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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 04 Dec 2013 17:37:41 -0500

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/2013/Dec/04/t1386196712eb1yxx86lq92aqk.htm/, Retrieved Thu, 18 Apr 2024 07:24:58 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=230837, Retrieved Thu, 18 Apr 2024 07:24:58 +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] [Workshop 9: ACF] [2010-12-04 15:14:11] [87d60b8864dc39f7ed759c345edfb471]
-    D  [(Partial) Autocorrelation Function] [] [2010-12-07 08:48:25] [1251ac2db27b84d4a3ba43449388906b]
- R         [(Partial) Autocorrelation Function] [] [2013-12-04 22:37:41] [0d95bc223fb54d4a417cab286c0d6b3b] [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	3 seconds
R Server	'Gertrude Mary Cox' @ cox.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 & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230837&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230837&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230837&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	3 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.070283	0.5964	0.2764
2	-0.236319	-2.0052	0.024349
3	0.066267	0.5623	0.287832
4	-0.141789	-1.2031	0.116436
5	-0.211318	-1.7931	0.038579
6	0.068015	0.5771	0.282827
7	-0.100071	-0.8491	0.199312
8	-0.051732	-0.439	0.331001
9	0.117903	1.0004	0.160223
10	-0.11271	-0.9564	0.171042
11	0.115481	0.9799	0.165212
12	0.46429	3.9396	9.3e-05
13	-0.03852	-0.3269	0.372363
14	-0.271878	-2.307	0.011968
15	0.056543	0.4798	0.316419
16	-0.13071	-1.1091	0.135536
17	-0.177655	-1.5075	0.068035
18	0.045438	0.3856	0.350482

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.070283 & 0.5964 & 0.2764 \tabularnewline
2 & -0.236319 & -2.0052 & 0.024349 \tabularnewline
3 & 0.066267 & 0.5623 & 0.287832 \tabularnewline
4 & -0.141789 & -1.2031 & 0.116436 \tabularnewline
5 & -0.211318 & -1.7931 & 0.038579 \tabularnewline
6 & 0.068015 & 0.5771 & 0.282827 \tabularnewline
7 & -0.100071 & -0.8491 & 0.199312 \tabularnewline
8 & -0.051732 & -0.439 & 0.331001 \tabularnewline
9 & 0.117903 & 1.0004 & 0.160223 \tabularnewline
10 & -0.11271 & -0.9564 & 0.171042 \tabularnewline
11 & 0.115481 & 0.9799 & 0.165212 \tabularnewline
12 & 0.46429 & 3.9396 & 9.3e-05 \tabularnewline
13 & -0.03852 & -0.3269 & 0.372363 \tabularnewline
14 & -0.271878 & -2.307 & 0.011968 \tabularnewline
15 & 0.056543 & 0.4798 & 0.316419 \tabularnewline
16 & -0.13071 & -1.1091 & 0.135536 \tabularnewline
17 & -0.177655 & -1.5075 & 0.068035 \tabularnewline
18 & 0.045438 & 0.3856 & 0.350482 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230837&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]0.070283[/C][C]0.5964[/C][C]0.2764[/C][/ROW]
[ROW][C]2[/C][C]-0.236319[/C][C]-2.0052[/C][C]0.024349[/C][/ROW]
[ROW][C]3[/C][C]0.066267[/C][C]0.5623[/C][C]0.287832[/C][/ROW]
[ROW][C]4[/C][C]-0.141789[/C][C]-1.2031[/C][C]0.116436[/C][/ROW]
[ROW][C]5[/C][C]-0.211318[/C][C]-1.7931[/C][C]0.038579[/C][/ROW]
[ROW][C]6[/C][C]0.068015[/C][C]0.5771[/C][C]0.282827[/C][/ROW]
[ROW][C]7[/C][C]-0.100071[/C][C]-0.8491[/C][C]0.199312[/C][/ROW]
[ROW][C]8[/C][C]-0.051732[/C][C]-0.439[/C][C]0.331001[/C][/ROW]
[ROW][C]9[/C][C]0.117903[/C][C]1.0004[/C][C]0.160223[/C][/ROW]
[ROW][C]10[/C][C]-0.11271[/C][C]-0.9564[/C][C]0.171042[/C][/ROW]
[ROW][C]11[/C][C]0.115481[/C][C]0.9799[/C][C]0.165212[/C][/ROW]
[ROW][C]12[/C][C]0.46429[/C][C]3.9396[/C][C]9.3e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.03852[/C][C]-0.3269[/C][C]0.372363[/C][/ROW]
[ROW][C]14[/C][C]-0.271878[/C][C]-2.307[/C][C]0.011968[/C][/ROW]
[ROW][C]15[/C][C]0.056543[/C][C]0.4798[/C][C]0.316419[/C][/ROW]
[ROW][C]16[/C][C]-0.13071[/C][C]-1.1091[/C][C]0.135536[/C][/ROW]
[ROW][C]17[/C][C]-0.177655[/C][C]-1.5075[/C][C]0.068035[/C][/ROW]
[ROW][C]18[/C][C]0.045438[/C][C]0.3856[/C][C]0.350482[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230837&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230837&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	0.070283	0.5964	0.2764
2	-0.236319	-2.0052	0.024349
3	0.066267	0.5623	0.287832
4	-0.141789	-1.2031	0.116436
5	-0.211318	-1.7931	0.038579
6	0.068015	0.5771	0.282827
7	-0.100071	-0.8491	0.199312
8	-0.051732	-0.439	0.331001
9	0.117903	1.0004	0.160223
10	-0.11271	-0.9564	0.171042
11	0.115481	0.9799	0.165212
12	0.46429	3.9396	9.3e-05
13	-0.03852	-0.3269	0.372363
14	-0.271878	-2.307	0.011968
15	0.056543	0.4798	0.316419
16	-0.13071	-1.1091	0.135536
17	-0.177655	-1.5075	0.068035
18	0.045438	0.3856	0.350482

