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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 23 Dec 2011 13:59:14 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/23/t1324666766ky8x6bhj8ounaiq.htm/, Retrieved Mon, 29 Apr 2024 17:41:12 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160654, Retrieved Mon, 29 Apr 2024 17:41:12 +0000

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

-     [Spectral Analysis] [] [2011-12-23 18:50:40] [2ba7ee2cbaa966a49160c7cfb7436069]
- RMP     [(Partial) Autocorrelation Function] [] [2011-12-23 18:59:14] [393d554610c677f923bed472882d0fdb] [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	'AstonUniversity' @ aston.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 & 2 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160654&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160654&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160654&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	'AstonUniversity' @ aston.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.21198	-2.0443	0.021877
2	-0.100078	-0.9651	0.168494
3	-0.12607	-1.2158	0.113574
4	-0.118869	-1.1463	0.127299
5	0.123239	1.1885	0.118836
6	-0.010678	-0.103	0.459102
7	-0.098423	-0.9492	0.172501
8	0.08346	0.8049	0.211476
9	0.026675	0.2572	0.398778
10	0.104306	1.0059	0.158538
11	-0.000317	-0.0031	0.498783
12	-0.452264	-4.3615	1.7e-05
13	0.227936	2.1981	0.015211
14	-0.045912	-0.4428	0.329482
15	0.139311	1.3435	0.091196
16	0.018717	0.1805	0.428575
17	-0.108474	-1.0461	0.149117
18	0.076809	0.7407	0.230364
19	0.041552	0.4007	0.344776
20	-0.10193	-0.983	0.164085

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.21198 & -2.0443 & 0.021877 \tabularnewline
2 & -0.100078 & -0.9651 & 0.168494 \tabularnewline
3 & -0.12607 & -1.2158 & 0.113574 \tabularnewline
4 & -0.118869 & -1.1463 & 0.127299 \tabularnewline
5 & 0.123239 & 1.1885 & 0.118836 \tabularnewline
6 & -0.010678 & -0.103 & 0.459102 \tabularnewline
7 & -0.098423 & -0.9492 & 0.172501 \tabularnewline
8 & 0.08346 & 0.8049 & 0.211476 \tabularnewline
9 & 0.026675 & 0.2572 & 0.398778 \tabularnewline
10 & 0.104306 & 1.0059 & 0.158538 \tabularnewline
11 & -0.000317 & -0.0031 & 0.498783 \tabularnewline
12 & -0.452264 & -4.3615 & 1.7e-05 \tabularnewline
13 & 0.227936 & 2.1981 & 0.015211 \tabularnewline
14 & -0.045912 & -0.4428 & 0.329482 \tabularnewline
