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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 21 Dec 2016 11:33:47 +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/21/t14823164398fa4jbmhq0iekcw.htm/, Retrieved Mon, 06 May 2024 11:49:38 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302086, Retrieved Mon, 06 May 2024 11:49:38 +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] [auto correlation] [2016-12-21 10:33:47] [63af9ed1c5670c0e3049894fd77d93e0] [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	2 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302086&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]

2 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=302086&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302086&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	2 seconds
R Server	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.243745	2.3882	0.009444
2	0.075853	0.7432	0.229588
3	0.17285	1.6936	0.046794
4	0.086486	0.8474	0.199444
5	-0.047159	-0.4621	0.322542
6	0.00462	0.0453	0.481993
7	-0.05057	-0.4955	0.310698
8	-0.182506	-1.7882	0.03845
9	-0.115488	-1.1315	0.130322
10	0.121581	1.1912	0.118248
11	-0.031385	-0.3075	0.379561
12	-0.227602	-2.23	0.014038
13	-0.045119	-0.4421	0.329715
14	-0.042721	-0.4186	0.338228
15	-0.115164	-1.1284	0.130988
16	0.020154	0.1975	0.421939
17	-0.013281	-0.1301	0.448371
18	-0.094392	-0.9248	0.178682
19	-0.072077	-0.7062	0.240886
20	0.016676	0.1634	0.435276

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.243745 & 2.3882 & 0.009444 \tabularnewline
2 & 0.075853 & 0.7432 & 0.229588 \tabularnewline
3 & 0.17285 & 1.6936 & 0.046794 \tabularnewline
4 & 0.086486 & 0.8474 & 0.199444 \tabularnewline
5 & -0.047159 & -0.4621 & 0.322542 \tabularnewline
6 & 0.00462 & 0.0453 & 0.481993 \tabularnewline
7 & -0.05057 & -0.4955 & 0.310698 \tabularnewline
8 & -0.182506 & -1.7882 & 0.03845 \tabularnewline
9 & -0.115488 & -1.1315 & 0.130322 \tabularnewline
10 & 0.121581 & 1.1912 & 0.118248 \tabularnewline
11 & -0.031385 & -0.3075 & 0.379561 \tabularnewline
12 & -0.227602 & -2.23 & 0.014038 \tabularnewline
13 & -0.045119 & -0.4421 & 0.329715 \tabularnewline
14 & -0.042721 & -0.4186 & 0.338228 \tabularnewline
15 & -0.115164 & -1.1284 & 0.130988 \tabularnewline
16 & 0.020154 & 0.1975 & 0.421939 \tabularnewline
