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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 15 Mar 2014 09:37:25 -0400

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/2014/Mar/15/t13948906751tken1oqjimlomi.htm/, Retrieved Tue, 14 May 2024 14:54:26 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234258, Retrieved Tue, 14 May 2024 14:54:26 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

166

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

-       [(Partial) Autocorrelation Function] [Verkoop Mini Nede...] [2014-03-15 13:37:25] [778963f9ed1fb67b9d5ff0854a52552f] [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	'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234258&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234258&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234258&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	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.357435	-3.8992	8e-05
2	-0.175138	-1.9105	0.029236
3	0.140352	1.5311	0.064204
4	0.032084	0.35	0.363481
5	-0.024259	-0.2646	0.395876
6	-0.125018	-1.3638	0.087605
7	0.177763	1.9392	0.027424
8	-0.152785	-1.6667	0.049103
9	-0.057479	-0.627	0.265922
10	0.087346	0.9528	0.171304
11	0.08586	0.9366	0.175426
12	-0.143281	-1.563	0.060352
13	-0.069698	-0.7603	0.224284
14	0.056166	0.6127	0.270623
15	0.140155	1.5289	0.064471
16	-0.183902	-2.0061	0.023555
17	0.019389	0.2115	0.416427
18	0.092557	1.0097	0.157348
19	-0.122124	-1.3322	0.092668
20	0.120931	1.3192	0.094818
21	-0.116111	-1.2666	0.103883

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.357435 & -3.8992 & 8e-05 \tabularnewline
2 & -0.175138 & -1.9105 & 0.029236 \tabularnewline
3 & 0.140352 & 1.5311 & 0.064204 \tabularnewline
4 & 0.032084 & 0.35 & 0.363481 \tabularnewline
5 & -0.024259 & -0.2646 & 0.395876 \tabularnewline
6 & -0.125018 & -1.3638 & 0.087605 \tabularnewline
7 & 0.177763 & 1.9392 & 0.027424 \tabularnewline
8 & -0.152785 & -1.6667 & 0.049103 \tabularnewline
9 & -0.057479 & -0.627 & 0.265922 \tabularnewline
10 & 0.087346 & 0.9528 & 0.171304 \tabularnewline
11 & 0.08586 & 0.9366 & 0.175426 \tabularnewline
12 & -0.143281 & -1.563 & 0.060352 \tabularnewline
13 & -0.069698 & -0.7603 & 0.224284 \tabularnewline
14 & 0.056166 & 0.6127 & 0.270623 \tabularnewline
15 & 0.140155 & 1.5289 & 0.064471 \tabularnewline
16 & -0.183902 & -2.0061 & 0.023555 \tabularnewline
17 & 0.019389 & 0.2115 & 0.416427 \tabularnewline
