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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 19 Dec 2016 20:37:23 +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/19/t1482176297akzfcjhn4hukdo9.htm/, Retrieved Fri, 17 May 2024 15:12:33 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301468, Retrieved Fri, 17 May 2024 15:12:33 +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] [N2044 ACF] [2016-12-19 19:37:23] [2e11ca31a00cf8de75c33c1af2d59434] [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=301468&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=301468&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301468&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	-0.442169	-4.4657	1e-05
2	0.008965	0.0905	0.464017
3	0.103324	1.0435	0.149588
4	-0.239383	-2.4176	0.008698
5	0.130657	1.3196	0.094966
6	0.041196	0.4161	0.339121
7	-0.158879	-1.6046	0.055837
8	0.224244	2.2648	0.012821
9	-0.192906	-1.9483	0.027066
10	0.151423	1.5293	0.064643
11	0.103218	1.0425	0.149833
12	-0.423723	-4.2794	2.1e-05
13	0.26359	2.6621	0.004512
14	-0.145477	-1.4692	0.072421
15	-0.006842	-0.0691	0.472522
16	0.246757	2.4921	0.007155
17	-0.190425	-1.9232	0.028622
18	0.046266	0.4673	0.320655
19	0.088294	0.8917	0.187319
20	-0.138999	-1.4038	0.081704

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.442169 & -4.4657 & 1e-05 \tabularnewline
2 & 0.008965 & 0.0905 & 0.464017 \tabularnewline
3 & 0.103324 & 1.0435 & 0.149588 \tabularnewline
4 & -0.239383 & -2.4176 & 0.008698 \tabularnewline
5 & 0.130657 & 1.3196 & 0.094966 \tabularnewline
6 & 0.041196 & 0.4161 & 0.339121 \tabularnewline
7 & -0.158879 & -1.6046 & 0.055837 \tabularnewline
8 & 0.224244 & 2.2648 & 0.012821 \tabularnewline
9 & -0.192906 & -1.9483 & 0.027066 \tabularnewline
10 & 0.151423 & 1.5293 & 0.064643 \tabularnewline
11 & 0.103218 & 1.0425 & 0.149833 \tabularnewline
12 & -0.423723 & -4.2794 & 2.1e-05 \tabularnewline
13 & 0.26359 & 2.6621 & 0.004512 \tabularnewline
14 & -0.145477 & -1.4692 & 0.072421 \tabularnewline
15 & -0.006842 & -0.0691 & 0.472522 \tabularnewline
16 & 0.246757 & 2.4921 & 0.007155 \tabularnewline
17 & -0.190425 & -1.9232 & 0.028622 \tabularnewline
18 & 0.046266 & 0.4673 & 0.320655 \tabularnewline
