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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 18 Dec 2015 21:29:22 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Dec/18/t1450474238lf2xcfb350wo6tb.htm/, Retrieved Thu, 16 May 2024 14:54:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=286933, Retrieved Thu, 16 May 2024 14:54:51 +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] [Autocorrelation H...] [2015-12-18 21:29:22] [07325d4e03e5d5deea478d79524d9715] [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	'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286933&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286933&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286933&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	'George Udny Yule' @ yule.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.515895	-4.527	1.1e-05
2	0.158575	1.3915	0.084042
3	-0.161575	-1.4178	0.08014
4	0.095075	0.8343	0.203353
5	-0.046465	-0.4077	0.342303
6	-0.074434	-0.6532	0.257801
7	0.198787	1.7443	0.042544
8	-0.170806	-1.4988	0.069005
9	0.196178	1.7215	0.044592
10	-0.27953	-2.4529	0.008217
11	0.441717	3.876	0.000111
12	-0.462379	-4.0574	5.9e-05
13	0.147046	1.2903	0.1004
14	-0.030961	-0.2717	0.393299
15	0.046583	0.4088	0.341925
16	-0.053914	-0.4731	0.318743
17	0.061148	0.5366	0.296555
18	0.081545	0.7156	0.238216
19	-0.17395	-1.5264	0.065504

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.515895 & -4.527 & 1.1e-05 \tabularnewline
2 & 0.158575 & 1.3915 & 0.084042 \tabularnewline
3 & -0.161575 & -1.4178 & 0.08014 \tabularnewline
4 & 0.095075 & 0.8343 & 0.203353 \tabularnewline
5 & -0.046465 & -0.4077 & 0.342303 \tabularnewline
6 & -0.074434 & -0.6532 & 0.257801 \tabularnewline
7 & 0.198787 & 1.7443 & 0.042544 \tabularnewline
8 & -0.170806 & -1.4988 & 0.069005 \tabularnewline
9 & 0.196178 & 1.7215 & 0.044592 \tabularnewline
10 & -0.27953 & -2.4529 & 0.008217 \tabularnewline
11 & 0.441717 & 3.876 & 0.000111 \tabularnewline
12 & -0.462379 & -4.0574 & 5.9e-05 \tabularnewline
13 & 0.147046 & 1.2903 & 0.1004 \tabularnewline
14 & -0.030961 & -0.2717 & 0.393299 \tabularnewline
15 & 0.046583 & 0.4088 & 0.341925 \tabularnewline
16 & -0.053914 & -0.4731 & 0.318743 \tabularnewline
17 & 0.061148 & 0.5366 & 0.296555 \tabularnewline
18 & 0.081545 & 0.7156 & 0.238216 \tabularnewline
19 & -0.17395 & -1.5264 & 0.065504 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286933&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]-0.515895[/C][C]-4.527[/C][C]1.1e-05[/C][/ROW]
[ROW][C]2[/C][C]0.158575[/C][C]1.3915[/C][C]0.084042[/C][/ROW]
[ROW][C]3[/C][C]-0.161575[/C][C]-1.4178[/C][C]0.08014[/C][/ROW]
[ROW][C]4[/C][C]0.095075[/C][C]0.8343[/C][C]0.203353[/C][/ROW]
[ROW][C]5[/C][C]-0.046465[/C][C]-0.4077[/C][C]0.342303[/C][/ROW]
[ROW][C]6[/C][C]-0.074434[/C][C]-0.6532[/C][C]0.257801[/C][/ROW]
[ROW][C]7[/C][C]0.198787[/C][C]1.7443[/C][C]0.042544[/C][/ROW]
[ROW][C]8[/C][C]-0.170806[/C][C]-1.4988[/C][C]0.069005[/C][/ROW]
[ROW][C]9[/C][C]0.196178[/C][C]1.7215[/C][C]0.044592[/C][/ROW]
[ROW][C]10[/C][C]-0.27953[/C][C]-2.4529[/C][C]0.008217[/C][/ROW]
[ROW][C]11[/C][C]0.441717[/C][C]3.876[/C][C]0.000111[/C][/ROW]
[ROW][C]12[/C][C]-0.462379[/C][C]-4.0574[/C][C]5.9e-05[/C][/ROW]
[ROW][C]13[/C][C]0.147046[/C][C]1.2903[/C][C]0.1004[/C][/ROW]
[ROW][C]14[/C][C]-0.030961[/C][C]-0.2717[/C][C]0.393299[/C][/ROW]
[ROW][C]15[/C][C]0.046583[/C][C]0.4088[/C][C]0.341925[/C][/ROW]
[ROW][C]16[/C][C]-0.053914[/C][C]-0.4731[/C][C]0.318743[/C][/ROW]
[ROW][C]17[/C][C]0.061148[/C][C]0.5366[/C][C]0.296555[/C][/ROW]
[ROW][C]18[/C][C]0.081545[/C][C]0.7156[/C][C]0.238216[/C][/ROW]
[ROW][C]19[/C][C]-0.17395[/C][C]-1.5264[/C][C]0.065504[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286933&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286933&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	-0.515895	-4.527	1.1e-05
2	0.158575	1.3915	0.084042
3	-0.161575	-1.4178	0.08014
4	0.095075	0.8343	0.203353
5	-0.046465	-0.4077	0.342303
6	-0.074434	-0.6532	0.257801
7	0.198787	1.7443	0.042544
8	-0.170806	-1.4988	0.069005
9	0.196178	1.7215	0.044592
10	-0.27953	-2.4529	0.008217
11	0.441717	3.876	0.000111
12	-0.462379	-4.0574	5.9e-05
13	0.147046	1.2903	0.1004
14	-0.030961	-0.2717	0.393299
15	0.046583	0.4088	0.341925
16	-0.053914	-0.4731	0.318743
17	0.061148	0.5366	0.296555
18	0.081545	0.7156	0.238216
19	-0.17395	-1.5264	0.065504