18 & 0.092557 & 1.0097 & 0.157348 \tabularnewline
19 & -0.122124 & -1.3322 & 0.092668 \tabularnewline
20 & 0.120931 & 1.3192 & 0.094818 \tabularnewline
21 & -0.116111 & -1.2666 & 0.103883 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234258&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]-0.357435[/C][C]-3.8992[/C][C]8e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.175138[/C][C]-1.9105[/C][C]0.029236[/C][/ROW]
[ROW][C]3[/C][C]0.140352[/C][C]1.5311[/C][C]0.064204[/C][/ROW]
[ROW][C]4[/C][C]0.032084[/C][C]0.35[/C][C]0.363481[/C][/ROW]
[ROW][C]5[/C][C]-0.024259[/C][C]-0.2646[/C][C]0.395876[/C][/ROW]
[ROW][C]6[/C][C]-0.125018[/C][C]-1.3638[/C][C]0.087605[/C][/ROW]
[ROW][C]7[/C][C]0.177763[/C][C]1.9392[/C][C]0.027424[/C][/ROW]
[ROW][C]8[/C][C]-0.152785[/C][C]-1.6667[/C][C]0.049103[/C][/ROW]
[ROW][C]9[/C][C]-0.057479[/C][C]-0.627[/C][C]0.265922[/C][/ROW]
[ROW][C]10[/C][C]0.087346[/C][C]0.9528[/C][C]0.171304[/C][/ROW]
[ROW][C]11[/C][C]0.08586[/C][C]0.9366[/C][C]0.175426[/C][/ROW]
[ROW][C]12[/C][C]-0.143281[/C][C]-1.563[/C][C]0.060352[/C][/ROW]
[ROW][C]13[/C][C]-0.069698[/C][C]-0.7603[/C][C]0.224284[/C][/ROW]
[ROW][C]14[/C][C]0.056166[/C][C]0.6127[/C][C]0.270623[/C][/ROW]
[ROW][C]15[/C][C]0.140155[/C][C]1.5289[/C][C]0.064471[/C][/ROW]
[ROW][C]16[/C][C]-0.183902[/C][C]-2.0061[/C][C]0.023555[/C][/ROW]
[ROW][C]17[/C][C]0.019389[/C][C]0.2115[/C][C]0.416427[/C][/ROW]
[ROW][C]18[/C][C]0.092557[/C][C]1.0097[/C][C]0.157348[/C][/ROW]
[ROW][C]19[/C][C]-0.122124[/C][C]-1.3322[/C][C]0.092668[/C][/ROW]
[ROW][C]20[/C][C]0.120931[/C][C]1.3192[/C][C]0.094818[/C][/ROW]
[ROW][C]21[/C][C]-0.116111[/C][C]-1.2666[/C][C]0.103883[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234258&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234258&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	-0.357435	-3.8992	8e-05
2	-0.175138	-1.9105	0.029236
3	0.140352	1.5311	0.064204
4	0.032084	0.35	0.363481
5	-0.024259	-0.2646	0.395876
6	-0.125018	-1.3638	0.087605
7	0.177763	1.9392	0.027424
8	-0.152785	-1.6667	0.049103
9	-0.057479	-0.627	0.265922
10	0.087346	0.9528	0.171304
11	0.08586	0.9366	0.175426
12	-0.143281	-1.563	0.060352
13	-0.069698	-0.7603	0.224284
14	0.056166	0.6127	0.270623
15	0.140155	1.5289	0.064471
16	-0.183902	-2.0061	0.023555
17	0.019389	0.2115	0.416427
18	0.092557	1.0097	0.157348
19	-0.122124	-1.3322	0.092668
20	0.120931	1.3192	0.094818
21	-0.116111	-1.2666	0.103883