17 & -0.013281 & -0.1301 & 0.448371 \tabularnewline
18 & -0.094392 & -0.9248 & 0.178682 \tabularnewline
19 & -0.072077 & -0.7062 & 0.240886 \tabularnewline
20 & 0.016676 & 0.1634 & 0.435276 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302086&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]0.243745[/C][C]2.3882[/C][C]0.009444[/C][/ROW]
[ROW][C]2[/C][C]0.075853[/C][C]0.7432[/C][C]0.229588[/C][/ROW]
[ROW][C]3[/C][C]0.17285[/C][C]1.6936[/C][C]0.046794[/C][/ROW]
[ROW][C]4[/C][C]0.086486[/C][C]0.8474[/C][C]0.199444[/C][/ROW]
[ROW][C]5[/C][C]-0.047159[/C][C]-0.4621[/C][C]0.322542[/C][/ROW]
[ROW][C]6[/C][C]0.00462[/C][C]0.0453[/C][C]0.481993[/C][/ROW]
[ROW][C]7[/C][C]-0.05057[/C][C]-0.4955[/C][C]0.310698[/C][/ROW]
[ROW][C]8[/C][C]-0.182506[/C][C]-1.7882[/C][C]0.03845[/C][/ROW]
[ROW][C]9[/C][C]-0.115488[/C][C]-1.1315[/C][C]0.130322[/C][/ROW]
[ROW][C]10[/C][C]0.121581[/C][C]1.1912[/C][C]0.118248[/C][/ROW]
[ROW][C]11[/C][C]-0.031385[/C][C]-0.3075[/C][C]0.379561[/C][/ROW]
[ROW][C]12[/C][C]-0.227602[/C][C]-2.23[/C][C]0.014038[/C][/ROW]
[ROW][C]13[/C][C]-0.045119[/C][C]-0.4421[/C][C]0.329715[/C][/ROW]
[ROW][C]14[/C][C]-0.042721[/C][C]-0.4186[/C][C]0.338228[/C][/ROW]
[ROW][C]15[/C][C]-0.115164[/C][C]-1.1284[/C][C]0.130988[/C][/ROW]
[ROW][C]16[/C][C]0.020154[/C][C]0.1975[/C][C]0.421939[/C][/ROW]
[ROW][C]17[/C][C]-0.013281[/C][C]-0.1301[/C][C]0.448371[/C][/ROW]
[ROW][C]18[/C][C]-0.094392[/C][C]-0.9248[/C][C]0.178682[/C][/ROW]
[ROW][C]19[/C][C]-0.072077[/C][C]-0.7062[/C][C]0.240886[/C][/ROW]
[ROW][C]20[/C][C]0.016676[/C][C]0.1634[/C][C]0.435276[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302086&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302086&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	0.243745	2.3882	0.009444
2	0.075853	0.7432	0.229588
3	0.17285	1.6936	0.046794
4	0.086486	0.8474	0.199444
5	-0.047159	-0.4621	0.322542
6	0.00462	0.0453	0.481993
7	-0.05057	-0.4955	0.310698
8	-0.182506	-1.7882	0.03845
9	-0.115488	-1.1315	0.130322
10	0.121581	1.1912	0.118248
11	-0.031385	-0.3075	0.379561
12	-0.227602	-2.23	0.014038
13	-0.045119	-0.4421	0.329715
14	-0.042721	-0.4186	0.338228
15	-0.115164	-1.1284	0.130988
16	0.020154	0.1975	0.421939
17	-0.013281	-0.1301	0.448371
18	-0.094392	-0.9248	0.178682
19	-0.072077	-0.7062	0.240886
20	0.016676	0.1634	0.435276

