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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 19 Dec 2016 17:35:24 +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/19/t1482165415nalq1khn1ls1j72.htm/, Retrieved Sat, 18 May 2024 02:56:07 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301413, Retrieved Sat, 18 May 2024 02:56:07 +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] [] [2016-12-19 16:35:24] [361c8dad91b3f1ef2e651cd04783c23b] [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=301413&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=301413&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301413&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	-0.416113	-4.6523	4e-06
2	-0.022525	-0.2518	0.400792
3	0.037666	0.4211	0.337195
4	-0.185901	-2.0784	0.019858
5	0.25527	2.854	0.002528
6	-0.172899	-1.9331	0.027745
7	0.100541	1.1241	0.131565
8	-0.075302	-0.8419	0.200725
9	-0.025985	-0.2905	0.38595
10	0.009744	0.1089	0.456714
11	-0.185278	-2.0715	0.020186
12	0.350038	3.9135	7.4e-05
13	-0.26886	-3.0059	0.0016
14	0.235857	2.637	0.004713
15	-0.00683	-0.0764	0.469627
16	-0.334674	-3.7418	0.000139
17	0.311791	3.4859	0.000339
18	-0.03995	-0.4467	0.327948
19	8.4e-05	9e-04	0.499625
20	-0.044342	-0.4958	0.310468
21	-0.080139	-0.896	0.185994

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.416113 & -4.6523 & 4e-06 \tabularnewline
2 & -0.022525 & -0.2518 & 0.400792 \tabularnewline
3 & 0.037666 & 0.4211 & 0.337195 \tabularnewline
4 & -0.185901 & -2.0784 & 0.019858 \tabularnewline
5 & 0.25527 & 2.854 & 0.002528 \tabularnewline
6 & -0.172899 & -1.9331 & 0.027745 \tabularnewline
7 & 0.100541 & 1.1241 & 0.131565 \tabularnewline
8 & -0.075302 & -0.8419 & 0.200725 \tabularnewline
9 & -0.025985 & -0.2905 & 0.38595 \tabularnewline
10 & 0.009744 & 0.1089 & 0.456714 \tabularnewline
11 & -0.185278 & -2.0715 & 0.020186 \tabularnewline
12 & 0.350038 & 3.9135 & 7.4e-05 \tabularnewline
13 & -0.26886 & -3.0059 & 0.0016 \tabularnewline
14 & 0.235857 & 2.637 & 0.004713 \tabularnewline
15 & -0.00683 & -0.0764 & 0.469627 \tabularnewline
16 & -0.334674 & -3.7418 & 0.000139 \tabularnewline
17 & 0.311791 & 3.4859 & 0.000339 \tabularnewline
18 & -0.03995 & -0.4467 & 0.327948 \tabularnewline
19 & 8.4e-05 & 9e-04 & 0.499625 \tabularnewline
