	0.105498	1.1842	0.119279
5	0.110506	1.2404	0.10856
6	-0.14627	-1.6419	0.051555
7	0.130709	1.4672	0.072407
8	-0.158658	-1.7809	0.038667
9	0.069076	0.7754	0.219784
10	0.126432	1.4192	0.079155
11	0.063127	0.7086	0.239941
12	0.056006	0.6287	0.265353
13	-0.157755	-1.7708	0.039506
14	-0.180183	-2.0225	0.022618
15	-0.028213	-0.3167	0.376003
16	-0.044143	-0.4955	0.310553
17	0.140962	1.5823	0.058045
18	-0.013853	-0.1555	0.438337
19	0.118959	1.3353	0.09209
20	-0.114543	-1.2857	0.100446
21	0.018787	0.2109	0.416661

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code