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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 16 Dec 2016 15:01:20 +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/16/t14818969148qunaw36hmagp5r.htm/, Retrieved Thu, 02 May 2024 17:21:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300278, Retrieved Thu, 02 May 2024 17:21:35 +0000

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Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [ARIMA Backward Selection] [] [2016-12-16 13:36:55] [683f400e1b95307fc738e729f07c4fce]
- RM D    [(Partial) Autocorrelation Function] [] [2016-12-16 14:01:20] [404ac5ee4f7301873f6a96ef36861981] [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=300278&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=300278&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300278&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	-0.367216	-3.938	7.1e-05
2	-0.157078	-1.6845	0.047401
3	0.049628	0.5322	0.297807
4	-0.089596	-0.9608	0.169332
5	0.212568	2.2795	0.01224
6	0.028561	0.3063	0.379971
7	-0.196149	-2.1035	0.018803
8	0.121595	1.304	0.097426
9	-0.003376	-0.0362	0.485592
10	-0.084249	-0.9035	0.184081
11	0.084469	0.9058	0.18346
12	-0.034544	-0.3704	0.355867
13	-0.006099	-0.0654	0.473984
14	0.132135	1.417	0.079595
15	-0.27379	-2.9361	0.002008
16	0.057317	0.6147	0.269998
17	0.159208	1.7073	0.045231
18	-0.11083	-1.1885	0.118539
19	0.165014	1.7696	0.039724
20	-0.215813	-2.3143	0.011212

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.367216 & -3.938 & 7.1e-05 \tabularnewline
2 & -0.157078 & -1.6845 & 0.047401 \tabularnewline
3 & 0.049628 & 0.5322 & 0.297807 \tabularnewline
4 & -0.089596 & -0.9608 & 0.169332 \tabularnewline
5 & 0.212568 & 2.2795 & 0.01224 \tabularnewline
6 & 0.028561 & 0.3063 & 0.379971 \tabularnewline
7 & -0.196149 & -2.1035 & 0.018803 \tabularnewline
8 & 0.121595 & 1.304 & 0.097426 \tabularnewline
9 & -0.003376 & -0.0362 & 0.485592 \tabularnewline
10 & -0.084249 & -0.9035 & 0.184081 \tabularnewline
11 & 0.084469 & 0.9058 & 0.18346 \tabularnewline
12 & -0.034544 & -0.3704 & 0.355867 \tabularnewline
13 & -0.006099 & -0.0654 & 0.473984 \tabularnewline
14 & 0.132135 & 1.417 & 0.079595 \tabularnewline
15 & -0.27379 & -2.9361 & 0.002008 \tabularnewline
16 & 0.057317 & 0.6147 & 0.269998 \tabularnewline