15 & 0.139311 & 1.3435 & 0.091196 \tabularnewline
16 & 0.018717 & 0.1805 & 0.428575 \tabularnewline
17 & -0.108474 & -1.0461 & 0.149117 \tabularnewline
18 & 0.076809 & 0.7407 & 0.230364 \tabularnewline
19 & 0.041552 & 0.4007 & 0.344776 \tabularnewline
20 & -0.10193 & -0.983 & 0.164085 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160654&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]-0.21198[/C][C]-2.0443[/C][C]0.021877[/C][/ROW]
[ROW][C]2[/C][C]-0.100078[/C][C]-0.9651[/C][C]0.168494[/C][/ROW]
[ROW][C]3[/C][C]-0.12607[/C][C]-1.2158[/C][C]0.113574[/C][/ROW]
[ROW][C]4[/C][C]-0.118869[/C][C]-1.1463[/C][C]0.127299[/C][/ROW]
[ROW][C]5[/C][C]0.123239[/C][C]1.1885[/C][C]0.118836[/C][/ROW]
[ROW][C]6[/C][C]-0.010678[/C][C]-0.103[/C][C]0.459102[/C][/ROW]
[ROW][C]7[/C][C]-0.098423[/C][C]-0.9492[/C][C]0.172501[/C][/ROW]
[ROW][C]8[/C][C]0.08346[/C][C]0.8049[/C][C]0.211476[/C][/ROW]
[ROW][C]9[/C][C]0.026675[/C][C]0.2572[/C][C]0.398778[/C][/ROW]
[ROW][C]10[/C][C]0.104306[/C][C]1.0059[/C][C]0.158538[/C][/ROW]
[ROW][C]11[/C][C]-0.000317[/C][C]-0.0031[/C][C]0.498783[/C][/ROW]
[ROW][C]12[/C][C]-0.452264[/C][C]-4.3615[/C][C]1.7e-05[/C][/ROW]
[ROW][C]13[/C][C]0.227936[/C][C]2.1981[/C][C]0.015211[/C][/ROW]
[ROW][C]14[/C][C]-0.045912[/C][C]-0.4428[/C][C]0.329482[/C][/ROW]
[ROW][C]15[/C][C]0.139311[/C][C]1.3435[/C][C]0.091196[/C][/ROW]
[ROW][C]16[/C][C]0.018717[/C][C]0.1805[/C][C]0.428575[/C][/ROW]
[ROW][C]17[/C][C]-0.108474[/C][C]-1.0461[/C][C]0.149117[/C][/ROW]
[ROW][C]18[/C][C]0.076809[/C][C]0.7407[/C][C]0.230364[/C][/ROW]
[ROW][C]19[/C][C]0.041552[/C][C]0.4007[/C][C]0.344776[/C][/ROW]
[ROW][C]20[/C][C]-0.10193[/C][C]-0.983[/C][C]0.164085[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160654&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160654&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	-0.21198	-2.0443	0.021877
2	-0.100078	-0.9651	0.168494
3	-0.12607	-1.2158	0.113574
4	-0.118869	-1.1463	0.127299
5	0.123239	1.1885	0.118836
6	-0.010678	-0.103	0.459102
7	-0.098423	-0.9492	0.172501
8	0.08346	0.8049	0.211476
9	0.026675	0.2572	0.398778
10	0.104306	1.0059	0.158538
11	-0.000317	-0.0031	0.498783
12	-0.452264	-4.3615	1.7e-05
13	0.227936	2.1981	0.015211
14	-0.045912	-0.4428	0.329482
15	0.139311	1.3435	0.091196
16	0.018717	0.1805	0.428575
17	-0.108474	-1.0461	0.149117
18	0.076809	0.7407	0.230364
19	0.041552	0.4007	0.344776
20	-0.10193	-0.983	0.164085

