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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 21 Dec 2016 14:03:43 +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/21/t1482325442mrx2sgsx5uw4m67.htm/, Retrieved Mon, 06 May 2024 14:31:23 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302247, Retrieved Mon, 06 May 2024 14:31:23 +0000

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-       [(Partial) Autocorrelation Function] [Autocorrelation] [2016-12-21 13:03:43] [02b5df5aa2382aa6805f6181aa5e25f1] [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=302247&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=302247&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302247&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	0.603418	6.4427	0
2	0.580964	6.203	0
3	0.566789	6.0516	0
4	0.506274	5.4055	0
5	0.530335	5.6624	0
6	0.516417	5.5138	0
7	0.488641	5.2173	0
8	0.411177	4.3902	1.3e-05
9	0.441293	4.7117	3e-06
10	0.420824	4.4932	8e-06
11	0.433907	4.6329	5e-06
12	0.732399	7.8199	0
13	0.429779	4.5888	6e-06
14	0.390415	4.1685	3e-05
15	0.38709	4.133	3.4e-05
16	0.312463	3.3362	0.000574
17	0.35232	3.7618	0.000134
18	0.339926	3.6294	0.000213
19	0.298614	3.1883	0.000924
20	0.243948	2.6047	0.005211

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.603418 & 6.4427 & 0 \tabularnewline
2 & 0.580964 & 6.203 & 0 \tabularnewline
3 & 0.566789 & 6.0516 & 0 \tabularnewline
4 & 0.506274 & 5.4055 & 0 \tabularnewline
5 & 0.530335 & 5.6624 & 0 \tabularnewline
6 & 0.516417 & 5.5138 & 0 \tabularnewline
7 & 0.488641 & 5.2173 & 0 \tabularnewline
8 & 0.411177 & 4.3902 & 1.3e-05 \tabularnewline
9 & 0.441293 & 4.7117 & 3e-06 \tabularnewline
10 & 0.420824 & 4.4932 & 8e-06 \tabularnewline
11 & 0.433907 & 4.6329 & 5e-06 \tabularnewline
12 & 0.732399 & 7.8199 & 0 \tabularnewline
13 & 0.429779 & 4.5888 & 6e-06 \tabularnewline
14 & 0.390415 & 4.1685 & 3e-05 \tabularnewline
15 & 0.38709 & 4.133 & 3.4e-05 \tabularnewline
16 & 0.312463 & 3.3362 & 0.000574 \tabularnewline
17 & 0.35232 & 3.7618 & 0.000134 \tabularnewline
18 & 0.339926 & 3.6294 & 0.000213 \tabularnewline
19 & 0.298614 & 3.1883 & 0.000924 \tabularnewline
20 & 0.243948 & 2.6047 & 0.005211 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302247&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]0.603418[/C][C]6.4427[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.580964[/C][C]6.203[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.566789[/C][C]6.0516[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.506274[/C][C]5.4055[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.530335[/C][C]5.6624[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.516417[/C][C]5.5138[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.488641[/C][C]5.2173[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.411177[/C][C]4.3902[/C][C]1.3e-05[/C][/ROW]
[ROW][C]9[/C][C]0.441293[/C][C]4.7117[/C][C]3e-06[/C][/ROW]
[ROW][C]10[/C][C]0.420824[/C][C]4.4932[/C][C]8e-06[/C][/ROW]
[ROW][C]11[/C][C]0.433907[/C][C]4.6329[/C][C]5e-06[/C][/ROW]
[ROW][C]12[/C][C]0.732399[/C][C]7.8199[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.429779[/C][C]4.5888[/C][C]6e-06[/C][/ROW]
[ROW][C]14[/C][C]0.390415[/C][C]4.1685[/C][C]3e-05[/C][/ROW]
[ROW][C]15[/C][C]0.38709[/C][C]4.133[/C][C]3.4e-05[/C][/ROW]
[ROW][C]16[/C][C]0.312463[/C][C]3.3362[/C][C]0.000574[/C][/ROW]
[ROW][C]17[/C][C]0.35232[/C][C]3.7618[/C][C]0.000134[/C][/ROW]
[ROW][C]18[/C][C]0.339926[/C][C]3.6294[/C][C]0.000213[/C][/ROW]
[ROW][C]19[/C][C]0.298614[/C][C]3.1883[/C][C]0.000924[/C][/ROW]
[ROW][C]20[/C][C]0.243948[/C][C]2.6047[/C][C]0.005211[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302247&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302247&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	0.603418	6.4427	0
2	0.580964	6.203	0
3	0.566789	6.0516	0
4	0.506274	5.4055	0
5	0.530335	5.6624	0
6	0.516417	5.5138	0
7	0.488641	5.2173	0
8	0.411177	4.3902	1.3e-05
9	0.441293	4.7117	3e-06
10	0.420824	4.4932	8e-06
11	0.433907	4.6329	5e-06
12	0.732399	7.8199	0
13	0.429779	4.5888	6e-06
14	0.390415	4.1685	3e-05
15	0.38709	4.133	3.4e-05
16	0.312463	3.3362	0.000574
17	0.35232	3.7618	0.000134
18	0.339926	3.6294	0.000213
19	0.298614	3.1883	0.000924
20	0.243948	2.6047	0.005211