19 & 0.088294 & 0.8917 & 0.187319 \tabularnewline
20 & -0.138999 & -1.4038 & 0.081704 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301468&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]-0.442169[/C][C]-4.4657[/C][C]1e-05[/C][/ROW]
[ROW][C]2[/C][C]0.008965[/C][C]0.0905[/C][C]0.464017[/C][/ROW]
[ROW][C]3[/C][C]0.103324[/C][C]1.0435[/C][C]0.149588[/C][/ROW]
[ROW][C]4[/C][C]-0.239383[/C][C]-2.4176[/C][C]0.008698[/C][/ROW]
[ROW][C]5[/C][C]0.130657[/C][C]1.3196[/C][C]0.094966[/C][/ROW]
[ROW][C]6[/C][C]0.041196[/C][C]0.4161[/C][C]0.339121[/C][/ROW]
[ROW][C]7[/C][C]-0.158879[/C][C]-1.6046[/C][C]0.055837[/C][/ROW]
[ROW][C]8[/C][C]0.224244[/C][C]2.2648[/C][C]0.012821[/C][/ROW]
[ROW][C]9[/C][C]-0.192906[/C][C]-1.9483[/C][C]0.027066[/C][/ROW]
[ROW][C]10[/C][C]0.151423[/C][C]1.5293[/C][C]0.064643[/C][/ROW]
[ROW][C]11[/C][C]0.103218[/C][C]1.0425[/C][C]0.149833[/C][/ROW]
[ROW][C]12[/C][C]-0.423723[/C][C]-4.2794[/C][C]2.1e-05[/C][/ROW]
[ROW][C]13[/C][C]0.26359[/C][C]2.6621[/C][C]0.004512[/C][/ROW]
[ROW][C]14[/C][C]-0.145477[/C][C]-1.4692[/C][C]0.072421[/C][/ROW]
[ROW][C]15[/C][C]-0.006842[/C][C]-0.0691[/C][C]0.472522[/C][/ROW]
[ROW][C]16[/C][C]0.246757[/C][C]2.4921[/C][C]0.007155[/C][/ROW]
[ROW][C]17[/C][C]-0.190425[/C][C]-1.9232[/C][C]0.028622[/C][/ROW]
[ROW][C]18[/C][C]0.046266[/C][C]0.4673[/C][C]0.320655[/C][/ROW]
[ROW][C]19[/C][C]0.088294[/C][C]0.8917[/C][C]0.187319[/C][/ROW]
[ROW][C]20[/C][C]-0.138999[/C][C]-1.4038[/C][C]0.081704[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301468&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301468&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	-0.442169	-4.4657	1e-05
2	0.008965	0.0905	0.464017
3	0.103324	1.0435	0.149588
4	-0.239383	-2.4176	0.008698
5	0.130657	1.3196	0.094966
6	0.041196	0.4161	0.339121
7	-0.158879	-1.6046	0.055837
8	0.224244	2.2648	0.012821
9	-0.192906	-1.9483	0.027066
10	0.151423	1.5293	0.064643
11	0.103218	1.0425	0.149833
12	-0.423723	-4.2794	2.1e-05
13	0.26359	2.6621	0.004512
14	-0.145477	-1.4692	0.072421
15	-0.006842	-0.0691	0.472522
16	0.246757	2.4921	0.007155
17	-0.190425	-1.9232	0.028622
18	0.046266	0.4673	0.320655
19	0.088294	0.8917	0.187319
20	-0.138999	-1.4038	0.081704