17 & 0.159208 & 1.7073 & 0.045231 \tabularnewline
18 & -0.11083 & -1.1885 & 0.118539 \tabularnewline
19 & 0.165014 & 1.7696 & 0.039724 \tabularnewline
20 & -0.215813 & -2.3143 & 0.011212 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300278&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]-0.367216[/C][C]-3.938[/C][C]7.1e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.157078[/C][C]-1.6845[/C][C]0.047401[/C][/ROW]
[ROW][C]3[/C][C]0.049628[/C][C]0.5322[/C][C]0.297807[/C][/ROW]
[ROW][C]4[/C][C]-0.089596[/C][C]-0.9608[/C][C]0.169332[/C][/ROW]
[ROW][C]5[/C][C]0.212568[/C][C]2.2795[/C][C]0.01224[/C][/ROW]
[ROW][C]6[/C][C]0.028561[/C][C]0.3063[/C][C]0.379971[/C][/ROW]
[ROW][C]7[/C][C]-0.196149[/C][C]-2.1035[/C][C]0.018803[/C][/ROW]
[ROW][C]8[/C][C]0.121595[/C][C]1.304[/C][C]0.097426[/C][/ROW]
[ROW][C]9[/C][C]-0.003376[/C][C]-0.0362[/C][C]0.485592[/C][/ROW]
[ROW][C]10[/C][C]-0.084249[/C][C]-0.9035[/C][C]0.184081[/C][/ROW]
[ROW][C]11[/C][C]0.084469[/C][C]0.9058[/C][C]0.18346[/C][/ROW]
[ROW][C]12[/C][C]-0.034544[/C][C]-0.3704[/C][C]0.355867[/C][/ROW]
[ROW][C]13[/C][C]-0.006099[/C][C]-0.0654[/C][C]0.473984[/C][/ROW]
[ROW][C]14[/C][C]0.132135[/C][C]1.417[/C][C]0.079595[/C][/ROW]
[ROW][C]15[/C][C]-0.27379[/C][C]-2.9361[/C][C]0.002008[/C][/ROW]
[ROW][C]16[/C][C]0.057317[/C][C]0.6147[/C][C]0.269998[/C][/ROW]
[ROW][C]17[/C][C]0.159208[/C][C]1.7073[/C][C]0.045231[/C][/ROW]
[ROW][C]18[/C][C]-0.11083[/C][C]-1.1885[/C][C]0.118539[/C][/ROW]
[ROW][C]19[/C][C]0.165014[/C][C]1.7696[/C][C]0.039724[/C][/ROW]
[ROW][C]20[/C][C]-0.215813[/C][C]-2.3143[/C][C]0.011212[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300278&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300278&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	-0.367216	-3.938	7.1e-05
2	-0.157078	-1.6845	0.047401
3	0.049628	0.5322	0.297807
4	-0.089596	-0.9608	0.169332
5	0.212568	2.2795	0.01224
6	0.028561	0.3063	0.379971
7	-0.196149	-2.1035	0.018803
8	0.121595	1.304	0.097426
9	-0.003376	-0.0362	0.485592
10	-0.084249	-0.9035	0.184081
11	0.084469	0.9058	0.18346
12	-0.034544	-0.3704	0.355867
13	-0.006099	-0.0654	0.473984
14	0.132135	1.417	0.079595
15	-0.27379	-2.9361	0.002008
16	0.057317	0.6147	0.269998
17	0.159208	1.7073	0.045231
18	-0.11083	-1.1885	0.118539
19	0.165014	1.7696	0.039724
20	-0.215813	-2.3143	0.011212