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.515895	-4.527	1.1e-05
2	-0.146586	-1.2863	0.101099
3	-0.199695	-1.7523	0.04185
4	-0.096127	-0.8435	0.200777
5	-0.059967	-0.5262	0.300128
6	-0.190561	-1.6722	0.049275
7	0.099665	0.8746	0.192267
8	-0.02995	-0.2628	0.3967
9	0.130671	1.1466	0.127542
10	-0.128667	-1.129	0.131192
11	0.348482	3.0579	0.001532
12	-0.133622	-1.1725	0.122299
13	-0.182912	-1.605	0.056289
14	-0.063438	-0.5567	0.289685
15	-0.061901	-0.5432	0.294287
16	-0.169691	-1.489	0.070282
17	0.083715	0.7346	0.232408
18	0.011319	0.0993	0.460571
19	-0.002493	-0.0219	0.4913

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.515895 & -4.527 & 1.1e-05 \tabularnewline
2 & -0.146586 & -1.2863 & 0.101099 \tabularnewline
3 & -0.199695 & -1.7523 & 0.04185 \tabularnewline
4 & -0.096127 & -0.8435 & 0.200777 \tabularnewline
5 & -0.059967 & -0.5262 & 0.300128 \tabularnewline
6 & -0.190561 & -1.6722 & 0.049275 \tabularnewline
7 & 0.099665 & 0.8746 & 0.192267 \tabularnewline
8 & -0.02995 & -0.2628 & 0.3967 \tabularnewline
9 & 0.130671 & 1.1466 & 0.127542 \tabularnewline
10 & -0.128667 & -1.129 & 0.131192 \tabularnewline
11 & 0.348482 & 3.0579 & 0.001532 \tabularnewline
12 & -0.133622 & -1.1725 & 0.122299 \tabularnewline
13 & -0.182912 & -1.605 & 0.056289 \tabularnewline
14 & -0.063438 & -0.5567 & 0.289685 \tabularnewline
15 & -0.061901 & -0.5432 & 0.294287 \tabularnewline
16 & -0.169691 & -1.489 & 0.070282 \tabularnewline
17 & 0.083715 & 0.7346 & 0.232408 \tabularnewline
18 & 0.011319 & 0.0993 & 0.460571 \tabularnewline
19 & -0.002493 & -0.0219 & 0.4913 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286933&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]-0.515895[/C][C]-4.527[/C][C]1.1e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.146586[/C][C]-1.2863[/C][C]0.101099[/C][/ROW]
[ROW][C]3[/C][C]-0.199695[/C][C]-1.7523[/C][C]0.04185[/C][/ROW]
[ROW][C]4[/C][C]-0.096127[/C][C]-0.8435[/C][C]0.200777[/C][/ROW]
[ROW][C]5[/C][C]-0.059967[/C][C]-0.5262[/C][C]0.300128[/C][/ROW]
[ROW][C]6[/C][C]-0.190561[/C][C]-1.6722[/C][C]0.049275[/C][/ROW]
[ROW][C]7[/C][C]0.099665[/C][C]0.8746[/C][C]0.192267[/C][/ROW]
[ROW][C]8[/C][C]-0.02995[/C][C]-0.2628[/C][C]0.3967[/C][/ROW]
[ROW][C]9[/C][C]0.130671[/C][C]1.1466[/C][C]0.127542[/C][/ROW]
[ROW][C]10[/C][C]-0.128667[/C][C]-1.129[/C][C]0.131192[/C][/ROW]
[ROW][C]11[/C][C]0.348482[/C][C]3.0579[/C][C]0.001532[/C][/ROW]
[ROW][C]12[/C][C]-0.133622[/C][C]-1.1725[/C][C]0.122299[/C][/ROW]
[ROW][C]13[/C][C]-0.182912[/C][C]-1.605[/C][C]0.056289[/C][/ROW]
[ROW][C]14[/C][C]-0.063438[/C][C]-0.5567[/C][C]0.289685[/C][/ROW]
[ROW][C]15[/C][C]-0.061901[/C][C]-0.5432[/C][C]0.294287[/C][/ROW]
[ROW][C]16[/C][C]-0.169691[/C][C]-1.489[/C][C]0.070282[/C][/ROW]
[ROW][C]17[/C][C]0.083715[/C][C]0.7346[/C][C]0.232408[/C][/ROW]
[ROW][C]18[/C][C]0.011319[/C][C]0.0993[/C][C]0.460571[/C][/ROW]
[ROW][C]19[/C][C]-0.002493[/C][C]-0.0219[/C][C]0.4913[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286933&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286933&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	-0.515895	-4.527	1.1e-05
2	-0.146586	-1.2863	0.101099
3	-0.199695	-1.7523	0.04185
4	-0.096127	-0.8435	0.200777
5	-0.059967	-0.5262	0.300128
6	-0.190561	-1.6722	0.049275
7	0.099665	0.8746	0.192267
8	-0.02995	-0.2628	0.3967
9	0.130671	1.1466	0.127542
10	-0.128667	-1.129	0.131192
11	0.348482	3.0579	0.001532
12	-0.133622	-1.1725	0.122299
13	-0.182912	-1.605	0.056289
14	-0.063438	-0.5567	0.289685
15	-0.061901	-0.5432	0.294287
16	-0.169691	-1.489	0.070282
17	0.083715	0.7346	0.232408
18	0.011319	0.0993	0.460571
19	-0.002493	-0.0219	0.4913

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 = 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 <- '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,hyperlink('basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),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,hyperlink('basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),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