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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 04 Dec 2013 07:04:48 -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/t1386158783cyws9tcasjh12ao.htm/, Retrieved Sat, 20 Apr 2024 00:05:18 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=230541, Retrieved Sat, 20 Apr 2024 00:05:18 +0000

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Estimated Impact

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

-     [Univariate Data Series] [] [2008-12-08 19:22:39] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMP   [Variance Reduction Matrix] [WS9:Variantie Red...] [2013-12-04 11:22:23] [fff8fef6abdb3da482127903f3b009ef]
- RMP       [(Partial) Autocorrelation Function] [WS9: (Partial) Au...] [2013-12-04 12:04:48] [0af71617a8b1f082fed242286206dd2f] [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	4 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 & 4 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230541&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]4 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=230541&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230541&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	4 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.785794	-5.3295	1e-06
2	0.375565	2.5472	0.007134
3	-0.081684	-0.554	0.291129
4	-0.054938	-0.3726	0.355575
5	0.084704	0.5745	0.284218
6	-0.018339	-0.1244	0.450779
7	-0.067032	-0.4546	0.325755
8	0.066833	0.4533	0.326237
9	0.024828	0.1684	0.433508
10	-0.168234	-1.141	0.129883
11	0.328034	2.2248	0.015519
12	-0.40751	-2.7639	0.004094
13	0.325264	2.206	0.016207
14	-0.170012	-1.1531	0.127418
15	0.066981	0.4543	0.325879
16	-0.010488	-0.0711	0.471801
17	-0.056387	-0.3824	0.351951
18	0.099121	0.6723	0.252388

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.785794 & -5.3295 & 1e-06 \tabularnewline
2 & 0.375565 & 2.5472 & 0.007134 \tabularnewline
3 & -0.081684 & -0.554 & 0.291129 \tabularnewline
4 & -0.054938 & -0.3726 & 0.355575 \tabularnewline
5 & 0.084704 & 0.5745 & 0.284218 \tabularnewline
6 & -0.018339 & -0.1244 & 0.450779 \tabularnewline
7 & -0.067032 & -0.4546 & 0.325755 \tabularnewline
8 & 0.066833 & 0.4533 & 0.326237 \tabularnewline
9 & 0.024828 & 0.1684 & 0.433508 \tabularnewline
10 & -0.168234 & -1.141 & 0.129883 \tabularnewline
11 & 0.328034 & 2.2248 & 0.015519 \tabularnewline
12 & -0.40751 & -2.7639 & 0.004094 \tabularnewline
13 & 0.325264 & 2.206 & 0.016207 \tabularnewline
14 & -0.170012 & -1.1531 & 0.127418 \tabularnewline
15 & 0.066981 & 0.4543 & 0.325879 \tabularnewline
16 & -0.010488 & -0.0711 & 0.471801 \tabularnewline
17 & -0.056387 & -0.3824 & 0.351951 \tabularnewline
18 & 0.099121 & 0.6723 & 0.252388 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230541&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]-0.785794[/C][C]-5.3295[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]0.375565[/C][C]2.5472[/C][C]0.007134[/C][/ROW]
[ROW][C]3[/C][C]-0.081684[/C][C]-0.554[/C][C]0.291129[/C][/ROW]
[ROW][C]4[/C][C]-0.054938[/C][C]-0.3726[/C][C]0.355575[/C][/ROW]
[ROW][C]5[/C][C]0.084704[/C][C]0.5745[/C][C]0.284218[/C][/ROW]
[ROW][C]6[/C][C]-0.018339[/C][C]-0.1244[/C][C]0.450779[/C][/ROW]
[ROW][C]7[/C][C]-0.067032[/C][C]-0.4546[/C][C]0.325755[/C][/ROW]
[ROW][C]8[/C][C]0.066833[/C][C]0.4533[/C][C]0.326237[/C][/ROW]
[ROW][C]9[/C][C]0.024828[/C][C]0.1684[/C][C]0.433508[/C][/ROW]
[ROW][C]10[/C][C]-0.168234[/C][C]-1.141[/C][C]0.129883[/C][/ROW]
[ROW][C]11[/C][C]0.328034[/C][C]2.2248[/C][C]0.015519[/C][/ROW]
[ROW][C]12[/C][C]-0.40751[/C][C]-2.7639[/C][C]0.004094[/C][/ROW]
[ROW][C]13[/C][C]0.325264[/C][C]2.206[/C][C]0.016207[/C][/ROW]
[ROW][C]14[/C][C]-0.170012[/C][C]-1.1531[/C][C]0.127418[/C][/ROW]
[ROW][C]15[/C][C]0.066981[/C][C]0.4543[/C][C]0.325879[/C][/ROW]
[ROW][C]16[/C][C]-0.010488[/C][C]-0.0711[/C][C]0.471801[/C][/ROW]
[ROW][C]17[/C][C]-0.056387[/C][C]-0.3824[/C][C]0.351951[/C][/ROW]
[ROW][C]18[/C][C]0.099121[/C][C]0.6723[/C][C]0.252388[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230541&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230541&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	-0.785794	-5.3295	1e-06
2	0.375565	2.5472	0.007134
3	-0.081684	-0.554	0.291129
4	-0.054938	-0.3726	0.355575
5	0.084704	0.5745	0.284218
6	-0.018339	-0.1244	0.450779
7	-0.067032	-0.4546	0.325755
8	0.066833	0.4533	0.326237
9	0.024828	0.1684	0.433508
10	-0.168234	-1.141	0.129883
11	0.328034	2.2248	0.015519
12	-0.40751	-2.7639	0.004094
13	0.325264	2.206	0.016207
14	-0.170012	-1.1531	0.127418
15	0.066981	0.4543	0.325879
16	-0.010488	-0.0711	0.471801
17	-0.056387	-0.3824	0.351951
18	0.099121	0.6723	0.252388