20 & -0.044342 & -0.4958 & 0.310468 \tabularnewline
21 & -0.080139 & -0.896 & 0.185994 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301413&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]-0.416113[/C][C]-4.6523[/C][C]4e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.022525[/C][C]-0.2518[/C][C]0.400792[/C][/ROW]
[ROW][C]3[/C][C]0.037666[/C][C]0.4211[/C][C]0.337195[/C][/ROW]
[ROW][C]4[/C][C]-0.185901[/C][C]-2.0784[/C][C]0.019858[/C][/ROW]
[ROW][C]5[/C][C]0.25527[/C][C]2.854[/C][C]0.002528[/C][/ROW]
[ROW][C]6[/C][C]-0.172899[/C][C]-1.9331[/C][C]0.027745[/C][/ROW]
[ROW][C]7[/C][C]0.100541[/C][C]1.1241[/C][C]0.131565[/C][/ROW]
[ROW][C]8[/C][C]-0.075302[/C][C]-0.8419[/C][C]0.200725[/C][/ROW]
[ROW][C]9[/C][C]-0.025985[/C][C]-0.2905[/C][C]0.38595[/C][/ROW]
[ROW][C]10[/C][C]0.009744[/C][C]0.1089[/C][C]0.456714[/C][/ROW]
[ROW][C]11[/C][C]-0.185278[/C][C]-2.0715[/C][C]0.020186[/C][/ROW]
[ROW][C]12[/C][C]0.350038[/C][C]3.9135[/C][C]7.4e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.26886[/C][C]-3.0059[/C][C]0.0016[/C][/ROW]
[ROW][C]14[/C][C]0.235857[/C][C]2.637[/C][C]0.004713[/C][/ROW]
[ROW][C]15[/C][C]-0.00683[/C][C]-0.0764[/C][C]0.469627[/C][/ROW]
[ROW][C]16[/C][C]-0.334674[/C][C]-3.7418[/C][C]0.000139[/C][/ROW]
[ROW][C]17[/C][C]0.311791[/C][C]3.4859[/C][C]0.000339[/C][/ROW]
[ROW][C]18[/C][C]-0.03995[/C][C]-0.4467[/C][C]0.327948[/C][/ROW]
[ROW][C]19[/C][C]8.4e-05[/C][C]9e-04[/C][C]0.499625[/C][/ROW]
[ROW][C]20[/C][C]-0.044342[/C][C]-0.4958[/C][C]0.310468[/C][/ROW]
[ROW][C]21[/C][C]-0.080139[/C][C]-0.896[/C][C]0.185994[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301413&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301413&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	-0.416113	-4.6523	4e-06
2	-0.022525	-0.2518	0.400792
3	0.037666	0.4211	0.337195
4	-0.185901	-2.0784	0.019858
5	0.25527	2.854	0.002528
6	-0.172899	-1.9331	0.027745
7	0.100541	1.1241	0.131565
8	-0.075302	-0.8419	0.200725
9	-0.025985	-0.2905	0.38595
10	0.009744	0.1089	0.456714
11	-0.185278	-2.0715	0.020186
12	0.350038	3.9135	7.4e-05
13	-0.26886	-3.0059	0.0016
14	0.235857	2.637	0.004713
15	-0.00683	-0.0764	0.469627
16	-0.334674	-3.7418	0.000139
17	0.311791	3.4859	0.000339
18	-0.03995	-0.4467	0.327948
19	8.4e-05	9e-04	0.499625
20	-0.044342	-0.4958	0.310468
21	-0.080139	-0.896	0.185994