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.357435	-3.8992	8e-05
2	-0.347264	-3.7882	0.00012
3	-0.088796	-0.9686	0.167343
4	0.005194	0.0567	0.477454
5	0.043882	0.4787	0.316515
6	-0.124929	-1.3628	0.087758
7	0.083402	0.9098	0.182381
8	-0.134235	-1.4643	0.07287
9	-0.134777	-1.4702	0.072068
10	-0.083625	-0.9122	0.181743
11	0.09473	1.0334	0.151759
12	-0.057886	-0.6315	0.264474
13	-0.115639	-1.2615	0.104804
14	-0.188123	-2.0522	0.021173
15	0.094843	1.0346	0.151474
16	-0.107834	-1.1763	0.120905
17	-0.039169	-0.4273	0.334972
18	-0.058212	-0.635	0.263318
19	-0.097798	-1.0668	0.1441
20	0.041579	0.4536	0.32548
21	-0.14943	-1.6301	0.052864

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.357435 & -3.8992 & 8e-05 \tabularnewline
2 & -0.347264 & -3.7882 & 0.00012 \tabularnewline
3 & -0.088796 & -0.9686 & 0.167343 \tabularnewline
4 & 0.005194 & 0.0567 & 0.477454 \tabularnewline
5 & 0.043882 & 0.4787 & 0.316515 \tabularnewline
6 & -0.124929 & -1.3628 & 0.087758 \tabularnewline
7 & 0.083402 & 0.9098 & 0.182381 \tabularnewline
8 & -0.134235 & -1.4643 & 0.07287 \tabularnewline
9 & -0.134777 & -1.4702 & 0.072068 \tabularnewline
10 & -0.083625 & -0.9122 & 0.181743 \tabularnewline
11 & 0.09473 & 1.0334 & 0.151759 \tabularnewline
12 & -0.057886 & -0.6315 & 0.264474 \tabularnewline
13 & -0.115639 & -1.2615 & 0.104804 \tabularnewline
14 & -0.188123 & -2.0522 & 0.021173 \tabularnewline
15 & 0.094843 & 1.0346 & 0.151474 \tabularnewline
16 & -0.107834 & -1.1763 & 0.120905 \tabularnewline
17 & -0.039169 & -0.4273 & 0.334972 \tabularnewline
18 & -0.058212 & -0.635 & 0.263318 \tabularnewline
19 & -0.097798 & -1.0668 & 0.1441 \tabularnewline
20 & 0.041579 & 0.4536 & 0.32548 \tabularnewline
21 & -0.14943 & -1.6301 & 0.052864 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234258&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]-0.357435[/C][C]-3.8992[/C][C]8e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.347264[/C][C]-3.7882[/C][C]0.00012[/C][/ROW]
[ROW][C]3[/C][C]-0.088796[/C][C]-0.9686[/C][C]0.167343[/C][/ROW]
[ROW][C]4[/C][C]0.005194[/C][C]0.0567[/C][C]0.477454[/C][/ROW]
[ROW][C]5[/C][C]0.043882[/C][C]0.4787[/C][C]0.316515[/C][/ROW]
[ROW][C]6[/C][C]-0.124929[/C][C]-1.3628[/C][C]0.087758[/C][/ROW]
[ROW][C]7[/C][C]0.083402[/C][C]0.9098[/C][C]0.182381[/C][/ROW]
[ROW][C]8[/C][C]-0.134235[/C][C]-1.4643[/C][C]0.07287[/C][/ROW]
[ROW][C]9[/C][C]-0.134777[/C][C]-1.4702[/C][C]0.072068[/C][/ROW]
[ROW][C]10[/C][C]-0.083625[/C][C]-0.9122[/C][C]0.181743[/C][/ROW]
[ROW][C]11[/C][C]0.09473[/C][C]1.0334[/C][C]0.151759[/C][/ROW]
[ROW][C]12[/C][C]-0.057886[/C][C]-0.6315[/C][C]0.264474[/C][/ROW]
[ROW][C]13[/C][C]-0.115639[/C][C]-1.2615[/C][C]0.104804[/C][/ROW]
[ROW][C]14[/C][C]-0.188123[/C][C]-2.0522[/C][C]0.021173[/C][/ROW]
[ROW][C]15[/C][C]0.094843[/C][C]1.0346[/C][C]0.151474[/C][/ROW]
[ROW][C]16[/C][C]-0.107834[/C][C]-1.1763[/C][C]0.120905[/C][/ROW]
[ROW][C]17[/C][C]-0.039169[/C][C]-0.4273[/C][C]0.334972[/C][/ROW]
[ROW][C]18[/C][C]-0.058212[/C][C]-0.635[/C][C]0.263318[/C][/ROW]
[ROW][C]19[/C][C]-0.097798[/C][C]-1.0668[/C][C]0.1441[/C][/ROW]
[ROW][C]20[/C][C]0.041579[/C][C]0.4536[/C][C]0.32548[/C][/ROW]
[ROW][C]21[/C][C]-0.14943[/C][C]-1.6301[/C][C]0.052864[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234258&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234258&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	-0.357435	-3.8992	8e-05
2	-0.347264	-3.7882	0.00012
3	-0.088796	-0.9686	0.167343
4	0.005194	0.0567	0.477454
5	0.043882	0.4787	0.316515
6	-0.124929	-1.3628	0.087758
7	0.083402	0.9098	0.182381
8	-0.134235	-1.4643	0.07287
9	-0.134777	-1.4702	0.072068
10	-0.083625	-0.9122	0.181743
11	0.09473	1.0334	0.151759
12	-0.057886	-0.6315	0.264474
13	-0.115639	-1.2615	0.104804
14	-0.188123	-2.0522	0.021173
15	0.094843	1.0346	0.151474
16	-0.107834	-1.1763	0.120905
17	-0.039169	-0.4273	0.334972
18	-0.058212	-0.635	0.263318
19	-0.097798	-1.0668	0.1441
20	0.041579	0.4536	0.32548
21	-0.14943	-1.6301	0.052864

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

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code