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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 20 Dec 2016 22:29:31 +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/2016/Dec/20/t1482269381i4zyx3f06phzbqy.htm/, Retrieved Sun, 28 Apr 2024 05:33:13 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301811, Retrieved Sun, 28 Apr 2024 05:33:13 +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] [auto1] [2016-12-20 21:29:31] [2d1dd91c3b5ba64567b1d6b2c9fe9017] [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=301811&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=301811&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301811&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	0.209368	2.2058	0.014728
2	0.069962	0.7371	0.231311
3	0.035016	0.3689	0.356446
4	-0.404593	-4.2627	2.1e-05
5	-0.175817	-1.8523	0.033317
6	0.066987	0.7058	0.240911
7	-0.007457	-0.0786	0.468758
8	0.013324	0.1404	0.444306
9	0.181586	1.9131	0.029154
10	-0.025854	-0.2724	0.392916
11	-0.038179	-0.4022	0.34414
12	0.003062	0.0323	0.487161
13	-0.088458	-0.932	0.176688
14	-0.024144	-0.2544	0.399838
15	0.033317	0.351	0.363122
16	-0.011547	-0.1217	0.451695
17	-0.090333	-0.9517	0.171654
18	-0.088468	-0.9321	0.176662
19	-0.043049	-0.4536	0.325519
20	-0.035601	-0.3751	0.354159

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.209368 & 2.2058 & 0.014728 \tabularnewline
2 & 0.069962 & 0.7371 & 0.231311 \tabularnewline
3 & 0.035016 & 0.3689 & 0.356446 \tabularnewline
4 & -0.404593 & -4.2627 & 2.1e-05 \tabularnewline
5 & -0.175817 & -1.8523 & 0.033317 \tabularnewline
6 & 0.066987 & 0.7058 & 0.240911 \tabularnewline
7 & -0.007457 & -0.0786 & 0.468758 \tabularnewline
8 & 0.013324 & 0.1404 & 0.444306 \tabularnewline
9 & 0.181586 & 1.9131 & 0.029154 \tabularnewline
10 & -0.025854 & -0.2724 & 0.392916 \tabularnewline
11 & -0.038179 & -0.4022 & 0.34414 \tabularnewline
12 & 0.003062 & 0.0323 & 0.487161 \tabularnewline
13 & -0.088458 & -0.932 & 0.176688 \tabularnewline
14 & -0.024144 & -0.2544 & 0.399838 \tabularnewline
15 & 0.033317 & 0.351 & 0.363122 \tabularnewline
16 & -0.011547 & -0.1217 & 0.451695 \tabularnewline
17 & -0.090333 & -0.9517 & 0.171654 \tabularnewline
18 & -0.088468 & -0.9321 & 0.176662 \tabularnewline