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.442169	-4.4657	1e-05
2	-0.231885	-2.3419	0.010564
3	0.007454	0.0753	0.470068
4	-0.23377	-2.361	0.010064
5	-0.100274	-1.0127	0.156796
6	0.025719	0.2597	0.397791
7	-0.128835	-1.3012	0.098066
8	0.079618	0.8041	0.211605
9	-0.087747	-0.8862	0.188796
10	0.114683	1.1582	0.124734
11	0.211904	2.1401	0.017365
12	-0.306991	-3.1005	0.001249
13	-0.105124	-1.0617	0.145439
14	-0.175537	-1.7728	0.03962
15	-0.091844	-0.9276	0.177908
16	0.052989	0.5352	0.29685
17	-0.002982	-0.0301	0.488017
18	-0.002006	-0.0203	0.491939
19	0.04446	0.449	0.327183
20	0.088193	0.8907	0.187591

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.442169 & -4.4657 & 1e-05 \tabularnewline
2 & -0.231885 & -2.3419 & 0.010564 \tabularnewline
3 & 0.007454 & 0.0753 & 0.470068 \tabularnewline
4 & -0.23377 & -2.361 & 0.010064 \tabularnewline
5 & -0.100274 & -1.0127 & 0.156796 \tabularnewline
6 & 0.025719 & 0.2597 & 0.397791 \tabularnewline
7 & -0.128835 & -1.3012 & 0.098066 \tabularnewline
8 & 0.079618 & 0.8041 & 0.211605 \tabularnewline
9 & -0.087747 & -0.8862 & 0.188796 \tabularnewline
10 & 0.114683 & 1.1582 & 0.124734 \tabularnewline
11 & 0.211904 & 2.1401 & 0.017365 \tabularnewline
12 & -0.306991 & -3.1005 & 0.001249 \tabularnewline
13 & -0.105124 & -1.0617 & 0.145439 \tabularnewline
14 & -0.175537 & -1.7728 & 0.03962 \tabularnewline
15 & -0.091844 & -0.9276 & 0.177908 \tabularnewline
16 & 0.052989 & 0.5352 & 0.29685 \tabularnewline
17 & -0.002982 & -0.0301 & 0.488017 \tabularnewline
18 & -0.002006 & -0.0203 & 0.491939 \tabularnewline
19 & 0.04446 & 0.449 & 0.327183 \tabularnewline
20 & 0.088193 & 0.8907 & 0.187591 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301468&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]-0.442169[/C][C]-4.4657[/C][C]1e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.231885[/C][C]-2.3419[/C][C]0.010564[/C][/ROW]
[ROW][C]3[/C][C]0.007454[/C][C]0.0753[/C][C]0.470068[/C][/ROW]
[ROW][C]4[/C][C]-0.23377[/C][C]-2.361[/C][C]0.010064[/C][/ROW]
[ROW][C]5[/C][C]-0.100274[/C][C]-1.0127[/C][C]0.156796[/C][/ROW]
[ROW][C]6[/C][C]0.025719[/C][C]0.2597[/C][C]0.397791[/C][/ROW]
[ROW][C]7[/C][C]-0.128835[/C][C]-1.3012[/C][C]0.098066[/C][/ROW]
[ROW][C]8[/C][C]0.079618[/C][C]0.8041[/C][C]0.211605[/C][/ROW]
[ROW][C]9[/C][C]-0.087747[/C][C]-0.8862[/C][C]0.188796[/C][/ROW]
[ROW][C]10[/C][C]0.114683[/C][C]1.1582[/C][C]0.124734[/C][/ROW]
[ROW][C]11[/C][C]0.211904[/C][C]2.1401[/C][C]0.017365[/C][/ROW]
[ROW][C]12[/C][C]-0.306991[/C][C]-3.1005[/C][C]0.001249[/C][/ROW]
[ROW][C]13[/C][C]-0.105124[/C][C]-1.0617[/C][C]0.145439[/C][/ROW]
[ROW][C]14[/C][C]-0.175537[/C][C]-1.7728[/C][C]0.03962[/C][/ROW]
[ROW][C]15[/C][C]-0.091844[/C][C]-0.9276[/C][C]0.177908[/C][/ROW]
[ROW][C]16[/C][C]0.052989[/C][C]0.5352[/C][C]0.29685[/C][/ROW]
[ROW][C]17[/C][C]-0.002982[/C][C]-0.0301[/C][C]0.488017[/C][/ROW]
[ROW][C]18[/C][C]-0.002006[/C][C]-0.0203[/C][C]0.491939[/C][/ROW]
[ROW][C]19[/C][C]0.04446[/C][C]0.449[/C][C]0.327183[/C][/ROW]
[ROW][C]20[/C][C]0.088193[/C][C]0.8907[/C][C]0.187591[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301468&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301468&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	-0.442169	-4.4657	1e-05
2	-0.231885	-2.3419	0.010564
3	0.007454	0.0753	0.470068
4	-0.23377	-2.361	0.010064
5	-0.100274	-1.0127	0.156796
6	0.025719	0.2597	0.397791
7	-0.128835	-1.3012	0.098066
8	0.079618	0.8041	0.211605
9	-0.087747	-0.8862	0.188796
10	0.114683	1.1582	0.124734
11	0.211904	2.1401	0.017365
12	-0.306991	-3.1005	0.001249
13	-0.105124	-1.0617	0.145439
14	-0.175537	-1.7728	0.03962
15	-0.091844	-0.9276	0.177908
16	0.052989	0.5352	0.29685
17	-0.002982	-0.0301	0.488017
18	-0.002006	-0.0203	0.491939
19	0.04446	0.449	0.327183
20	0.088193	0.8907	0.187591

Figure 1

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Postscript link

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Figure 2

PNG link

Postscript link

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Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

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

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code