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.21198	-2.0443	0.021877
2	-0.151837	-1.4643	0.073247
3	-0.195802	-1.8882	0.031055
4	-0.239487	-2.3095	0.011564
5	-0.027212	-0.2624	0.396788
6	-0.076923	-0.7418	0.230032
7	-0.187874	-1.8118	0.036623
8	-0.020614	-0.1988	0.421428
9	0.011216	0.1082	0.457049
10	0.090565	0.8734	0.192353
11	0.071723	0.6917	0.245433
12	-0.42911	-4.1382	3.8e-05
13	0.028905	0.2788	0.390526
14	-0.137393	-1.325	0.094213
15	-0.02898	-0.2795	0.390251
16	-0.07948	-0.7665	0.222667
17	-0.060221	-0.5808	0.281406
18	0.005654	0.0545	0.478317
19	-0.009777	-0.0943	0.462542
20	-0.089931	-0.8673	0.194016

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.21198 & -2.0443 & 0.021877 \tabularnewline
2 & -0.151837 & -1.4643 & 0.073247 \tabularnewline
3 & -0.195802 & -1.8882 & 0.031055 \tabularnewline
4 & -0.239487 & -2.3095 & 0.011564 \tabularnewline
5 & -0.027212 & -0.2624 & 0.396788 \tabularnewline
6 & -0.076923 & -0.7418 & 0.230032 \tabularnewline
7 & -0.187874 & -1.8118 & 0.036623 \tabularnewline
8 & -0.020614 & -0.1988 & 0.421428 \tabularnewline
9 & 0.011216 & 0.1082 & 0.457049 \tabularnewline
10 & 0.090565 & 0.8734 & 0.192353 \tabularnewline
11 & 0.071723 & 0.6917 & 0.245433 \tabularnewline
12 & -0.42911 & -4.1382 & 3.8e-05 \tabularnewline
13 & 0.028905 & 0.2788 & 0.390526 \tabularnewline
14 & -0.137393 & -1.325 & 0.094213 \tabularnewline
15 & -0.02898 & -0.2795 & 0.390251 \tabularnewline
16 & -0.07948 & -0.7665 & 0.222667 \tabularnewline
17 & -0.060221 & -0.5808 & 0.281406 \tabularnewline
18 & 0.005654 & 0.0545 & 0.478317 \tabularnewline
19 & -0.009777 & -0.0943 & 0.462542 \tabularnewline
20 & -0.089931 & -0.8673 & 0.194016 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160654&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]-0.21198[/C][C]-2.0443[/C][C]0.021877[/C][/ROW]
[ROW][C]2[/C][C]-0.151837[/C][C]-1.4643[/C][C]0.073247[/C][/ROW]
[ROW][C]3[/C][C]-0.195802[/C][C]-1.8882[/C][C]0.031055[/C][/ROW]
[ROW][C]4[/C][C]-0.239487[/C][C]-2.3095[/C][C]0.011564[/C][/ROW]
[ROW][C]5[/C][C]-0.027212[/C][C]-0.2624[/C][C]0.396788[/C][/ROW]
[ROW][C]6[/C][C]-0.076923[/C][C]-0.7418[/C][C]0.230032[/C][/ROW]
[ROW][C]7[/C][C]-0.187874[/C][C]-1.8118[/C][C]0.036623[/C][/ROW]
[ROW][C]8[/C][C]-0.020614[/C][C]-0.1988[/C][C]0.421428[/C][/ROW]
[ROW][C]9[/C][C]0.011216[/C][C]0.1082[/C][C]0.457049[/C][/ROW]
[ROW][C]10[/C][C]0.090565[/C][C]0.8734[/C][C]0.192353[/C][/ROW]
[ROW][C]11[/C][C]0.071723[/C][C]0.6917[/C][C]0.245433[/C][/ROW]
[ROW][C]12[/C][C]-0.42911[/C][C]-4.1382[/C][C]3.8e-05[/C][/ROW]
[ROW][C]13[/C][C]0.028905[/C][C]0.2788[/C][C]0.390526[/C][/ROW]
[ROW][C]14[/C][C]-0.137393[/C][C]-1.325[/C][C]0.094213[/C][/ROW]
[ROW][C]15[/C][C]-0.02898[/C][C]-0.2795[/C][C]0.390251[/C][/ROW]
[ROW][C]16[/C][C]-0.07948[/C][C]-0.7665[/C][C]0.222667[/C][/ROW]
[ROW][C]17[/C][C]-0.060221[/C][C]-0.5808[/C][C]0.281406[/C][/ROW]
[ROW][C]18[/C][C]0.005654[/C][C]0.0545[/C][C]0.478317[/C][/ROW]
[ROW][C]19[/C][C]-0.009777[/C][C]-0.0943[/C][C]0.462542[/C][/ROW]
[ROW][C]20[/C][C]-0.089931[/C][C]-0.8673[/C][C]0.194016[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160654&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160654&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	-0.21198	-2.0443	0.021877
2	-0.151837	-1.4643	0.073247
3	-0.195802	-1.8882	0.031055
4	-0.239487	-2.3095	0.011564
5	-0.027212	-0.2624	0.396788
6	-0.076923	-0.7418	0.230032
7	-0.187874	-1.8118	0.036623
8	-0.020614	-0.1988	0.421428
9	0.011216	0.1082	0.457049
10	0.090565	0.8734	0.192353
11	0.071723	0.6917	0.245433
12	-0.42911	-4.1382	3.8e-05
13	0.028905	0.2788	0.390526
14	-0.137393	-1.325	0.094213
15	-0.02898	-0.2795	0.390251
16	-0.07948	-0.7665	0.222667
17	-0.060221	-0.5808	0.281406
18	0.005654	0.0545	0.478317
19	-0.009777	-0.0943	0.462542
20	-0.089931	-0.8673	0.194016

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):

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)
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