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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 17 Dec 2016 22:09:32 +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/Dec/17/t1482009041ydwhfjrio5tcjf8.htm/, Retrieved Thu, 02 May 2024 03:03:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300956, Retrieved Thu, 02 May 2024 03:03:10 +0000

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-       [(Partial) Autocorrelation Function] [Autocorrelation ] [2016-12-17 21:09:32] [06fd994a2f2098873ec640c3e39346e5] [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	2 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300956&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]

2 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300956&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300956&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	2 seconds
R Server	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.625264	7.0186	0
2	0.479038	5.3772	0
3	0.217369	2.44	0.00804
4	-0.158793	-1.7825	0.038542
5	-0.245322	-2.7537	0.003382
6	-0.404499	-4.5405	6e-06
7	-0.284683	-3.1956	0.000882
8	-0.199349	-2.2377	0.013499
9	0.134892	1.5142	0.066244
10	0.362448	4.0685	4.1e-05
11	0.502697	5.6428	0
12	0.725943	8.1487	0
13	0.450289	5.0545	1e-06
14	0.39135	4.3929	1.2e-05
15	0.12441	1.3965	0.08251
16	-0.203473	-2.284	0.012023
17	-0.276572	-3.1045	0.001177
18	-0.452894	-5.0837	1e-06
19	-0.342078	-3.8398	9.7e-05
20	-0.231222	-2.5955	0.005284
21	0.031369	0.3521	0.362671

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.625264 & 7.0186 & 0 \tabularnewline
2 & 0.479038 & 5.3772 & 0 \tabularnewline
3 & 0.217369 & 2.44 & 0.00804 \tabularnewline
4 & -0.158793 & -1.7825 & 0.038542 \tabularnewline
5 & -0.245322 & -2.7537 & 0.003382 \tabularnewline
6 & -0.404499 & -4.5405 & 6e-06 \tabularnewline
7 & -0.284683 & -3.1956 & 0.000882 \tabularnewline
8 & -0.199349 & -2.2377 & 0.013499 \tabularnewline
9 & 0.134892 & 1.5142 & 0.066244 \tabularnewline
10 & 0.362448 & 4.0685 & 4.1e-05 \tabularnewline
11 & 0.502697 & 5.6428 & 0 \tabularnewline
12 & 0.725943 & 8.1487 & 0 \tabularnewline
13 & 0.450289 & 5.0545 & 1e-06 \tabularnewline
14 & 0.39135 & 4.3929 & 1.2e-05 \tabularnewline
15 & 0.12441 & 1.3965 & 0.08251 \tabularnewline
16 & -0.203473 & -2.284 & 0.012023 \tabularnewline
17 & -0.276572 & -3.1045 & 0.001177 \tabularnewline