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.367216	-3.938	7.1e-05
2	-0.337427	-3.6185	0.000221
3	-0.197517	-2.1181	0.018159
4	-0.275112	-2.9502	0.001924
5	0.042676	0.4577	0.324033
6	0.14814	1.5886	0.057446
7	-0.02047	-0.2195	0.41332
8	0.104692	1.1227	0.131953
9	0.091396	0.9801	0.164543
10	-0.06355	-0.6815	0.248465
11	-0.038868	-0.4168	0.338797
12	-0.01685	-0.1807	0.42846
13	-0.035505	-0.3808	0.352045
14	0.122522	1.3139	0.095748
15	-0.161707	-1.7341	0.042789
16	-0.145044	-1.5554	0.061297
17	-0.005865	-0.0629	0.474979
18	-0.060924	-0.6533	0.257421
19	0.162567	1.7433	0.041973
20	-0.02112	-0.2265	0.410612

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.367216 & -3.938 & 7.1e-05 \tabularnewline
2 & -0.337427 & -3.6185 & 0.000221 \tabularnewline
3 & -0.197517 & -2.1181 & 0.018159 \tabularnewline
4 & -0.275112 & -2.9502 & 0.001924 \tabularnewline
5 & 0.042676 & 0.4577 & 0.324033 \tabularnewline
6 & 0.14814 & 1.5886 & 0.057446 \tabularnewline
7 & -0.02047 & -0.2195 & 0.41332 \tabularnewline
8 & 0.104692 & 1.1227 & 0.131953 \tabularnewline
9 & 0.091396 & 0.9801 & 0.164543 \tabularnewline
10 & -0.06355 & -0.6815 & 0.248465 \tabularnewline
11 & -0.038868 & -0.4168 & 0.338797 \tabularnewline
12 & -0.01685 & -0.1807 & 0.42846 \tabularnewline
13 & -0.035505 & -0.3808 & 0.352045 \tabularnewline
14 & 0.122522 & 1.3139 & 0.095748 \tabularnewline
15 & -0.161707 & -1.7341 & 0.042789 \tabularnewline
16 & -0.145044 & -1.5554 & 0.061297 \tabularnewline
17 & -0.005865 & -0.0629 & 0.474979 \tabularnewline
18 & -0.060924 & -0.6533 & 0.257421 \tabularnewline
19 & 0.162567 & 1.7433 & 0.041973 \tabularnewline
20 & -0.02112 & -0.2265 & 0.410612 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300278&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]-0.367216[/C][C]-3.938[/C][C]7.1e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.337427[/C][C]-3.6185[/C][C]0.000221[/C][/ROW]
[ROW][C]3[/C][C]-0.197517[/C][C]-2.1181[/C][C]0.018159[/C][/ROW]
[ROW][C]4[/C][C]-0.275112[/C][C]-2.9502[/C][C]0.001924[/C][/ROW]
[ROW][C]5[/C][C]0.042676[/C][C]0.4577[/C][C]0.324033[/C][/ROW]
[ROW][C]6[/C][C]0.14814[/C][C]1.5886[/C][C]0.057446[/C][/ROW]
[ROW][C]7[/C][C]-0.02047[/C][C]-0.2195[/C][C]0.41332[/C][/ROW]
[ROW][C]8[/C][C]0.104692[/C][C]1.1227[/C][C]0.131953[/C][/ROW]
[ROW][C]9[/C][C]0.091396[/C][C]0.9801[/C][C]0.164543[/C][/ROW]
[ROW][C]10[/C][C]-0.06355[/C][C]-0.6815[/C][C]0.248465[/C][/ROW]
[ROW][C]11[/C][C]-0.038868[/C][C]-0.4168[/C][C]0.338797[/C][/ROW]
[ROW][C]12[/C][C]-0.01685[/C][C]-0.1807[/C][C]0.42846[/C][/ROW]
[ROW][C]13[/C][C]-0.035505[/C][C]-0.3808[/C][C]0.352045[/C][/ROW]
[ROW][C]14[/C][C]0.122522[/C][C]1.3139[/C][C]0.095748[/C][/ROW]
[ROW][C]15[/C][C]-0.161707[/C][C]-1.7341[/C][C]0.042789[/C][/ROW]
[ROW][C]16[/C][C]-0.145044[/C][C]-1.5554[/C][C]0.061297[/C][/ROW]
[ROW][C]17[/C][C]-0.005865[/C][C]-0.0629[/C][C]0.474979[/C][/ROW]
[ROW][C]18[/C][C]-0.060924[/C][C]-0.6533[/C][C]0.257421[/C][/ROW]
[ROW][C]19[/C][C]0.162567[/C][C]1.7433[/C][C]0.041973[/C][/ROW]
[ROW][C]20[/C][C]-0.02112[/C][C]-0.2265[/C][C]0.410612[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300278&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300278&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	-0.367216	-3.938	7.1e-05
2	-0.337427	-3.6185	0.000221
3	-0.197517	-2.1181	0.018159
4	-0.275112	-2.9502	0.001924
5	0.042676	0.4577	0.324033
6	0.14814	1.5886	0.057446
7	-0.02047	-0.2195	0.41332
8	0.104692	1.1227	0.131953
9	0.091396	0.9801	0.164543
10	-0.06355	-0.6815	0.248465
11	-0.038868	-0.4168	0.338797
12	-0.01685	-0.1807	0.42846
13	-0.035505	-0.3808	0.352045
14	0.122522	1.3139	0.095748
15	-0.161707	-1.7341	0.042789
16	-0.145044	-1.5554	0.061297
17	-0.005865	-0.0629	0.474979
18	-0.060924	-0.6533	0.257421
19	0.162567	1.7433	0.041973
20	-0.02112	-0.2265	0.410612

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = FALSE ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 1 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 0 ;

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):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '0'
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

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code