19 & -0.043049 & -0.4536 & 0.325519 \tabularnewline
20 & -0.035601 & -0.3751 & 0.354159 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301811&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]0.209368[/C][C]2.2058[/C][C]0.014728[/C][/ROW]
[ROW][C]2[/C][C]0.069962[/C][C]0.7371[/C][C]0.231311[/C][/ROW]
[ROW][C]3[/C][C]0.035016[/C][C]0.3689[/C][C]0.356446[/C][/ROW]
[ROW][C]4[/C][C]-0.404593[/C][C]-4.2627[/C][C]2.1e-05[/C][/ROW]
[ROW][C]5[/C][C]-0.175817[/C][C]-1.8523[/C][C]0.033317[/C][/ROW]
[ROW][C]6[/C][C]0.066987[/C][C]0.7058[/C][C]0.240911[/C][/ROW]
[ROW][C]7[/C][C]-0.007457[/C][C]-0.0786[/C][C]0.468758[/C][/ROW]
[ROW][C]8[/C][C]0.013324[/C][C]0.1404[/C][C]0.444306[/C][/ROW]
[ROW][C]9[/C][C]0.181586[/C][C]1.9131[/C][C]0.029154[/C][/ROW]
[ROW][C]10[/C][C]-0.025854[/C][C]-0.2724[/C][C]0.392916[/C][/ROW]
[ROW][C]11[/C][C]-0.038179[/C][C]-0.4022[/C][C]0.34414[/C][/ROW]
[ROW][C]12[/C][C]0.003062[/C][C]0.0323[/C][C]0.487161[/C][/ROW]
[ROW][C]13[/C][C]-0.088458[/C][C]-0.932[/C][C]0.176688[/C][/ROW]
[ROW][C]14[/C][C]-0.024144[/C][C]-0.2544[/C][C]0.399838[/C][/ROW]
[ROW][C]15[/C][C]0.033317[/C][C]0.351[/C][C]0.363122[/C][/ROW]
[ROW][C]16[/C][C]-0.011547[/C][C]-0.1217[/C][C]0.451695[/C][/ROW]
[ROW][C]17[/C][C]-0.090333[/C][C]-0.9517[/C][C]0.171654[/C][/ROW]
[ROW][C]18[/C][C]-0.088468[/C][C]-0.9321[/C][C]0.176662[/C][/ROW]
[ROW][C]19[/C][C]-0.043049[/C][C]-0.4536[/C][C]0.325519[/C][/ROW]
[ROW][C]20[/C][C]-0.035601[/C][C]-0.3751[/C][C]0.354159[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301811&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301811&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	0.209368	2.2058	0.014728
2	0.069962	0.7371	0.231311
3	0.035016	0.3689	0.356446
4	-0.404593	-4.2627	2.1e-05
5	-0.175817	-1.8523	0.033317
6	0.066987	0.7058	0.240911
7	-0.007457	-0.0786	0.468758
8	0.013324	0.1404	0.444306
9	0.181586	1.9131	0.029154
10	-0.025854	-0.2724	0.392916
11	-0.038179	-0.4022	0.34414
12	0.003062	0.0323	0.487161
13	-0.088458	-0.932	0.176688
14	-0.024144	-0.2544	0.399838
15	0.033317	0.351	0.363122
16	-0.011547	-0.1217	0.451695
17	-0.090333	-0.9517	0.171654
18	-0.088468	-0.9321	0.176662
19	-0.043049	-0.4536	0.325519
20	-0.035601	-0.3751	0.354159