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.070283	0.5964	0.2764
2	-0.242456	-2.0573	0.02164
3	0.110983	0.9417	0.174741
4	-0.234312	-1.9882	0.025296
5	-0.139309	-1.1821	0.120533
6	0.002478	0.021	0.491641
7	-0.203712	-1.7286	0.044088
8	-0.003387	-0.0287	0.488575
9	-0.037476	-0.318	0.375703
10	-0.178389	-1.5137	0.067242
11	0.180301	1.5299	0.065212
12	0.349548	2.966	0.002045
13	-0.013323	-0.1131	0.455152
14	-0.124226	-1.0541	0.147683
15	0.0459	0.3895	0.349037
16	-0.05767	-0.4893	0.313043
17	-0.030067	-0.2551	0.399677
18	-0.083436	-0.708	0.240623

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.070283 & 0.5964 & 0.2764 \tabularnewline
2 & -0.242456 & -2.0573 & 0.02164 \tabularnewline
3 & 0.110983 & 0.9417 & 0.174741 \tabularnewline
4 & -0.234312 & -1.9882 & 0.025296 \tabularnewline
5 & -0.139309 & -1.1821 & 0.120533 \tabularnewline
6 & 0.002478 & 0.021 & 0.491641 \tabularnewline
7 & -0.203712 & -1.7286 & 0.044088 \tabularnewline
8 & -0.003387 & -0.0287 & 0.488575 \tabularnewline
9 & -0.037476 & -0.318 & 0.375703 \tabularnewline
10 & -0.178389 & -1.5137 & 0.067242 \tabularnewline
11 & 0.180301 & 1.5299 & 0.065212 \tabularnewline
12 & 0.349548 & 2.966 & 0.002045 \tabularnewline
13 & -0.013323 & -0.1131 & 0.455152 \tabularnewline
14 & -0.124226 & -1.0541 & 0.147683 \tabularnewline
15 & 0.0459 & 0.3895 & 0.349037 \tabularnewline
16 & -0.05767 & -0.4893 & 0.313043 \tabularnewline
17 & -0.030067 & -0.2551 & 0.399677 \tabularnewline
18 & -0.083436 & -0.708 & 0.240623 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230837&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]0.070283[/C][C]0.5964[/C][C]0.2764[/C][/ROW]
[ROW][C]2[/C][C]-0.242456[/C][C]-2.0573[/C][C]0.02164[/C][/ROW]
[ROW][C]3[/C][C]0.110983[/C][C]0.9417[/C][C]0.174741[/C][/ROW]
[ROW][C]4[/C][C]-0.234312[/C][C]-1.9882[/C][C]0.025296[/C][/ROW]
[ROW][C]5[/C][C]-0.139309[/C][C]-1.1821[/C][C]0.120533[/C][/ROW]
[ROW][C]6[/C][C]0.002478[/C][C]0.021[/C][C]0.491641[/C][/ROW]
[ROW][C]7[/C][C]-0.203712[/C][C]-1.7286[/C][C]0.044088[/C][/ROW]
[ROW][C]8[/C][C]-0.003387[/C][C]-0.0287[/C][C]0.488575[/C][/ROW]
[ROW][C]9[/C][C]-0.037476[/C][C]-0.318[/C][C]0.375703[/C][/ROW]
[ROW][C]10[/C][C]-0.178389[/C][C]-1.5137[/C][C]0.067242[/C][/ROW]
[ROW][C]11[/C][C]0.180301[/C][C]1.5299[/C][C]0.065212[/C][/ROW]
[ROW][C]12[/C][C]0.349548[/C][C]2.966[/C][C]0.002045[/C][/ROW]
[ROW][C]13[/C][C]-0.013323[/C][C]-0.1131[/C][C]0.455152[/C][/ROW]
[ROW][C]14[/C][C]-0.124226[/C][C]-1.0541[/C][C]0.147683[/C][/ROW]
[ROW][C]15[/C][C]0.0459[/C][C]0.3895[/C][C]0.349037[/C][/ROW]
[ROW][C]16[/C][C]-0.05767[/C][C]-0.4893[/C][C]0.313043[/C][/ROW]
[ROW][C]17[/C][C]-0.030067[/C][C]-0.2551[/C][C]0.399677[/C][/ROW]
[ROW][C]18[/C][C]-0.083436[/C][C]-0.708[/C][C]0.240623[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230837&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230837&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	0.070283	0.5964	0.2764
2	-0.242456	-2.0573	0.02164
3	0.110983	0.9417	0.174741
4	-0.234312	-1.9882	0.025296
5	-0.139309	-1.1821	0.120533
6	0.002478	0.021	0.491641
7	-0.203712	-1.7286	0.044088
8	-0.003387	-0.0287	0.488575
9	-0.037476	-0.318	0.375703
10	-0.178389	-1.5137	0.067242
11	0.180301	1.5299	0.065212
12	0.349548	2.966	0.002045
13	-0.013323	-0.1131	0.455152
14	-0.124226	-1.0541	0.147683
15	0.0459	0.3895	0.349037
16	-0.05767	-0.4893	0.313043
17	-0.030067	-0.2551	0.399677
18	-0.083436	-0.708	0.240623

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 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

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

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code