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.785794	-5.3295	1e-06
2	-0.632389	-4.2891	4.6e-05
3	-0.42198	-2.862	0.003158
4	-0.383267	-2.5994	0.006255
5	-0.382489	-2.5942	0.006339
6	-0.116425	-0.7896	0.216897
7	0.057845	0.3923	0.348316
8	-0.038676	-0.2623	0.397126
9	0.142689	0.9678	0.169111
10	-0.23596	-1.6004	0.058183
11	0.051002	0.3459	0.365492
12	0.097978	0.6645	0.254838
13	0.025693	0.1743	0.431213
14	-0.149979	-1.0172	0.157188
15	-0.138805	-0.9414	0.175703
16	-0.040164	-0.2724	0.393263
17	-0.246984	-1.6751	0.050348
18	-0.222953	-1.5121	0.068669

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.785794 & -5.3295 & 1e-06 \tabularnewline
2 & -0.632389 & -4.2891 & 4.6e-05 \tabularnewline
3 & -0.42198 & -2.862 & 0.003158 \tabularnewline
4 & -0.383267 & -2.5994 & 0.006255 \tabularnewline
5 & -0.382489 & -2.5942 & 0.006339 \tabularnewline
6 & -0.116425 & -0.7896 & 0.216897 \tabularnewline
7 & 0.057845 & 0.3923 & 0.348316 \tabularnewline
8 & -0.038676 & -0.2623 & 0.397126 \tabularnewline
9 & 0.142689 & 0.9678 & 0.169111 \tabularnewline
10 & -0.23596 & -1.6004 & 0.058183 \tabularnewline
11 & 0.051002 & 0.3459 & 0.365492 \tabularnewline
12 & 0.097978 & 0.6645 & 0.254838 \tabularnewline
13 & 0.025693 & 0.1743 & 0.431213 \tabularnewline
14 & -0.149979 & -1.0172 & 0.157188 \tabularnewline
15 & -0.138805 & -0.9414 & 0.175703 \tabularnewline
16 & -0.040164 & -0.2724 & 0.393263 \tabularnewline
17 & -0.246984 & -1.6751 & 0.050348 \tabularnewline
18 & -0.222953 & -1.5121 & 0.068669 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230541&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]-0.785794[/C][C]-5.3295[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.632389[/C][C]-4.2891[/C][C]4.6e-05[/C][/ROW]
[ROW][C]3[/C][C]-0.42198[/C][C]-2.862[/C][C]0.003158[/C][/ROW]
[ROW][C]4[/C][C]-0.383267[/C][C]-2.5994[/C][C]0.006255[/C][/ROW]
[ROW][C]5[/C][C]-0.382489[/C][C]-2.5942[/C][C]0.006339[/C][/ROW]
[ROW][C]6[/C][C]-0.116425[/C][C]-0.7896[/C][C]0.216897[/C][/ROW]
[ROW][C]7[/C][C]0.057845[/C][C]0.3923[/C][C]0.348316[/C][/ROW]
[ROW][C]8[/C][C]-0.038676[/C][C]-0.2623[/C][C]0.397126[/C][/ROW]
[ROW][C]9[/C][C]0.142689[/C][C]0.9678[/C][C]0.169111[/C][/ROW]
[ROW][C]10[/C][C]-0.23596[/C][C]-1.6004[/C][C]0.058183[/C][/ROW]
[ROW][C]11[/C][C]0.051002[/C][C]0.3459[/C][C]0.365492[/C][/ROW]
[ROW][C]12[/C][C]0.097978[/C][C]0.6645[/C][C]0.254838[/C][/ROW]
[ROW][C]13[/C][C]0.025693[/C][C]0.1743[/C][C]0.431213[/C][/ROW]
[ROW][C]14[/C][C]-0.149979[/C][C]-1.0172[/C][C]0.157188[/C][/ROW]
[ROW][C]15[/C][C]-0.138805[/C][C]-0.9414[/C][C]0.175703[/C][/ROW]
[ROW][C]16[/C][C]-0.040164[/C][C]-0.2724[/C][C]0.393263[/C][/ROW]
[ROW][C]17[/C][C]-0.246984[/C][C]-1.6751[/C][C]0.050348[/C][/ROW]
[ROW][C]18[/C][C]-0.222953[/C][C]-1.5121[/C][C]0.068669[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230541&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230541&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	-0.785794	-5.3295	1e-06
2	-0.632389	-4.2891	4.6e-05
3	-0.42198	-2.862	0.003158
4	-0.383267	-2.5994	0.006255
5	-0.382489	-2.5942	0.006339
6	-0.116425	-0.7896	0.216897
7	0.057845	0.3923	0.348316
8	-0.038676	-0.2623	0.397126
9	0.142689	0.9678	0.169111
10	-0.23596	-1.6004	0.058183
11	0.051002	0.3459	0.365492
12	0.097978	0.6645	0.254838
13	0.025693	0.1743	0.431213
14	-0.149979	-1.0172	0.157188
15	-0.138805	-0.9414	0.175703
16	-0.040164	-0.2724	0.393263
17	-0.246984	-1.6751	0.050348
18	-0.222953	-1.5121	0.068669

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 = 2 ; par4 = 2 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 2 ; par4 = 2 ; 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

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code