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.209368	2.2058	0.014728
2	0.027324	0.2879	0.386987
3	0.015749	0.1659	0.434257
4	-0.436231	-4.596	6e-06
5	-0.010345	-0.109	0.456704
6	0.189365	1.9951	0.024242
7	0.017389	0.1832	0.427486
8	-0.228898	-2.4116	0.008762
9	0.145574	1.5337	0.063973
10	0.059286	0.6246	0.266751
11	-0.038215	-0.4026	0.344002
12	-0.152201	-1.6035	0.055829
13	0.07623	0.8031	0.211808
14	0.080698	0.8502	0.198521
15	-0.049078	-0.5171	0.30307
16	-0.120121	-1.2656	0.104161
17	-0.080118	-0.8441	0.200217
18	-0.042892	-0.4519	0.326112
19	0.053371	0.5623	0.287522
20	-0.046939	-0.4945	0.310954

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.209368 & 2.2058 & 0.014728 \tabularnewline
2 & 0.027324 & 0.2879 & 0.386987 \tabularnewline
3 & 0.015749 & 0.1659 & 0.434257 \tabularnewline
4 & -0.436231 & -4.596 & 6e-06 \tabularnewline
5 & -0.010345 & -0.109 & 0.456704 \tabularnewline
6 & 0.189365 & 1.9951 & 0.024242 \tabularnewline
7 & 0.017389 & 0.1832 & 0.427486 \tabularnewline
8 & -0.228898 & -2.4116 & 0.008762 \tabularnewline
9 & 0.145574 & 1.5337 & 0.063973 \tabularnewline
10 & 0.059286 & 0.6246 & 0.266751 \tabularnewline
11 & -0.038215 & -0.4026 & 0.344002 \tabularnewline
12 & -0.152201 & -1.6035 & 0.055829 \tabularnewline
13 & 0.07623 & 0.8031 & 0.211808 \tabularnewline
14 & 0.080698 & 0.8502 & 0.198521 \tabularnewline
15 & -0.049078 & -0.5171 & 0.30307 \tabularnewline
16 & -0.120121 & -1.2656 & 0.104161 \tabularnewline
17 & -0.080118 & -0.8441 & 0.200217 \tabularnewline
18 & -0.042892 & -0.4519 & 0.326112 \tabularnewline
19 & 0.053371 & 0.5623 & 0.287522 \tabularnewline
20 & -0.046939 & -0.4945 & 0.310954 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301811&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]0.209368[/C][C]2.2058[/C][C]0.014728[/C][/ROW]
[ROW][C]2[/C][C]0.027324[/C][C]0.2879[/C][C]0.386987[/C][/ROW]
[ROW][C]3[/C][C]0.015749[/C][C]0.1659[/C][C]0.434257[/C][/ROW]
[ROW][C]4[/C][C]-0.436231[/C][C]-4.596[/C][C]6e-06[/C][/ROW]
[ROW][C]5[/C][C]-0.010345[/C][C]-0.109[/C][C]0.456704[/C][/ROW]
[ROW][C]6[/C][C]0.189365[/C][C]1.9951[/C][C]0.024242[/C][/ROW]
[ROW][C]7[/C][C]0.017389[/C][C]0.1832[/C][C]0.427486[/C][/ROW]
[ROW][C]8[/C][C]-0.228898[/C][C]-2.4116[/C][C]0.008762[/C][/ROW]
[ROW][C]9[/C][C]0.145574[/C][C]1.5337[/C][C]0.063973[/C][/ROW]
[ROW][C]10[/C][C]0.059286[/C][C]0.6246[/C][C]0.266751[/C][/ROW]
[ROW][C]11[/C][C]-0.038215[/C][C]-0.4026[/C][C]0.344002[/C][/ROW]
[ROW][C]12[/C][C]-0.152201[/C][C]-1.6035[/C][C]0.055829[/C][/ROW]
[ROW][C]13[/C][C]0.07623[/C][C]0.8031[/C][C]0.211808[/C][/ROW]
[ROW][C]14[/C][C]0.080698[/C][C]0.8502[/C][C]0.198521[/C][/ROW]
[ROW][C]15[/C][C]-0.049078[/C][C]-0.5171[/C][C]0.30307[/C][/ROW]
[ROW][C]16[/C][C]-0.120121[/C][C]-1.2656[/C][C]0.104161[/C][/ROW]
[ROW][C]17[/C][C]-0.080118[/C][C]-0.8441[/C][C]0.200217[/C][/ROW]
[ROW][C]18[/C][C]-0.042892[/C][C]-0.4519[/C][C]0.326112[/C][/ROW]
[ROW][C]19[/C][C]0.053371[/C][C]0.5623[/C][C]0.287522[/C][/ROW]
[ROW][C]20[/C][C]-0.046939[/C][C]-0.4945[/C][C]0.310954[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301811&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301811&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	0.209368	2.2058	0.014728
2	0.027324	0.2879	0.386987
3	0.015749	0.1659	0.434257
4	-0.436231	-4.596	6e-06
5	-0.010345	-0.109	0.456704
6	0.189365	1.9951	0.024242
7	0.017389	0.1832	0.427486
8	-0.228898	-2.4116	0.008762
9	0.145574	1.5337	0.063973
10	0.059286	0.6246	0.266751
11	-0.038215	-0.4026	0.344002
12	-0.152201	-1.6035	0.055829
13	0.07623	0.8031	0.211808
14	0.080698	0.8502	0.198521
15	-0.049078	-0.5171	0.30307
16	-0.120121	-1.2656	0.104161
17	-0.080118	-0.8441	0.200217
18	-0.042892	-0.4519	0.326112
19	0.053371	0.5623	0.287522
20	-0.046939	-0.4945	0.310954

Figure 1

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Postscript link

PDF link

Figure 2

PNG link

Postscript link

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Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 4 ; 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