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.243745	2.3882	0.009444
2	0.017479	0.1713	0.43219
3	0.159975	1.5674	0.060153
4	0.008907	0.0873	0.465319
5	-0.085228	-0.8351	0.202879
6	0.00876	0.0858	0.465891
7	-0.072492	-0.7103	0.239628
8	-0.149929	-1.469	0.072551
9	-0.036574	-0.3584	0.360433
10	0.195657	1.917	0.029103
11	-0.045032	-0.4412	0.330021
12	-0.216588	-2.1221	0.018201
13	-0.002564	-0.0251	0.490004
14	-0.033523	-0.3285	0.371642
15	-0.036913	-0.3617	0.359195
16	0.056355	0.5522	0.29106
17	-0.044502	-0.436	0.331898
18	-0.022204	-0.2176	0.414119
19	-0.063854	-0.6256	0.266519
20	-0.061954	-0.607	0.272633

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.243745 & 2.3882 & 0.009444 \tabularnewline
2 & 0.017479 & 0.1713 & 0.43219 \tabularnewline
3 & 0.159975 & 1.5674 & 0.060153 \tabularnewline
4 & 0.008907 & 0.0873 & 0.465319 \tabularnewline
5 & -0.085228 & -0.8351 & 0.202879 \tabularnewline
6 & 0.00876 & 0.0858 & 0.465891 \tabularnewline
7 & -0.072492 & -0.7103 & 0.239628 \tabularnewline
8 & -0.149929 & -1.469 & 0.072551 \tabularnewline
9 & -0.036574 & -0.3584 & 0.360433 \tabularnewline
10 & 0.195657 & 1.917 & 0.029103 \tabularnewline
11 & -0.045032 & -0.4412 & 0.330021 \tabularnewline
12 & -0.216588 & -2.1221 & 0.018201 \tabularnewline
13 & -0.002564 & -0.0251 & 0.490004 \tabularnewline
14 & -0.033523 & -0.3285 & 0.371642 \tabularnewline
15 & -0.036913 & -0.3617 & 0.359195 \tabularnewline
16 & 0.056355 & 0.5522 & 0.29106 \tabularnewline
17 & -0.044502 & -0.436 & 0.331898 \tabularnewline
18 & -0.022204 & -0.2176 & 0.414119 \tabularnewline
19 & -0.063854 & -0.6256 & 0.266519 \tabularnewline
20 & -0.061954 & -0.607 & 0.272633 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302086&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]0.243745[/C][C]2.3882[/C][C]0.009444[/C][/ROW]
[ROW][C]2[/C][C]0.017479[/C][C]0.1713[/C][C]0.43219[/C][/ROW]
[ROW][C]3[/C][C]0.159975[/C][C]1.5674[/C][C]0.060153[/C][/ROW]
[ROW][C]4[/C][C]0.008907[/C][C]0.0873[/C][C]0.465319[/C][/ROW]
[ROW][C]5[/C][C]-0.085228[/C][C]-0.8351[/C][C]0.202879[/C][/ROW]
[ROW][C]6[/C][C]0.00876[/C][C]0.0858[/C][C]0.465891[/C][/ROW]
[ROW][C]7[/C][C]-0.072492[/C][C]-0.7103[/C][C]0.239628[/C][/ROW]
[ROW][C]8[/C][C]-0.149929[/C][C]-1.469[/C][C]0.072551[/C][/ROW]
[ROW][C]9[/C][C]-0.036574[/C][C]-0.3584[/C][C]0.360433[/C][/ROW]
[ROW][C]10[/C][C]0.195657[/C][C]1.917[/C][C]0.029103[/C][/ROW]
[ROW][C]11[/C][C]-0.045032[/C][C]-0.4412[/C][C]0.330021[/C][/ROW]
[ROW][C]12[/C][C]-0.216588[/C][C]-2.1221[/C][C]0.018201[/C][/ROW]
[ROW][C]13[/C][C]-0.002564[/C][C]-0.0251[/C][C]0.490004[/C][/ROW]
[ROW][C]14[/C][C]-0.033523[/C][C]-0.3285[/C][C]0.371642[/C][/ROW]
[ROW][C]15[/C][C]-0.036913[/C][C]-0.3617[/C][C]0.359195[/C][/ROW]
[ROW][C]16[/C][C]0.056355[/C][C]0.5522[/C][C]0.29106[/C][/ROW]
[ROW][C]17[/C][C]-0.044502[/C][C]-0.436[/C][C]0.331898[/C][/ROW]
[ROW][C]18[/C][C]-0.022204[/C][C]-0.2176[/C][C]0.414119[/C][/ROW]
[ROW][C]19[/C][C]-0.063854[/C][C]-0.6256[/C][C]0.266519[/C][/ROW]
[ROW][C]20[/C][C]-0.061954[/C][C]-0.607[/C][C]0.272633[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302086&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302086&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	0.243745	2.3882	0.009444
2	0.017479	0.1713	0.43219
3	0.159975	1.5674	0.060153
4	0.008907	0.0873	0.465319
5	-0.085228	-0.8351	0.202879
6	0.00876	0.0858	0.465891
7	-0.072492	-0.7103	0.239628
8	-0.149929	-1.469	0.072551
9	-0.036574	-0.3584	0.360433
10	0.195657	1.917	0.029103
11	-0.045032	-0.4412	0.330021
12	-0.216588	-2.1221	0.018201
13	-0.002564	-0.0251	0.490004
14	-0.033523	-0.3285	0.371642
15	-0.036913	-0.3617	0.359195
16	0.056355	0.5522	0.29106
17	-0.044502	-0.436	0.331898
18	-0.022204	-0.2176	0.414119
19	-0.063854	-0.6256	0.266519
20	-0.061954	-0.607	0.272633

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 = 3 ; par2 = 1 ; par3 = 2 ; par4 = TRUE ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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