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.416113	-4.6523	4e-06
2	-0.23665	-2.6458	0.004598
3	-0.092753	-1.037	0.150866
4	-0.272273	-3.0441	0.001423
5	0.063903	0.7145	0.238138
6	-0.09665	-1.0806	0.140981
7	0.039615	0.4429	0.329297
8	-0.088521	-0.9897	0.162117
9	-0.03744	-0.4186	0.338118
10	-0.137664	-1.5391	0.06315
11	-0.294949	-3.2976	0.000635
12	0.106259	1.188	0.11854
13	-0.170016	-1.9008	0.029813
14	0.181274	2.0267	0.02241
15	0.132996	1.4869	0.069775
16	-0.202135	-2.2599	0.012778
17	-0.038484	-0.4303	0.333871
18	0.168147	1.8799	0.031222
19	-0.04782	-0.5346	0.296925
20	-0.093079	-1.0407	0.150023
21	-0.038111	-0.4261	0.335384

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.416113 & -4.6523 & 4e-06 \tabularnewline
2 & -0.23665 & -2.6458 & 0.004598 \tabularnewline
3 & -0.092753 & -1.037 & 0.150866 \tabularnewline
4 & -0.272273 & -3.0441 & 0.001423 \tabularnewline
5 & 0.063903 & 0.7145 & 0.238138 \tabularnewline
6 & -0.09665 & -1.0806 & 0.140981 \tabularnewline
7 & 0.039615 & 0.4429 & 0.329297 \tabularnewline
8 & -0.088521 & -0.9897 & 0.162117 \tabularnewline
9 & -0.03744 & -0.4186 & 0.338118 \tabularnewline
10 & -0.137664 & -1.5391 & 0.06315 \tabularnewline
11 & -0.294949 & -3.2976 & 0.000635 \tabularnewline
12 & 0.106259 & 1.188 & 0.11854 \tabularnewline
13 & -0.170016 & -1.9008 & 0.029813 \tabularnewline
14 & 0.181274 & 2.0267 & 0.02241 \tabularnewline
15 & 0.132996 & 1.4869 & 0.069775 \tabularnewline
16 & -0.202135 & -2.2599 & 0.012778 \tabularnewline
17 & -0.038484 & -0.4303 & 0.333871 \tabularnewline
18 & 0.168147 & 1.8799 & 0.031222 \tabularnewline
19 & -0.04782 & -0.5346 & 0.296925 \tabularnewline
20 & -0.093079 & -1.0407 & 0.150023 \tabularnewline
21 & -0.038111 & -0.4261 & 0.335384 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301413&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]-0.416113[/C][C]-4.6523[/C][C]4e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.23665[/C][C]-2.6458[/C][C]0.004598[/C][/ROW]
[ROW][C]3[/C][C]-0.092753[/C][C]-1.037[/C][C]0.150866[/C][/ROW]
[ROW][C]4[/C][C]-0.272273[/C][C]-3.0441[/C][C]0.001423[/C][/ROW]
[ROW][C]5[/C][C]0.063903[/C][C]0.7145[/C][C]0.238138[/C][/ROW]
[ROW][C]6[/C][C]-0.09665[/C][C]-1.0806[/C][C]0.140981[/C][/ROW]
[ROW][C]7[/C][C]0.039615[/C][C]0.4429[/C][C]0.329297[/C][/ROW]
[ROW][C]8[/C][C]-0.088521[/C][C]-0.9897[/C][C]0.162117[/C][/ROW]
[ROW][C]9[/C][C]-0.03744[/C][C]-0.4186[/C][C]0.338118[/C][/ROW]
[ROW][C]10[/C][C]-0.137664[/C][C]-1.5391[/C][C]0.06315[/C][/ROW]
[ROW][C]11[/C][C]-0.294949[/C][C]-3.2976[/C][C]0.000635[/C][/ROW]
[ROW][C]12[/C][C]0.106259[/C][C]1.188[/C][C]0.11854[/C][/ROW]
[ROW][C]13[/C][C]-0.170016[/C][C]-1.9008[/C][C]0.029813[/C][/ROW]
[ROW][C]14[/C][C]0.181274[/C][C]2.0267[/C][C]0.02241[/C][/ROW]
[ROW][C]15[/C][C]0.132996[/C][C]1.4869[/C][C]0.069775[/C][/ROW]
[ROW][C]16[/C][C]-0.202135[/C][C]-2.2599[/C][C]0.012778[/C][/ROW]
[ROW][C]17[/C][C]-0.038484[/C][C]-0.4303[/C][C]0.333871[/C][/ROW]
[ROW][C]18[/C][C]0.168147[/C][C]1.8799[/C][C]0.031222[/C][/ROW]
[ROW][C]19[/C][C]-0.04782[/C][C]-0.5346[/C][C]0.296925[/C][/ROW]
[ROW][C]20[/C][C]-0.093079[/C][C]-1.0407[/C][C]0.150023[/C][/ROW]
[ROW][C]21[/C][C]-0.038111[/C][C]-0.4261[/C][C]0.335384[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301413&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301413&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	-0.416113	-4.6523	4e-06
2	-0.23665	-2.6458	0.004598
3	-0.092753	-1.037	0.150866
4	-0.272273	-3.0441	0.001423
5	0.063903	0.7145	0.238138
6	-0.09665	-1.0806	0.140981
7	0.039615	0.4429	0.329297
8	-0.088521	-0.9897	0.162117
9	-0.03744	-0.4186	0.338118
10	-0.137664	-1.5391	0.06315
11	-0.294949	-3.2976	0.000635
12	0.106259	1.188	0.11854
13	-0.170016	-1.9008	0.029813
14	0.181274	2.0267	0.02241
15	0.132996	1.4869	0.069775
16	-0.202135	-2.2599	0.012778
17	-0.038484	-0.4303	0.333871
18	0.168147	1.8799	0.031222
19	-0.04782	-0.5346	0.296925
20	-0.093079	-1.0407	0.150023
21	-0.038111	-0.4261	0.335384

Figure 1

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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 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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