18 & -0.452894 & -5.0837 & 1e-06 \tabularnewline
19 & -0.342078 & -3.8398 & 9.7e-05 \tabularnewline
20 & -0.231222 & -2.5955 & 0.005284 \tabularnewline
21 & 0.031369 & 0.3521 & 0.362671 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300956&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]0.625264[/C][C]7.0186[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.479038[/C][C]5.3772[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.217369[/C][C]2.44[/C][C]0.00804[/C][/ROW]
[ROW][C]4[/C][C]-0.158793[/C][C]-1.7825[/C][C]0.038542[/C][/ROW]
[ROW][C]5[/C][C]-0.245322[/C][C]-2.7537[/C][C]0.003382[/C][/ROW]
[ROW][C]6[/C][C]-0.404499[/C][C]-4.5405[/C][C]6e-06[/C][/ROW]
[ROW][C]7[/C][C]-0.284683[/C][C]-3.1956[/C][C]0.000882[/C][/ROW]
[ROW][C]8[/C][C]-0.199349[/C][C]-2.2377[/C][C]0.013499[/C][/ROW]
[ROW][C]9[/C][C]0.134892[/C][C]1.5142[/C][C]0.066244[/C][/ROW]
[ROW][C]10[/C][C]0.362448[/C][C]4.0685[/C][C]4.1e-05[/C][/ROW]
[ROW][C]11[/C][C]0.502697[/C][C]5.6428[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.725943[/C][C]8.1487[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.450289[/C][C]5.0545[/C][C]1e-06[/C][/ROW]
[ROW][C]14[/C][C]0.39135[/C][C]4.3929[/C][C]1.2e-05[/C][/ROW]
[ROW][C]15[/C][C]0.12441[/C][C]1.3965[/C][C]0.08251[/C][/ROW]
[ROW][C]16[/C][C]-0.203473[/C][C]-2.284[/C][C]0.012023[/C][/ROW]
[ROW][C]17[/C][C]-0.276572[/C][C]-3.1045[/C][C]0.001177[/C][/ROW]
[ROW][C]18[/C][C]-0.452894[/C][C]-5.0837[/C][C]1e-06[/C][/ROW]
[ROW][C]19[/C][C]-0.342078[/C][C]-3.8398[/C][C]9.7e-05[/C][/ROW]
[ROW][C]20[/C][C]-0.231222[/C][C]-2.5955[/C][C]0.005284[/C][/ROW]
[ROW][C]21[/C][C]0.031369[/C][C]0.3521[/C][C]0.362671[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300956&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300956&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	0.625264	7.0186	0
2	0.479038	5.3772	0
3	0.217369	2.44	0.00804
4	-0.158793	-1.7825	0.038542
5	-0.245322	-2.7537	0.003382
6	-0.404499	-4.5405	6e-06
7	-0.284683	-3.1956	0.000882
8	-0.199349	-2.2377	0.013499
9	0.134892	1.5142	0.066244
10	0.362448	4.0685	4.1e-05
11	0.502697	5.6428	0
12	0.725943	8.1487	0
13	0.450289	5.0545	1e-06
14	0.39135	4.3929	1.2e-05
15	0.12441	1.3965	0.08251
16	-0.203473	-2.284	0.012023
17	-0.276572	-3.1045	0.001177
18	-0.452894	-5.0837	1e-06
19	-0.342078	-3.8398	9.7e-05
20	-0.231222	-2.5955	0.005284
21	0.031369	0.3521	0.362671