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.603418	6.4427	0
2	0.341021	3.6411	0.000205
3	0.231336	2.47	0.007496
4	0.077725	0.8299	0.204172
5	0.153183	1.6355	0.052346
6	0.106549	1.1376	0.128829
7	0.050457	0.5387	0.29556
8	-0.092773	-0.9905	0.162002
9	0.065332	0.6976	0.243437
10	0.035023	0.3739	0.35457
11	0.081081	0.8657	0.194233
12	0.643931	6.8753	0
13	-0.386767	-4.1295	3.5e-05
14	-0.328575	-3.5082	0.000323
15	-0.112052	-1.1964	0.117014
16	-0.131444	-1.4034	0.081601
17	0.078141	0.8343	0.202922
18	0.084885	0.9063	0.183338
19	-0.020196	-0.2156	0.41483
20	0.135544	1.4472	0.075291

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.603418 & 6.4427 & 0 \tabularnewline
2 & 0.341021 & 3.6411 & 0.000205 \tabularnewline
3 & 0.231336 & 2.47 & 0.007496 \tabularnewline
4 & 0.077725 & 0.8299 & 0.204172 \tabularnewline
5 & 0.153183 & 1.6355 & 0.052346 \tabularnewline
6 & 0.106549 & 1.1376 & 0.128829 \tabularnewline
7 & 0.050457 & 0.5387 & 0.29556 \tabularnewline
8 & -0.092773 & -0.9905 & 0.162002 \tabularnewline
9 & 0.065332 & 0.6976 & 0.243437 \tabularnewline
10 & 0.035023 & 0.3739 & 0.35457 \tabularnewline
11 & 0.081081 & 0.8657 & 0.194233 \tabularnewline
12 & 0.643931 & 6.8753 & 0 \tabularnewline
13 & -0.386767 & -4.1295 & 3.5e-05 \tabularnewline
14 & -0.328575 & -3.5082 & 0.000323 \tabularnewline
15 & -0.112052 & -1.1964 & 0.117014 \tabularnewline
16 & -0.131444 & -1.4034 & 0.081601 \tabularnewline
17 & 0.078141 & 0.8343 & 0.202922 \tabularnewline
18 & 0.084885 & 0.9063 & 0.183338 \tabularnewline
19 & -0.020196 & -0.2156 & 0.41483 \tabularnewline
20 & 0.135544 & 1.4472 & 0.075291 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302247&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]0.603418[/C][C]6.4427[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.341021[/C][C]3.6411[/C][C]0.000205[/C][/ROW]
[ROW][C]3[/C][C]0.231336[/C][C]2.47[/C][C]0.007496[/C][/ROW]
[ROW][C]4[/C][C]0.077725[/C][C]0.8299[/C][C]0.204172[/C][/ROW]
[ROW][C]5[/C][C]0.153183[/C][C]1.6355[/C][C]0.052346[/C][/ROW]
[ROW][C]6[/C][C]0.106549[/C][C]1.1376[/C][C]0.128829[/C][/ROW]
[ROW][C]7[/C][C]0.050457[/C][C]0.5387[/C][C]0.29556[/C][/ROW]
[ROW][C]8[/C][C]-0.092773[/C][C]-0.9905[/C][C]0.162002[/C][/ROW]
[ROW][C]9[/C][C]0.065332[/C][C]0.6976[/C][C]0.243437[/C][/ROW]
[ROW][C]10[/C][C]0.035023[/C][C]0.3739[/C][C]0.35457[/C][/ROW]
[ROW][C]11[/C][C]0.081081[/C][C]0.8657[/C][C]0.194233[/C][/ROW]
[ROW][C]12[/C][C]0.643931[/C][C]6.8753[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.386767[/C][C]-4.1295[/C][C]3.5e-05[/C][/ROW]
[ROW][C]14[/C][C]-0.328575[/C][C]-3.5082[/C][C]0.000323[/C][/ROW]
[ROW][C]15[/C][C]-0.112052[/C][C]-1.1964[/C][C]0.117014[/C][/ROW]
[ROW][C]16[/C][C]-0.131444[/C][C]-1.4034[/C][C]0.081601[/C][/ROW]
[ROW][C]17[/C][C]0.078141[/C][C]0.8343[/C][C]0.202922[/C][/ROW]
[ROW][C]18[/C][C]0.084885[/C][C]0.9063[/C][C]0.183338[/C][/ROW]
[ROW][C]19[/C][C]-0.020196[/C][C]-0.2156[/C][C]0.41483[/C][/ROW]
[ROW][C]20[/C][C]0.135544[/C][C]1.4472[/C][C]0.075291[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302247&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302247&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	0.603418	6.4427	0
2	0.341021	3.6411	0.000205
3	0.231336	2.47	0.007496
4	0.077725	0.8299	0.204172
5	0.153183	1.6355	0.052346
6	0.106549	1.1376	0.128829
7	0.050457	0.5387	0.29556
8	-0.092773	-0.9905	0.162002
9	0.065332	0.6976	0.243437
10	0.035023	0.3739	0.35457
11	0.081081	0.8657	0.194233
12	0.643931	6.8753	0
13	-0.386767	-4.1295	3.5e-05
14	-0.328575	-3.5082	0.000323
15	-0.112052	-1.1964	0.117014
16	-0.131444	-1.4034	0.081601
17	0.078141	0.8343	0.202922
18	0.084885	0.9063	0.183338
19	-0.020196	-0.2156	0.41483
20	0.135544	1.4472	0.075291

Figure 1

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Figure 2

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Figure 3

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Parameters (Session):

par4 = 4 ;

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):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '4'
par4 <- '1'
par3 <- '1'
par2 <- '1'
par1 <- 'Default'
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

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code