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.625264	7.0186	0
2	0.144625	1.6234	0.0535
3	-0.216779	-2.4333	0.008182
4	-0.477124	-5.3557	0
5	0.039334	0.4415	0.329798
6	-0.048396	-0.5432	0.293961
7	0.249648	2.8023	0.002938
8	-0.065816	-0.7388	0.230708
9	0.497324	5.5824	0
10	0.087248	0.9794	0.164639
11	0.193812	2.1755	0.015728
12	0.200204	2.2473	0.013181
13	-0.293673	-3.2965	0.000636
14	0.061463	0.6899	0.245757
15	-0.062377	-0.7002	0.242554
16	-0.097243	-1.0916	0.138556
17	-0.001635	-0.0184	0.492691
18	-0.047248	-0.5304	0.298398
19	-0.003224	-0.0362	0.485592
20	0.025081	0.2815	0.389382
21	-0.056321	-0.6322	0.264201

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.625264 & 7.0186 & 0 \tabularnewline
2 & 0.144625 & 1.6234 & 0.0535 \tabularnewline
3 & -0.216779 & -2.4333 & 0.008182 \tabularnewline
4 & -0.477124 & -5.3557 & 0 \tabularnewline
5 & 0.039334 & 0.4415 & 0.329798 \tabularnewline
6 & -0.048396 & -0.5432 & 0.293961 \tabularnewline
7 & 0.249648 & 2.8023 & 0.002938 \tabularnewline
8 & -0.065816 & -0.7388 & 0.230708 \tabularnewline
9 & 0.497324 & 5.5824 & 0 \tabularnewline
10 & 0.087248 & 0.9794 & 0.164639 \tabularnewline
11 & 0.193812 & 2.1755 & 0.015728 \tabularnewline
12 & 0.200204 & 2.2473 & 0.013181 \tabularnewline
13 & -0.293673 & -3.2965 & 0.000636 \tabularnewline
14 & 0.061463 & 0.6899 & 0.245757 \tabularnewline
15 & -0.062377 & -0.7002 & 0.242554 \tabularnewline
16 & -0.097243 & -1.0916 & 0.138556 \tabularnewline
17 & -0.001635 & -0.0184 & 0.492691 \tabularnewline
18 & -0.047248 & -0.5304 & 0.298398 \tabularnewline
19 & -0.003224 & -0.0362 & 0.485592 \tabularnewline
20 & 0.025081 & 0.2815 & 0.389382 \tabularnewline
21 & -0.056321 & -0.6322 & 0.264201 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300956&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]0.625264[/C][C]7.0186[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.144625[/C][C]1.6234[/C][C]0.0535[/C][/ROW]
[ROW][C]3[/C][C]-0.216779[/C][C]-2.4333[/C][C]0.008182[/C][/ROW]
[ROW][C]4[/C][C]-0.477124[/C][C]-5.3557[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.039334[/C][C]0.4415[/C][C]0.329798[/C][/ROW]
[ROW][C]6[/C][C]-0.048396[/C][C]-0.5432[/C][C]0.293961[/C][/ROW]
[ROW][C]7[/C][C]0.249648[/C][C]2.8023[/C][C]0.002938[/C][/ROW]
[ROW][C]8[/C][C]-0.065816[/C][C]-0.7388[/C][C]0.230708[/C][/ROW]
[ROW][C]9[/C][C]0.497324[/C][C]5.5824[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.087248[/C][C]0.9794[/C][C]0.164639[/C][/ROW]
[ROW][C]11[/C][C]0.193812[/C][C]2.1755[/C][C]0.015728[/C][/ROW]
[ROW][C]12[/C][C]0.200204[/C][C]2.2473[/C][C]0.013181[/C][/ROW]
[ROW][C]13[/C][C]-0.293673[/C][C]-3.2965[/C][C]0.000636[/C][/ROW]
[ROW][C]14[/C][C]0.061463[/C][C]0.6899[/C][C]0.245757[/C][/ROW]
[ROW][C]15[/C][C]-0.062377[/C][C]-0.7002[/C][C]0.242554[/C][/ROW]
[ROW][C]16[/C][C]-0.097243[/C][C]-1.0916[/C][C]0.138556[/C][/ROW]
[ROW][C]17[/C][C]-0.001635[/C][C]-0.0184[/C][C]0.492691[/C][/ROW]
[ROW][C]18[/C][C]-0.047248[/C][C]-0.5304[/C][C]0.298398[/C][/ROW]
[ROW][C]19[/C][C]-0.003224[/C][C]-0.0362[/C][C]0.485592[/C][/ROW]
[ROW][C]20[/C][C]0.025081[/C][C]0.2815[/C][C]0.389382[/C][/ROW]
[ROW][C]21[/C][C]-0.056321[/C][C]-0.6322[/C][C]0.264201[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300956&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300956&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	0.625264	7.0186	0
2	0.144625	1.6234	0.0535
3	-0.216779	-2.4333	0.008182
4	-0.477124	-5.3557	0
5	0.039334	0.4415	0.329798
6	-0.048396	-0.5432	0.293961
7	0.249648	2.8023	0.002938
8	-0.065816	-0.7388	0.230708
9	0.497324	5.5824	0
10	0.087248	0.9794	0.164639
11	0.193812	2.1755	0.015728
12	0.200204	2.2473	0.013181
13	-0.293673	-3.2965	0.000636
14	0.061463	0.6899	0.245757
15	-0.062377	-0.7002	0.242554
16	-0.097243	-1.0916	0.138556
17	-0.001635	-0.0184	0.492691
18	-0.047248	-0.5304	0.298398
19	-0.003224	-0.0362	0.485592
20	0.025081	0.2815	0.389382
21	-0.056321	-0.6322	0.264201

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

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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